2cos (problem 3.3.5)

Time bar (total: 13.6s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze82.0ms (0.6%)

Memory
2.3MiB live, 99.9MiB allocated; 22ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample8.8s (64.5%)

Memory
161.1MiB live, 7 209.8MiB allocated; 2.6s collecting garbage
Samples
3.8s26 319×0invalid
2.6s5 707×2valid
619.0ms2 485×1valid
8.0ms64×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.9s
ival-cos: 2.1s (43.3% of total)
const: 608.0ms (12.5% of total)
adjust: 512.0ms (10.5% of total)
ival-add: 306.0ms (6.3% of total)
ival-mult: 289.0ms (5.9% of total)
ival-fabs: 265.0ms (5.4% of total)
ival-sub: 253.0ms (5.2% of total)
ival-<=: 213.0ms (4.4% of total)
ival-<: 157.0ms (3.2% of total)
ival-and: 105.0ms (2.2% of total)
exact: 46.0ms (0.9% of total)
ival-assert: 13.0ms (0.3% of total)
Bogosity

explain191.0ms (1.4%)

Memory
27.4MiB live, 129.7MiB allocated; 8ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1522(-3.543180167973922e-158 2.6007477406965264e-166)0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
20-0-(cos.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(cos.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))cancellation1540
cos.f64(cos.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+1530
-2101
Precision
0.9870967741935484
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+15300
-20101
Precision?
0.9870967741935484
Recall?
1.0
Freqs
test
numberfreq
0101
1154
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
120.0ms334×2valid
23.0ms174×1valid
0.0ms0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 121.0ms
ival-cos: 85.0ms (70.5% of total)
adjust: 24.0ms (19.9% of total)
ival-sub: 6.0ms (5% of total)
ival-add: 4.0ms (3.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess16.0ms (0.1%)

Memory
-26.8MiB live, 19.1MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01841
14641
28641
311641
411841
067
0107
1227
2407
3647
4717
0717
Stop Event
iter limit
saturated
iter limit
saturated
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Outputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Memory
3.8MiB live, 3.8MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(+.f64 x eps)
cost-diff0
(cos.f64 (+.f64 x eps))
cost-diff0
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
12218
24018
36418
47118
07118
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(cos.f64 x)
Outputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(cos.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(cos.f64 x)

localize82.0ms (0.6%)

Memory
34.2MiB live, 79.4MiB allocated; 5ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(cos.f64 x)
accuracy0.06077040761505644
(cos.f64 (+.f64 x eps))
accuracy34.33711242388212
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Samples
59.0ms167×2valid
15.0ms87×1valid
0.0ms0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
ival-cos: 41.0ms (64.9% of total)
adjust: 13.0ms (20.6% of total)
ival-sub: 7.0ms (11.1% of total)
ival-add: 2.0ms (3.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series6.0ms (0%)

Memory
-52.9MiB live, 2.1MiB allocated; 4ms collecting garbage
Counts
4 → 33
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(cos.f64 x)
Outputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(cos x)
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* eps (+ 1 (/ x eps)))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
1.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify142.0ms (1%)

Memory
27.1MiB live, 72.8MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105296
1308293
2779293
32454292
46244292
08035272
Stop Event
iter limit
node limit
Counts
33 → 31
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
eps
(+ eps x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(- (cos (+ eps x)) (cos x))
(cos (+ eps x))
x
(* x (+ 1 (/ eps x)))
(cos x)
(- (cos (- eps (* -1 x))) (cos x))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(* eps (+ 1 (/ x eps)))
(- (cos (- x (* -1 eps))) (cos x))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (fma.f64 x (fma.f64 #s(literal 1/2 binary64) (cos.f64 eps) #s(literal -1/2 binary64)) (sin.f64 eps)) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(fma.f64 (neg.f64 x) (sin.f64 eps) (cos.f64 eps))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) (neg.f64 x) (cos.f64 eps))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 (sin.f64 eps) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/2 binary64))) x (cos.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/720 binary64) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 x x) #s(literal 1 binary64))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(cos x)
(cos.f64 x)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64))) eps) (sin.f64 x)) eps)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps (cos.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

rewrite147.0ms (1.1%)

Memory
14.9MiB live, 59.5MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
16216
261516
0813016
Stop Event
iter limit
node limit
iter limit
Counts
4 → 138
Calls
Call 1
Inputs
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
(cos.f64 x)
Outputs
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))))))
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))))))
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))))))
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))))))
(*.f64 (/.f64 (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal -2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
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(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (*.f64 (neg.f64 (cos.f64 x)) (cos.f64 x)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))) (-.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))) (cos.f64 (+.f64 (neg.f64 x) eps)))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) (*.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps))))))
(/.f64 (neg.f64 (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) (neg.f64 (cos.f64 (-.f64 eps x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) eps)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 eps x))) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))))) #s(literal 4 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) eps)) (cos.f64 (+.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 eps x))) (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x)))) #s(literal 2 binary64))
(/.f64 (*.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 eps x))) (cos.f64 (-.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(fma.f64 (neg.f64 (sin.f64 (+.f64 eps x))) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x)) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x))))
(fma.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (sin.f64 eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (-.f64 (neg.f64 x) eps) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 (+.f64 eps x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(sin.f64 (+.f64 eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (cos.f64 (-.f64 eps x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))))))
(-.f64 (*.f64 (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (cos.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) (*.f64 (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (sin.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 (neg.f64 eps)) (neg.f64 (sin.f64 x))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 (neg.f64 eps))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 (+.f64 eps x)))))
(cos.f64 (neg.f64 (-.f64 (neg.f64 x) eps)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 eps x))))
(cos.f64 (-.f64 (neg.f64 x) eps))
(cos.f64 (neg.f64 (+.f64 eps x)))
(cos.f64 (+.f64 eps x))
(+.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (*.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)))))
(+.f64 (*.f64 (neg.f64 (sin.f64 (+.f64 eps x))) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps x))) (*.f64 #s(literal 0 binary64) (sin.f64 (+.f64 eps x))))
(+.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 x))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (+.f64 eps (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 eps) (cos.f64 x)))
(+.f64 (*.f64 (sin.f64 (+.f64 eps x)) #s(literal 0 binary64)) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64)))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (-.f64 (*.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)))) (neg.f64 (neg.f64 (-.f64 x eps))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x eps)) (*.f64 (-.f64 x eps) (*.f64 eps eps))) (*.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64))) (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))) (-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (sin.f64 x) #s(literal 0 binary64)) (-.f64 (*.f64 (*.f64 (cos.f64 x) #s(literal 1 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))) (*.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64))))))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))

eval32.0ms (0.2%)

Memory
-30.0MiB live, 15.7MiB allocated; 3ms collecting garbage
Compiler

Compiled 4 780 to 715 computations (85% saved)

prune7.0ms (0%)

Memory
9.2MiB live, 9.2MiB allocated; 0ms collecting garbage
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1538161
Fresh000
Picked011
Done000
Total1539162
Accuracy
99.8%
Counts
162 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
46.3%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
46.2%
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
46.2%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
46.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.3%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
99.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
76.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
Compiler

Compiled 235 to 186 computations (20.9% saved)

simplify102.0ms (0.7%)

Memory
28.3MiB live, 28.3MiB allocated; 0ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 x)
cost-diff0
(cos.f64 eps)
cost-diff0
(*.f64 (cos.f64 eps) (cos.f64 x))
cost-diff0
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
cost-diff0
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
cost-diff0
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
cost-diff0
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
cost-diff4
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
cost-diff0
(sin.f64 x)
cost-diff0
(neg.f64 eps)
cost-diff0
(*.f64 (neg.f64 eps) (sin.f64 x))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
cost-diff0
(cos.f64 eps)
cost-diff0
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
cost-diff0
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036204
061204
1110196
2248196
3658196
41847196
53853196
65763196
77836196
08269196
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(cos.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
eps
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
x
eps
(cos.f64 x)
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 eps)
eps
(cos.f64 x)
x
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(sin.f64 eps)
(sin.f64 x)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (neg.f64 eps)))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (neg.f64 eps))
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(neg.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (sin.f64 x)) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(cos.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
eps
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
eps
(sin.f64 x)
x
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(cos.f64 (+.f64 eps x))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(literal 2 binary64)
x
eps
(cos.f64 x)
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 eps)
eps
(cos.f64 x)
x
(fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x))
(sin.f64 eps)
(sin.f64 x)

localize570.0ms (4.2%)

Memory
-19.4MiB live, 221.8MiB allocated; 22ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(cos.f64 x)
accuracy0.0
(cos.f64 eps)
accuracy0.0078125
(*.f64 (cos.f64 eps) (cos.f64 x))
accuracy34.33711242388212
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
accuracy0.0078125
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
accuracy0.02734375
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
accuracy0.07708485831082909
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
accuracy34.33711242388212
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
accuracy0.0
(sin.f64 x)
accuracy0.0
(neg.f64 eps)
accuracy0.015625
(*.f64 (neg.f64 eps) (sin.f64 x))
accuracy14.917115745464926
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
accuracy0.0
(cos.f64 eps)
accuracy33.486960489562414
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy34.44225853413244
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy0.0078125
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
accuracy0.01171875
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
accuracy0.1171875
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
Samples
361.0ms169×2valid
175.0ms86×1valid
0.0ms0valid
Compiler

Compiled 184 to 37 computations (79.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 387.0ms
ival-sin: 148.0ms (38.2% of total)
ival-cos: 70.0ms (18.1% of total)
adjust: 56.0ms (14.5% of total)
ival-sub: 49.0ms (12.7% of total)
ival-mult: 35.0ms (9% of total)
ival-add: 16.0ms (4.1% of total)
ival-div: 4.0ms (1% of total)
ival-pi: 4.0ms (1% of total)
const: 4.0ms (1% of total)
exact: 1.0ms (0.3% of total)
ival-neg: 1.0ms (0.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series28.0ms (0.2%)

Memory
-15.4MiB live, 30.3MiB allocated; 5ms collecting garbage
Counts
18 → 102
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 x)
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
Outputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(sin (+ eps (* 1/2 (PI))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(- (sin (+ eps (* 1/2 (PI)))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)
(+ eps (* 1/2 (PI)))
(+ eps (+ x (* 1/2 (PI))))
(* 1/2 (PI))
(+ x (* 1/2 (PI)))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* -1 (* eps (sin x)))
(sin (+ eps (+ x (* 1/2 (PI)))))
(- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))
(* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))
(* x (+ 1 (* 1/2 (/ (PI) x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* (cos eps) (cos x))
(cos x)
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (cos x))
(sin (- (+ eps (* 1/2 (PI))) (* -1 x)))
(- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))
(* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 eps)
(sin (+ x (* 1/2 (PI))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))
(- (sin (+ x (* 1/2 (PI)))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
eps
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(sin (- (+ x (* 1/2 (PI))) (* -1 eps)))
(- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
9.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin (+ (+ (/ (PI) 2) x) eps)) (- (sin (+ (+ (/ (PI) 2) x) eps)) (cos x)) (+ (+ (/ (PI) 2) x) eps) (+ (/ (PI) 2) x) (- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x))) (* (cos eps) (cos x)) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin (+ (+ (/ (PI) 2) x) eps)) (- (sin (+ (+ (/ (PI) 2) x) eps)) (cos x)) (+ (+ (/ (PI) 2) x) eps) (+ (/ (PI) 2) x) (- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x))) (* (cos eps) (cos x)) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin (+ (+ (/ (PI) 2) x) eps)) (- (sin (+ (+ (/ (PI) 2) x) eps)) (cos x)) (+ (+ (/ (PI) 2) x) eps) (+ (/ (PI) 2) x) (- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x))) (* (cos eps) (cos x)) (cos x) (* (* (cos x) -1/2) eps))
3.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin (+ (+ (/ (PI) 2) x) eps)) (- (sin (+ (+ (/ (PI) 2) x) eps)) (cos x)) (+ (+ (/ (PI) 2) x) eps) (+ (/ (PI) 2) x) (- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x))) (* (cos eps) (cos x)) (cos x) (* (* (cos x) -1/2) eps))
3.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin (+ (+ (/ (PI) 2) x) eps)) (- (sin (+ (+ (/ (PI) 2) x) eps)) (cos x)) (+ (+ (/ (PI) 2) x) eps) (+ (/ (PI) 2) x) (- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x))) (* (cos eps) (cos x)) (cos x) (* (* (cos x) -1/2) eps))

simplify162.0ms (1.2%)

Memory
57.0MiB live, 137.1MiB allocated; 30ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03551492
112371466
244861450
085021302
Stop Event
iter limit
node limit
Counts
102 → 100
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(sin (+ eps (* 1/2 (PI))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(- (sin (+ eps (* 1/2 (PI)))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)
(+ eps (* 1/2 (PI)))
(+ eps (+ x (* 1/2 (PI))))
(* 1/2 (PI))
(+ x (* 1/2 (PI)))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* -1 (* eps (sin x)))
(sin (+ eps (+ x (* 1/2 (PI)))))
(- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))
(* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))
(* x (+ 1 (* 1/2 (/ (PI) x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* (cos eps) (cos x))
(cos x)
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (cos x))
(sin (- (+ eps (* 1/2 (PI))) (* -1 x)))
(- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))
(* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))
(* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 eps)
(sin (+ x (* 1/2 (PI))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))
(- (sin (+ x (* 1/2 (PI)))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
eps
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(sin (- (+ x (* 1/2 (PI))) (* -1 eps)))
(- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))
Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (fma.f64 #s(literal -1/2 binary64) (cos.f64 eps) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 x) eps))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 x) eps))
(sin (+ eps (* 1/2 (PI))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI))))))
(fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* -1/2 (* x (sin (+ eps (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)))
(- (sin (+ eps (* 1/2 (PI)))) 1)
(-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64))
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (cos (+ eps (* 1/2 (PI)))))) 1)
(fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) x (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (* -1/2 (sin (+ eps (* 1/2 (PI)))))))))) 1)
(fma.f64 (fma.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(- (+ (sin (+ eps (* 1/2 (PI)))) (* x (+ (cos (+ eps (* 1/2 (PI)))) (* x (+ 1/2 (+ (* -1/2 (sin (+ eps (* 1/2 (PI))))) (* -1/6 (* x (cos (+ eps (* 1/2 (PI)))))))))))) 1)
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps))) x (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)) #s(literal 1 binary64)))
(+ eps (* 1/2 (PI)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) eps)
(+ eps (+ x (* 1/2 (PI))))
(+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)
(* 1/2 (PI))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(+ x (* 1/2 (PI)))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) x)
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(fma.f64 (*.f64 (cos.f64 eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (cos.f64 eps))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (cos.f64 eps) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/4 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (sin.f64 x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))))
(sin x)
(sin.f64 x)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(sin (+ eps (+ x (* 1/2 (PI)))))
(sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps))
(- (sin (+ eps (+ x (* 1/2 (PI))))) (cos x))
(-.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) (cos.f64 x))
(* x (+ 1 (+ (* 1/2 (/ (PI) x)) (/ eps x))))
(fma.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) eps) x) x x)
(* x (+ 1 (* 1/2 (/ (PI) x))))
(*.f64 (fma.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(* (cos eps) (cos x))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos x)
(cos.f64 x)
(* -1/2 (* eps (cos x)))
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(sin (- (+ eps (* 1/2 (PI))) (* -1 x)))
(sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps))
(- (sin (- (+ eps (* 1/2 (PI))) (* -1 x))) (cos x))
(-.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) (cos.f64 x))
(* -1 (* x (- (* -1 (/ (+ eps (* 1/2 (PI))) x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (neg.f64 eps)) x) #s(literal 1 binary64)))
(* -1 (* x (- (* -1/2 (/ (PI) x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (*.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x))) eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(*.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(*.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/40320 binary64) (*.f64 eps eps)) #s(literal 1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps))
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(* -1 eps)
(neg.f64 eps)
(sin (+ x (* 1/2 (PI))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI))))))
(fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI)))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)))
(- (sin (+ x (* 1/2 (PI)))) (cos x))
(-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (cos (+ x (* 1/2 (PI)))))) (cos x))
(fma.f64 (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x)))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* -1/2 (* eps (sin (+ x (* 1/2 (PI))))))))) (cos x))
(fma.f64 (fma.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x)))
(- (+ (sin (+ x (* 1/2 (PI)))) (* eps (+ (cos (+ x (* 1/2 (PI)))) (* eps (+ (* -1/2 (sin (+ x (* 1/2 (PI))))) (* -1/6 (* eps (cos (+ x (* 1/2 (PI))))))))))) (cos x))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) #s(literal -1/2 binary64))) eps (cos.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))) eps (-.f64 (sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) (cos.f64 x)))
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(fma.f64 (*.f64 (cos.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64))) (*.f64 eps eps) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64)) (cos.f64 x) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 (cos.f64 x) (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)))))
(* 1/6 (* (pow eps 3) (sin x)))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)))
(* 1/6 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps))
eps
(* eps (+ 1 (+ (* 1/2 (/ (PI) eps)) (/ x eps))))
(fma.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps) eps eps)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(*.f64 (neg.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps))) (*.f64 eps eps))
(sin (- (+ x (* 1/2 (PI))) (* -1 eps)))
(sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps))
(- (sin (- (+ x (* 1/2 (PI))) (* -1 eps))) (cos x))
(-.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) eps)) (cos.f64 x))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (PI))) eps)) 1)))
(*.f64 (-.f64 (/.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (neg.f64 eps)) #s(literal 1 binary64)) (neg.f64 eps))

rewrite177.0ms (1.3%)

Memory
-43.4MiB live, 59.3MiB allocated; 27ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036154
061152
1264140
22435140
08327140
Stop Event
iter limit
node limit
iter limit
Counts
18 → 328
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
(neg.f64 eps)
(sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(cos.f64 x)
(*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)) eps)
(*.f64 eps (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps)))
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps)))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps))
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(/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))) (/.f64 (pow.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)) (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 x)) (pow.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (cos.f64 (+.f64 eps x))) (pow.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (-.f64 (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)) (cos.f64 x)))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x))) (sin.f64 (+.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) x)) (sin.f64 (+.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) (neg.f64 (neg.f64 x)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 eps)))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 (neg.f64 eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 eps))) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (neg.f64 eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) eps)) (sin.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) eps))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 eps)))) (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (neg.f64 (neg.f64 eps))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (+.f64 (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps))) (cos.f64 (+.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64))))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (neg.f64 eps) (/.f64 (PI.f64) #s(literal 2 binary64)))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 eps)) (neg.f64 x))) (cos.f64 (-.f64 (neg.f64 (neg.f64 eps)) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 eps)) x)) (cos.f64 (-.f64 (neg.f64 (neg.f64 eps)) x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 eps) (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 (neg.f64 eps) (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps (neg.f64 (neg.f64 x)))) (cos.f64 (-.f64 eps (neg.f64 (neg.f64 x))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 eps)))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 eps))) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 (neg.f64 x)) eps)) (cos.f64 (-.f64 (neg.f64 (neg.f64 x)) eps))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 eps)))) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 (neg.f64 eps))))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 (neg.f64 eps)))) (cos.f64 (-.f64 x (neg.f64 (neg.f64 eps))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -2 binary64))
(/.f64 (-.f64 (fma.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (fma.f64 (neg.f64 (sin.f64 x)) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 (neg.f64 eps) (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 (neg.f64 eps) x)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps (neg.f64 x))) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 eps x)) (cos.f64 (-.f64 (neg.f64 x) (neg.f64 eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x (neg.f64 eps))) (cos.f64 (-.f64 x (neg.f64 eps)))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 2 binary64))
(+.f64 (/.f64 (cos.f64 (+.f64 eps x)) #s(literal 2 binary64)) (/.f64 (cos.f64 (-.f64 x eps)) #s(literal 2 binary64)))
(fma.f64 (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (*.f64 (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(-.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (/.f64 (*.f64 x x) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))) (*.f64 (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (sin.f64 (/.f64 (*.f64 x x) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x)))))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (*.f64 (sin.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (cos.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))) (*.f64 (cos.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))) (sin.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x))
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 #s(literal -1/2 binary64) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))

eval59.0ms (0.4%)

Memory
-0.2MiB live, 44.5MiB allocated; 5ms collecting garbage
Compiler

Compiled 12 893 to 1 971 computations (84.7% saved)

prune19.0ms (0.1%)

Memory
26.4MiB live, 26.4MiB allocated; 0ms collecting garbage
Pruning

23 alts after pruning (19 fresh and 4 done)

PrunedKeptTotal
New46116477
Fresh033
Picked235
Done011
Total46323486
Accuracy
100.0%
Counts
486 → 23
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.3%
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
46.3%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
45.3%
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
46.2%
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
46.2%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
46.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.3%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
82.2%
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps))))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
76.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
46.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.7%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
76.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
75.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
Compiler

Compiled 1 193 to 809 computations (32.2% saved)

simplify135.0ms (1%)

Memory
4.4MiB live, 50.6MiB allocated; 2ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
cost-diff0
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff2
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
cost-diff2
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff4
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
cost-diff0
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
cost-diff0
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
cost-diff0
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
cost-diff0
(neg.f64 x)
cost-diff0
(*.f64 (neg.f64 x) eps)
cost-diff0
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
cost-diff0
(*.f64 (cos.f64 x) eps)
cost-diff0
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
cost-diff0
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062608
099608
1199608
2527603
31589591
44367588
56829588
08401571
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(literal 1/2 binary64)
(sin.f64 x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal 1 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
(*.f64 (*.f64 #s(literal -1/6 binary64) eps) x)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
x
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
#s(literal 1/4 binary64)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))) eps))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))) eps)
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(literal 1/2 binary64)
(sin.f64 x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
x
eps
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal 1 binary64)
x
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64))))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64)))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) x))
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
(*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal 1/4 binary64) eps)) eps)
(*.f64 (*.f64 #s(literal -1/6 binary64) eps) x)
(*.f64 #s(literal -1/6 binary64) eps)
#s(literal -1/6 binary64)
eps
x
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
#s(literal 1/4 binary64)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/2 binary64)
#s(literal 1 binary64)

localize308.0ms (2.3%)

Memory
-28.4MiB live, 116.8MiB allocated; 12ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.01171875
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
accuracy0.1171875
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
accuracy1.009247409308289
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy0.21484375
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy0.3046875
(*.f64 #s(literal -1/6 binary64) eps)
accuracy0.9508929347407479
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
accuracy0.1171875
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
accuracy0.21484375
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
accuracy1.3575994535911415
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
accuracy0.0
(*.f64 (neg.f64 x) eps)
accuracy0.0
(neg.f64 x)
accuracy1.355099882793054
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
accuracy14.917115745464926
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
accuracy0.00390625
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
accuracy0.01171875
(*.f64 (cos.f64 x) eps)
accuracy0.12109375
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
accuracy0.3470373468585129
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
Samples
202.0ms167×2valid
59.0ms87×1valid
1.0ms0valid
Compiler

Compiled 389 to 50 computations (87.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 195.0ms
ival-mult: 57.0ms (29.2% of total)
adjust: 54.0ms (27.7% of total)
ival-cos: 43.0ms (22% of total)
ival-add: 19.0ms (9.7% of total)
const: 10.0ms (5.1% of total)
ival-sub: 5.0ms (2.6% of total)
ival-sin: 5.0ms (2.6% of total)
ival-neg: 2.0ms (1% of total)
exact: 1.0ms (0.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series29.0ms (0.2%)

Memory
17.4MiB live, 17.4MiB allocated; 0ms collecting garbage
Counts
25 → 129
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(*.f64 (cos.f64 x) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
Outputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* eps (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(* 1/4 (pow eps 2))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(sin x)
(cos x)
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* 1/6 (pow eps 2))
(* -1/6 eps)
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* -1/36 (* (pow eps 3) x))
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))
Calls

6 calls:

TimeVariablePointExpression
8.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (* (* eps eps) 1/6) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 eps) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (* (* eps eps) 1/6) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 eps) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (* (* eps eps) 1/6) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 eps) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (* (* eps eps) 1/6) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 eps) (cos x) (* (* (cos x) -1/2) eps))
4.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (+ (* (* (cos x) eps) 1/2) (sin x)) (* (cos x) eps) (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg x) eps) (neg x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (- (cos (+ x eps)) (cos x)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (* (* eps eps) 1/6) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (* -1/6 eps) (cos x) (* (* (cos x) -1/2) eps))

simplify145.0ms (1.1%)

Memory
14.2MiB live, 57.8MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04642057
116742011
265971998
084421862
Stop Event
iter limit
node limit
Counts
129 → 127
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 x)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* eps (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(* 1/4 (pow eps 2))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(* eps (cos x))
(* -1 (* eps (sin x)))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(sin x)
(cos x)
(* -1/2 (* eps (cos x)))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* 1/6 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* 1/6 (pow eps 2))
(* -1/6 eps)
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* -1/36 (* (pow eps 3) x))
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))
Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 (fma.f64 (*.f64 (*.f64 eps x) eps) #s(literal 1/4 binary64) (neg.f64 eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ (* 1/2 eps) (* x (+ 1 (* -1/4 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (*.f64 eps x) #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))
(+ (* 1/2 eps) (* x (+ 1 (* x (+ (* -1/4 eps) (* -1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/24 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 x) eps))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 x) eps))
(* -1 x)
(neg.f64 x)
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 1/4 binary64))) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps x) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(* eps (- (* 1/6 (pow eps 2)) 1))
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps)
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps (*.f64 (*.f64 (*.f64 eps x) eps) #s(literal 1/4 binary64)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps))
(* 1/4 (pow eps 2))
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
(+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) eps (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/4 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (+ (sin x) (* 1/2 (* eps (cos x))))))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* -1 (* eps (sin x)))
(*.f64 (neg.f64 (sin.f64 x)) eps)
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) (sin.f64 x))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) (sin.f64 x)))
(* x (- (* 1/6 (pow eps 2)) 1))
(*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x)
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x)
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) x) x) #s(literal -1/6 binary64)) eps)
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(*.f64 (*.f64 (fma.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))) x) x)
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)) x)) (*.f64 x x))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)) x)))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)) x))) (pow.f64 x #s(literal 3 binary64)))
(* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)))
(* x (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(*.f64 (fma.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))) x)
(sin x)
(sin.f64 x)
(cos x)
(cos.f64 x)
(* -1/2 (* eps (cos x)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps)
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(*.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) x)
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)) x)) (*.f64 x x))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) x)) x)))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (fma.f64 (neg.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64))) eps (*.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/2 binary64))) (neg.f64 x))) (neg.f64 x))))
(* -1 (* x (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(*.f64 (fma.f64 (*.f64 eps (/.f64 eps x)) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))) x)
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps x) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) eps (neg.f64 x))
(* eps (- (* 1/6 (pow x 2)) 1))
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(*.f64 (-.f64 (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps))) #s(literal 1 binary64)) eps)
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) #s(literal 1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x) eps (-.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) x) x) #s(literal 1/2 binary64))) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)
(* 1/6 (* eps x))
(*.f64 (*.f64 eps x) #s(literal 1/6 binary64))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps)
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)
(* 1/6 (pow eps 2))
(*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps)
(* -1/6 eps)
(*.f64 #s(literal -1/6 binary64) eps)
(* -1/2 (* (pow eps 2) (cos x)))
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) eps) eps)
(* 1/2 (* eps (cos x)))
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64))
(* eps (+ (* 1/2 (cos x)) (/ (sin x) eps)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)
(* 1/6 (* (pow eps 3) (sin x)))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 3 binary64)))
(* 1/6 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))
(* 1/6 (* (pow eps 2) x))
(*.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps) x)
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)) eps) eps)
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(*.f64 (-.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/36 binary64) x) x (/.f64 (fma.f64 (*.f64 x (/.f64 x eps)) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) x)) eps)) #s(literal 1/6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 x (+.f64 (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) eps) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/36 (* (pow eps 3) x))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal -1/36 binary64))
(* (pow eps 3) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x)))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) eps)
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal -1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1/2 binary64)) eps)) eps) eps)
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 x eps) #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (fma.f64 (*.f64 #s(literal 1/36 binary64) x) x (/.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (neg.f64 eps))) (neg.f64 eps))) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(*.f64 (*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) x) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x (/.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))) #s(literal 1/2 binary64)) (neg.f64 eps))))
(* -1 (* (pow eps 3) (- (* 1/36 x) (* 1/4 (/ 1 eps)))))
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 #s(literal 1/36 binary64) x (/.f64 #s(literal -1/4 binary64) eps)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/4 (* 1/6 (/ x eps))) eps)) (* 1/36 x))))
(*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))

rewrite183.0ms (1.3%)

Memory
-20.5MiB live, 76.5MiB allocated; 8ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062498
099498
1351498
22761498
09004493
Stop Event
iter limit
node limit
iter limit
Counts
25 → 303
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps))
(fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x))
(*.f64 (cos.f64 x) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps))
(*.f64 (neg.f64 x) eps)
(neg.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(*.f64 #s(literal -1/6 binary64) eps)
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x))) eps)
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps) (sin.f64 x)) (neg.f64 eps))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x)))
(/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (neg.f64 eps)) (fma.f64 (pow.f64 (*.f64 (cos.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (sin.f64 x) (-.f64 (sin.f64 x) (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps))))))
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(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)))
(fma.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps)))
(fma.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 eps (*.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x)) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps)))
(fma.f64 eps (*.f64 (*.f64 #s(literal 1/6 binary64) eps) (sin.f64 x)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 eps (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps))) (/.f64 (pow.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps))))
(-.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (neg.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (*.f64 #s(literal -1/2 binary64) eps)))
(-.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (neg.f64 eps) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64))))
(-.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps))
(-.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (neg.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) (sin.f64 x)))
(-.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps))) (neg.f64 (sin.f64 x)))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (-.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (-.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))))
(+.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps)) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64)) eps)))
(+.f64 (*.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))))
(+.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (neg.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal 1/2 binary64))) eps))
(+.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)))
(+.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)))
(sin.f64 x)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/6 binary64) (neg.f64 eps))) eps)
(*.f64 (fabs.f64 (*.f64 #s(literal 1/6 binary64) eps)) eps)
(*.f64 (*.f64 #s(literal 1/6 binary64) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (*.f64 #s(literal 1/6 binary64) eps) eps)
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (fabs.f64 (*.f64 (*.f64 eps eps) #s(literal 1 binary64))))
(*.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1 binary64)))
(*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/6 binary64)))
(*.f64 eps (fabs.f64 (*.f64 (neg.f64 eps) #s(literal 1/6 binary64))))
(*.f64 eps (fabs.f64 (*.f64 (*.f64 #s(literal 1/6 binary64) eps) #s(literal 1 binary64))))
(*.f64 eps (fabs.f64 (*.f64 #s(literal 1/6 binary64) eps)))
(*.f64 eps (*.f64 (*.f64 #s(literal 1/6 binary64) eps) #s(literal 1 binary64)))
(*.f64 eps (*.f64 #s(literal 1/6 binary64) eps))
(sqrt.f64 (*.f64 #s(literal 1/36 binary64) (pow.f64 eps #s(literal 4 binary64))))
(fabs.f64 (neg.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))))
(fabs.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 eps #s(literal -1/6 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 eps #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(*.f64 #s(literal -1/2 binary64) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
(*.f64 eps (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)))

eval63.0ms (0.5%)

Memory
0.2MiB live, 45.2MiB allocated; 4ms collecting garbage
Compiler

Compiled 29 565 to 2 367 computations (92% saved)

prune25.0ms (0.2%)

Memory
29.8MiB live, 29.8MiB allocated; 0ms collecting garbage
Pruning

28 alts after pruning (21 fresh and 7 done)

PrunedKeptTotal
New44812460
Fresh5914
Picked235
Done044
Total45528483
Accuracy
100.0%
Counts
483 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.3%
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
46.3%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
45.3%
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
46.2%
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
46.2%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
46.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.3%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
82.1%
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
76.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
46.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
76.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
75.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
Compiler

Compiled 1 714 to 1 093 computations (36.2% saved)

simplify130.0ms (1%)

Memory
-1.4MiB live, 46.0MiB allocated; 1ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
cost-diff0
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
cost-diff0
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
cost-diff0
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff0
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff0
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
cost-diff0
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
cost-diff0
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
cost-diff0
(*.f64 #s(literal -1/2 binary64) eps)
cost-diff0
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
cost-diff0
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps))
cost-diff0
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
cost-diff0
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077984
0119984
1234984
2647966
31949950
44488950
56727950
08194930
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64))
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal 1 binary64)
eps
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64))
#s(literal -1/36 binary64)
(*.f64 eps x)
eps
x
#s(literal 1/4 binary64)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 eps eps)
#s(literal 1 binary64)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
eps
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps))
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal 1 binary64)
eps
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)
(*.f64 eps eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)))
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps))
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps))
#s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)
(*.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64))
(fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64))
#s(literal -1/36 binary64)
(*.f64 eps x)
eps
x
#s(literal 1/4 binary64)
(*.f64 #s(literal 1/6 binary64) x)
#s(literal 1/6 binary64)
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(*.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) #s(literal 1 binary64))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) (*.f64 eps eps))
(*.f64 eps eps)
#s(literal 1 binary64)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps)))
(sin.f64 x)
x
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(*.f64 eps eps)
eps
#s(literal 1/6 binary64)
#s(literal -1 binary64)
(*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize409.0ms (3%)

Memory
-55.8MiB live, 203.6MiB allocated; 105ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.1171875
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
accuracy0.19140625
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
accuracy0.8869677780004327
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy0.21875
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
accuracy0.29296875
(*.f64 #s(literal 1/6 binary64) x)
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy0.9508929347407479
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
accuracy0.19140625
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
accuracy0.5596284927389816
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
accuracy0.9508929347407479
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
accuracy0.0
(*.f64 #s(literal -1/2 binary64) eps)
accuracy0.1171875
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
accuracy59.535661298103
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
accuracy0.01171875
(*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)
accuracy0.1171875
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
accuracy0.2931237827012279
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
accuracy1.3459318658246873
#s(approx (cos x) #s(literal 1 binary64))
Samples
210.0ms166×2valid
72.0ms87×1valid
2.0ms3valid
1.0ms0valid
Compiler

Compiled 551 to 54 computations (90.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 229.0ms
adjust: 77.0ms (33.6% of total)
ival-mult: 57.0ms (24.9% of total)
ival-cos: 42.0ms (18.3% of total)
const: 23.0ms (10% of total)
ival-add: 17.0ms (7.4% of total)
ival-sub: 8.0ms (3.5% of total)
ival-sin: 3.0ms (1.3% of total)
exact: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series16.0ms (0.1%)

Memory
18.9MiB live, 18.9MiB allocated; 0ms collecting garbage
Counts
26 → 96
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
Outputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* eps (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/4 eps)
(+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* 1/24 (pow x 2))
(- (cos (+ eps x)) (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(cos x)
(* -1/2 (* eps (cos x)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (- (* 1/36 (pow eps 2)) 1/6)))
(* -1 (* x (- (+ (* -1/4 (/ eps x)) (* 1/36 (pow eps 2))) 1/6)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (cos x) (* (* (cos x) -1/2) eps) (* (* x x) 1/6) (* 1/6 x) (+ (* (+ (* -1/36 (* eps x)) 1/4) eps) (* 1/6 x)) (cos x) (* 1/24 (* x x)))
3.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (cos x) (* (* (cos x) -1/2) eps) (* (* x x) 1/6) (* 1/6 x) (+ (* (+ (* -1/36 (* eps x)) 1/4) eps) (* 1/6 x)) (cos x) (* 1/24 (* x x)))
2.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (cos x) (* (* (cos x) -1/2) eps) (* (* x x) 1/6) (* 1/6 x) (+ (* (+ (* -1/36 (* eps x)) 1/4) eps) (* 1/6 x)) (cos x) (* 1/24 (* x x)))
2.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (cos x) (* (* (cos x) -1/2) eps) (* (* x x) 1/6) (* 1/6 x) (+ (* (+ (* -1/36 (* eps x)) 1/4) eps) (* 1/6 x)) (cos x) (* 1/24 (* x x)))
2.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (sin x) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (* -1/2 eps) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (- (cos (+ x eps)) (cos x)) (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (cos x) (* (* (cos x) -1/2) eps) (* (* x x) 1/6) (* 1/6 x) (+ (* (+ (* -1/36 (* eps x)) 1/4) eps) (* 1/6 x)) (cos x) (* 1/24 (* x x)))

simplify156.0ms (1.1%)

Memory
15.2MiB live, 103.3MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03781631
112961599
249981592
082871481
Stop Event
iter limit
node limit
Counts
96 → 95
Calls
Call 1
Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(* eps (- (* 1/6 (pow eps 2)) 1))
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/4 eps)
(+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* 1/24 (pow x 2))
(- (cos (+ eps x)) (cos x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(sin x)
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(cos x)
(* -1/2 (* eps (cos x)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* x (+ 1/6 (+ (* -1/36 (pow eps 2)) (* 1/4 (/ eps x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (- (* 1/36 (pow eps 2)) 1/6)))
(* -1 (* x (- (+ (* -1/4 (/ eps x)) (* 1/36 (pow eps 2))) 1/6)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (- (* 1/6 (pow x 2)) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(- (cos (- x (* -1 eps))) (cos x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1 (* (pow eps 3) (* x (- (* 1/36 (pow x 2)) 1/6))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (* x (+ 1 (* -1/6 (pow x 2)))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* x (- (* 1/36 (pow x 2)) 1/6)))))
(* -1 (* (pow eps 3) (- (* 1/36 (pow x 2)) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1/4 (/ x eps)) (* 1/36 (pow x 2))) 1/6)))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
Outputs
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 (sin.f64 eps) x #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(fma.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal 1/6 binary64) (fma.f64 (cos.f64 eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* -1/2 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps) #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal 1/4 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) #s(literal -1/6 binary64) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x)
(* eps (- (* 1/6 (pow eps 2)) 1))
(*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)
(+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
(+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))
(fma.f64 (fma.f64 (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps) #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/4 binary64) eps)) x) x (*.f64 #s(literal -1/2 binary64) eps))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/1440 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/48 binary64) eps)) x) x (*.f64 #s(literal 1/4 binary64) eps)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) eps))
(* 1/6 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/4 eps)
(*.f64 #s(literal 1/4 binary64) eps)
(+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(* 1/24 (pow x 2))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (sin.f64 x))) eps)
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(sin x)
(sin.f64 x)
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(*.f64 (*.f64 #s(literal -1/6 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(*.f64 (fma.f64 (/.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) #s(literal -1/6 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) eps (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
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(* -1/6 (* eps (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))))
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(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
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(* (pow x 2) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
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(cos x)
(cos.f64 x)
(* -1/2 (* eps (cos x)))
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(* x (+ 1/6 (* -1/36 (pow eps 2))))
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(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
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(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
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(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1)))))
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(* -1 (* x (- (* 1/36 (pow eps 2)) 1/6)))
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(* -1 (* eps (sin x)))
(*.f64 (neg.f64 eps) (sin.f64 x))
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(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
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(* -1 (sin x))
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(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (neg.f64 (sin.f64 x)))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps)
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1/2 binary64))) eps (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x)) eps)
(* eps (- (* 1/6 (pow x 2)) 1))
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(* eps (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1))
(*.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) eps) x (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)
(* eps (- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1))
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(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(* 1/6 (* (pow eps 3) (sin x)))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 1/6 binary64)) (sin.f64 x))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (pow.f64 eps #s(literal 3 binary64)))
(* 1/6 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal 1/6 binary64))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(*.f64 (*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 x) (/.f64 (sin.f64 x) eps)) (neg.f64 eps))) (*.f64 eps eps))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(*.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) x (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 x (+.f64 (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) eps) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ 1/6 (* -1/36 (pow x 2))))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow eps 3) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(*.f64 (-.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/36 binary64) x) x (/.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal 1/4 binary64) x)) eps)) #s(literal 1/6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1/36 (* (pow eps 2) x))
(*.f64 (*.f64 #s(literal -1/36 binary64) (*.f64 eps x)) eps)
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 #s(literal 1/4 binary64) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) x (/.f64 (fma.f64 (/.f64 x eps) #s(literal 1/6 binary64) #s(literal 1/4 binary64)) eps)) eps) eps)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 #s(literal 1/6 binary64) (sin.f64 x))) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
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(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
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(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x #s(literal -1/2 binary64)) eps))))
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(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x (/.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) (neg.f64 eps))) #s(literal 1/2 binary64)) (neg.f64 eps))))
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(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64)))
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(*.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 (/.f64 x eps) #s(literal -1/4 binary64) (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) #s(literal 1/6 binary64))))
(* -1 (* (pow eps 3) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow x 2))) eps)) (* 1/4 x)) eps)) (* 1/36 (pow x 2))) 1/6)))
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(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) x (neg.f64 (/.f64 (fma.f64 (/.f64 x eps) #s(literal -1/6 binary64) #s(literal -1/4 binary64)) eps))) eps) eps)

rewrite195.0ms (1.4%)

Memory
-10.9MiB live, 133.4MiB allocated; 31ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077761
0119761
1442761
23499761
08138742
Stop Event
iter limit
node limit
iter limit
Counts
26 → 261
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps))
(sin.f64 x)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))
(fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps))
#s(approx (cos x) #s(literal 1 binary64))
(*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)) eps))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)) eps)
(*.f64 eps (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps))
(fma.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 eps (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 eps (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))))
(+.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps))
(+.f64 (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps))
(+.f64 (*.f64 eps (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)) (*.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))))
(+.f64 (*.f64 eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (*.f64 eps (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(/.f64 (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))))
(/.f64 (fma.f64 (pow.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x))) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 (*.f64 eps #s(approx (cos x) #s(literal 1 binary64))) #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 (sin.f64 x) #s(literal 1/6 binary64)) (*.f64 eps eps) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal 1/6 binary64) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 (sin.f64 x) eps) (*.f64 #s(literal 1/6 binary64) eps) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 (sin.f64 x) eps) (*.f64 #s(literal 1/6 binary64) eps) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) (sin.f64 x) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 eps eps)) (sin.f64 x) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(approx (cos x) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (*.f64 #s(literal -1/2 binary64) eps) (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64)))) eps))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps))
(fma.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (sin.f64 x)) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) (sin.f64 x)) (fma.f64 #s(literal -1 binary64) (sin.f64 x) (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
(fma.f64 (*.f64 eps eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (-.f64 (neg.f64 (sin.f64 x)) (*.f64 (*.f64 #s(literal 1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps)))
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(*.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal 1/6 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 #s(literal 1/6 binary64) (*.f64 x x))
(*.f64 x (*.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1 binary64)))
(*.f64 x (*.f64 #s(literal 1/6 binary64) x))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/6 binary64))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (-.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (*.f64 #s(literal -1/216 binary64) (pow.f64 x #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 #s(literal -1/6 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (*.f64 x x)))) (neg.f64 (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/6 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (*.f64 #s(literal 1/36 binary64) (*.f64 x x))) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/6 binary64) x)))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64))) (fma.f64 #s(literal 1/36 binary64) (*.f64 x x) (-.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 1/6 binary64)) x))))
(/.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps))
(fma.f64 eps (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/6 binary64) x))) (/.f64 (*.f64 #s(literal 1/36 binary64) (*.f64 x x)) (fma.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps (*.f64 #s(literal -1/6 binary64) x))))
(-.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) (*.f64 (neg.f64 x) #s(literal 1/6 binary64)))
(-.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) (*.f64 #s(literal -1/6 binary64) x))
(-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (neg.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64))) eps))
(-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64))))
(+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (-.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps)) (pow.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) #s(literal 2 binary64)))))
(+.f64 (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps) (*.f64 #s(literal 1/6 binary64) x))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (fma.f64 (*.f64 eps x) #s(literal -1/36 binary64) #s(literal 1/4 binary64)) eps))
#s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1/24 binary64) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 #s(literal 1/24 binary64) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(literal 1/24 binary64) x) x)
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/24 binary64)))
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1/24 binary64)))
(*.f64 #s(literal 1/24 binary64) (*.f64 x x))
(*.f64 (*.f64 x x) #s(literal 1/24 binary64))
(*.f64 x (*.f64 #s(literal 1/24 binary64) x))

eval46.0ms (0.3%)

Memory
-2.3MiB live, 44.0MiB allocated; 3ms collecting garbage
Compiler

Compiled 23 585 to 1 825 computations (92.3% saved)

prune28.0ms (0.2%)

Memory
-12.8MiB live, 34.6MiB allocated; 2ms collecting garbage
Pruning

30 alts after pruning (18 fresh and 12 done)

PrunedKeptTotal
New3472349
Fresh01616
Picked055
Done077
Total34730377
Accuracy
100.0%
Counts
377 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
77.3%
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
46.3%
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
45.3%
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
46.2%
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
46.2%
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
46.3%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
45.3%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
99.1%
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
82.1%
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
45.2%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
99.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
98.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
76.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
46.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.3%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
98.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
76.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
75.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
Compiler

Compiled 2 400 to 926 computations (61.4% saved)

regimes26.0ms (0.2%)

Memory
22.3MiB live, 22.3MiB allocated; 0ms collecting garbage
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 eps)) (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 x) eps)) (sin.f64 x))))
#s(approx (- (cos (+ x eps)) (cos x)) (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) eps))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
Calls

3 calls:

9.0ms
eps
9.0ms
x
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes23.0ms (0.2%)

Memory
19.8MiB live, 19.8MiB allocated; 0ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) (cos.f64 x))
(-.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
Calls

3 calls:

8.0ms
eps
8.0ms
x
6.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.3%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.2%)

Memory
-42.3MiB live, 17.3MiB allocated; 2ms collecting garbage
Counts
31 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 x x) eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1/2 binary64)) eps)) eps))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (sin.f64 (+.f64 #s(approx (+ (/ (PI) 2) x) (fma.f64 (PI.f64) #s(literal 1/2 binary64) x)) eps)) (cos.f64 x))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
Calls

3 calls:

19.0ms
eps
7.0ms
x
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.1%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated; 0ms collecting garbage
Counts
25 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
Calls

3 calls:

6.0ms
eps
6.0ms
x
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory
12.7MiB live, 12.7MiB allocated; 0ms collecting garbage
Counts
24 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
Calls

3 calls:

6.0ms
eps
6.0ms
x
4.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.8%1x
98.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes17.0ms (0.1%)

Memory
-35.0MiB live, 12.0MiB allocated; 1ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 #s(literal -1/6 binary64) eps) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) eps)) #s(approx (cos x) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

6.0ms
eps
6.0ms
x
5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory
9.8MiB live, 9.8MiB allocated; 0ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) (*.f64 #s(literal 1/4 binary64) eps)) x (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

4.0ms
eps
4.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory
12.1MiB live, 12.1MiB allocated; 0ms collecting garbage
Counts
15 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

4.0ms
eps
4.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes10.0ms (0.1%)

Memory
13.1MiB live, 13.1MiB allocated; 0ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) (*.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x (*.f64 #s(literal -1/4 binary64) eps)) x #s(literal 1 binary64)) x (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) eps (*.f64 #s(literal 1/6 binary64) x)) eps) x (neg.f64 eps)) x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

4.0ms
eps
3.0ms
x
3.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
98.5%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory
-36.7MiB live, 10.2MiB allocated; 3ms collecting garbage
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) #s(approx (+ (* (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (fma.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

2.0ms
eps
2.0ms
x
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.9%1x
97.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory
5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 #s(approx (cos eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps #s(literal 1 binary64))) #s(literal 1 binary64)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
Calls

3 calls:

2.0ms
eps
2.0ms
x
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.8%1x
97.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory
4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Accuracy

Total -19.1b remaining (-123.3%)

Threshold costs -19.1b (-123.3%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
Calls

3 calls:

1.0ms
x
1.0ms
eps
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
75.9%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
75.9%1x
75.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify52.0ms (0.4%)

Memory
17.7MiB live, 17.7MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0119516
1204516
2452508
31244496
43129496
55474496
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 (cos.f64 x) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64)) (sin.f64 x)) eps (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) #s(approx (cos x) #s(literal 1 binary64))) eps) eps)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (*.f64 (*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (fma.f64 #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps eps)) #s(literal 1/2 binary64) (sin.f64 x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps x) #s(literal 1/4 binary64)) eps (*.f64 #s(literal 1/6 binary64) x)) eps)) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 x x) #s(literal 1/6 binary64)) eps (*.f64 #s(literal 1/4 binary64) x)) eps (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64))) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 (fma.f64 #s(approx (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) (*.f64 (*.f64 eps x) #s(literal 1/6 binary64))) x (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (sin x) (+ (* (* eps eps) 1/6) -1)) (* (* (cos x) -1/2) eps)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (* -1/6 eps) x) (- (* (* eps eps) 1/6) 1)) (* 1/4 (* eps eps))) x) (* (- (* (* eps eps) 1/6) 1) eps)) (*.f64 (-.f64 (*.f64 (*.f64 x x) #s(literal 1/6 binary64)) #s(literal 1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (+ (* (* (cos x) eps) 1/2) (sin x)) (neg eps)) (fma.f64 (neg.f64 x) eps (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (+ (* (* (cos x) eps) 1/2) (sin x)) (fma.f64 #s(literal 1/2 binary64) eps x)) (neg.f64 eps)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 x) eps)))

derivations810.0ms (5.9%)

Memory
8.5MiB live, 248.9MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03551492
112371466
244861450
085021302
04642057
116742011
265971998
084421862
0105296
1308293
2779293
32454292
46244292
08035272
077761
0119761
1442761
23499761
08138742
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 516 to 125 computations (75.8% saved)

preprocess97.0ms (0.7%)

Memory
3.5MiB live, 56.8MiB allocated; 6ms collecting garbage
Compiler

Compiled 1 080 to 292 computations (73% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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