2cos (problem 3.3.5)

Time bar (total: 11.6s)

start0.0ms (0%)

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

analyze52.0ms (0.4%)

Memory
-23.9MiB live, 116.4MiB allocated; 16ms 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 (75.8%)

Memory
53.3MiB live, 7 631.8MiB allocated; 2.7s collecting garbage
Samples
3.1s5 776×2valid
3.1s26 412×0invalid
584.0ms2 425×1valid
54.0ms55×0valid
Precisions
Click to see histograms. Total time spent on operations: 5.2s
ival-cos: 2.2s (42.1% of total)
const: 772.0ms (14.8% of total)
adjust: 460.0ms (8.8% of total)
ival-add: 305.0ms (5.8% of total)
ival-mult: 305.0ms (5.8% of total)
ival-sub: 293.0ms (5.6% of total)
ival-fabs: 266.0ms (5.1% of total)
ival-<=: 242.0ms (4.6% of total)
ival-<: 221.0ms (4.2% of total)
ival-and: 104.0ms (2% of total)
exact: 42.0ms (0.8% of total)
ival-assert: 12.0ms (0.2% of total)
Bogosity

explain198.0ms (1.7%)

Memory
-28.8MiB live, 63.0MiB allocated; 12ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1282(-8.66964865312651e-160 8.608952818588859e-165)0-(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
30-1(140.94885510227076 7.174700119376859e-6)(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))cancellation1300
cos.f64(cos.f64 (+.f64 x eps))sensitivity21
Confusion
Predicted +Predicted -
+1280
-2126
Precision
0.9846153846153847
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+12800
-20126
Precision?
0.9846153846153847
Recall?
1.0
Freqs
test
numberfreq
0126
1128
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
136.0ms370×2valid
18.0ms142×1valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 132.0ms
ival-cos: 97.0ms (73.6% of total)
adjust: 24.0ms (18.2% of total)
ival-sub: 6.0ms (4.6% of total)
ival-add: 4.0ms (3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess238.0ms (2.1%)

Memory
-4.4MiB live, 48.1MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01841
14641
28641
311741
412541
514741
623141
779241
8514441
067
0107
1227
2407
3657
4787
51007
61847
77427
850737
085057
Stop Event
iter limit
node limit
iter limit
node limit
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
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.0%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

series4.0ms (0%)

Memory
2.7MiB live, 2.7MiB allocated; 0ms collecting garbage
Counts
6 → 33
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
(- (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)
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 (+ 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
1.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
1.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))
0.0ms
eps
@0
((- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) x eps (cos x))

simplify129.0ms (1.1%)

Memory
-1.5MiB live, 45.3MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105296
1308293
2814293
32685292
46556292
08099272
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)
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 (+ 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)
(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)))
(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 (-.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 eps) x) (*.f64 #s(literal -1/2 binary64) (cos.f64 eps))) x) (sin.f64 eps)) x (cos.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
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 (fma.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 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #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 (+ 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 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (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 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) 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)

rewrite124.0ms (1.1%)

Memory
14.1MiB live, 59.1MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
16218
261518
0814118
Stop Event
iter limit
node limit
iter limit
Counts
6 → 140
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 (/.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)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (neg.f64 (+.f64 eps x))) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 (neg.f64 x))) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (neg.f64 (+.f64 eps x)) x) #s(literal 2 binary64)))))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (+.f64 eps x) (neg.f64 x)) #s(literal 2 binary64)))))
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(/.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)
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)))

eval18.0ms (0.2%)

Memory
16.1MiB live, 16.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 4 801 to 712 computations (85.2% saved)

prune8.0ms (0.1%)

Memory
9.4MiB live, 9.4MiB allocated; 0ms collecting garbage
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1568164
Fresh000
Picked011
Done000
Total1569165
Accuracy
99.8%
Counts
165 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
55.0%
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
53.8%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
82.2%
(*.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))
55.3%
(*.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)))))
53.6%
#s(approx (- (cos (+ x eps)) (cos x)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
99.5%
#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)))
99.8%
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
80.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
Compiler

Compiled 333 to 220 computations (33.9% saved)

series37.0ms (0.3%)

Memory
-26.7MiB live, 19.8MiB allocated; 2ms collecting garbage
Counts
40 → 180
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(*.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 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(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 (cos.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
x
#s(literal 1/6 binary64)
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#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)
#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)
(*.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 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #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 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 x) 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)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(* 1/24 eps)
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
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))))
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
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
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -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)))))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ eps (* 2 x))
(+ eps x)
(* -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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))
(- (* 1/6 (* eps x)) 1/2)
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(sin x)
(* 1/24 (* eps (cos x)))
(* eps (cos x))
(cos x)
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* eps (sin x))
(- (cos (- eps (* -1 x))) (cos x))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos 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)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* 1/6 (sin x))
(* (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)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(cos eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (/ 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 (* eps (sin x)))
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -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 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
Calls

6 calls:

TimeVariablePointExpression
9.0ms
x
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps))
6.0ms
x
@0
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps))
5.0ms
x
@inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps))
5.0ms
eps
@-inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps))
5.0ms
eps
@inf
((- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) (sin x) x 1/6 (* (* (cos x) eps) 1/24) (* (cos x) eps) (cos x) eps 1/24 (* (cos x) -1/2) -1/2 (- (cos (+ x eps)) (cos x)) (- (cos eps) 1) (cos eps) 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (sin (/ (+ (+ eps x) x) 2)) (/ (+ (+ eps x) x) 2) (+ (+ eps x) x) (+ eps x) 2 (sin (/ (- (+ eps x) x) 2)) (/ (- (+ eps x) x) 2) (- (+ eps x) x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (* (sin x) eps))

simplify145.0ms (1.3%)

Memory
9.6MiB live, 59.6MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05932732
122092682
086242460
Stop Event
iter limit
node limit
Counts
180 → 178
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)
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))) (* (pow eps 2) (+ 1/4 (* -1/48 (pow eps 2)))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2)))))) 1)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* eps (+ 1/4 (* -1/48 (pow eps 2)))) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* 1/6 (* (pow eps 2) x)) (* eps (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* eps (* x (+ 1/4 (* -1/48 (pow eps 2))))))))
(+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* eps (+ 1/4 (* -1/48 (pow eps 2)))))))))
(- (* 1/24 (pow eps 2)) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* 1/6 (* eps x))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) 1/2)
(- (+ (* 1/24 (pow eps 2)) (* x (+ (* 1/6 eps) (* x (+ 1/4 (+ (* -1/36 (* eps x)) (* -1/48 (pow eps 2)))))))) 1/2)
(* 1/24 eps)
(+ (* 1/24 eps) (* 1/6 x))
(+ (* 1/24 eps) (* x (+ 1/6 (* -1/48 (* eps x)))))
(+ (* 1/24 eps) (* x (+ 1/6 (* x (+ (* -1/36 x) (* -1/48 eps))))))
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))))
(+ (* -1/48 (* eps (pow x 2))) (* 1/24 eps))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/576 (* eps (pow x 2))))))
(+ (* 1/24 eps) (* (pow x 2) (+ (* -1/48 eps) (* (pow x 2) (+ (* -1/17280 (* eps (pow x 2))) (* 1/576 eps))))))
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
(+ 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
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -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)))))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ eps (* 2 x))
(+ eps x)
(* -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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(+ (* -1/2 eps) (* 1/6 (* (pow eps 2) x)))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x)))))
(+ (* -1/2 eps) (* x (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/36 (* (pow eps 2) x)) (* 1/4 eps))))))
(- (* 1/6 (* eps x)) 1/2)
(- (* x (+ (* 1/6 eps) (* 1/4 x))) 1/2)
(- (* x (+ (* 1/6 eps) (* x (+ 1/4 (* -1/36 (* eps x)))))) 1/2)
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))
(+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))))
(+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x)))
(sin x)
(* 1/24 (* eps (cos x)))
(* eps (cos x))
(cos x)
(* -1/2 (cos x))
(* -1 (* eps (sin x)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(sin (* 1/2 (+ eps (* 2 x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))
(+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))
(* eps (sin x))
(- (cos (- eps (* -1 x))) (cos x))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 (- eps (* -2 x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (- (* -1/2 (* eps (cos 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)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* 1/24 (* eps (cos x))) (* 1/6 (sin x))))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* 1/6 (sin x))
(* (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)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* 1/24 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 4) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 4) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 3) (cos x)))
(* (pow eps 3) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 3))) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))))
(* 1/24 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) (pow eps 2))) (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps)))))
(* eps (+ (* 1/24 (cos x)) (* 1/6 (/ (sin x) eps))))
(cos eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (/ 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 (* eps (sin x)))
(* eps (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(- (cos (- x (* -1 eps))) (cos x))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x))) eps)) (* 1/24 (cos x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))) eps)) (* -1/24 (cos x)))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -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 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
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)))
(* (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)
(+ (* eps (* x (- (* 1/6 (pow eps 2)) 1))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #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))
(+ (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* (pow eps 2) (* x (+ 1/4 (* -1/48 (pow eps 2))))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
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(* (pow eps 2) (+ (* -1 (/ (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps))) eps)) (* 1/24 (cos x))))
(*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal -1/2 binary64) (*.f64 (sin.f64 x) #s(literal 1/6 binary64))) eps)) (*.f64 eps eps))
(* -1 (* eps (+ (* -1/6 (/ (sin x) eps)) (* -1/24 (cos x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/24 binary64) (cos.f64 x) (*.f64 (/.f64 (sin.f64 x) eps) #s(literal -1/6 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -2 binary64)) #s(literal 1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 (neg.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 (neg.f64 (pow.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 (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 (*.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)) (neg.f64 eps))) eps) eps)
(* -1 (* eps (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (cos.f64 x) eps) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) #s(literal -1/6 binary64))))

rewrite85.0ms (0.7%)

Memory
-15.7MiB live, 31.1MiB allocated; 1ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044345
075333
1275325
02348321
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
40 → 294
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(*.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 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(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 (cos.f64 x) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) #s(literal 1/6 binary64) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64)))
(sin.f64 x)
x
#s(literal 1/6 binary64)
(*.f64 (*.f64 (cos.f64 x) eps) #s(literal 1/24 binary64))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
eps
#s(literal 1/24 binary64)
(*.f64 (cos.f64 x) #s(literal -1/2 binary64))
#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)
#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)
(*.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 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #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 (+.f64 eps x) x) #s(literal 2 binary64))
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
#s(literal 2 binary64)
(sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))
(-.f64 (+.f64 eps x) x)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps)
(-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 x) eps)
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps))
(*.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)) eps)
(*.f64 eps (-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) eps) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (sin.f64 x)) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) #s(literal 2 binary64)))))
(-.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps) (sin.f64 x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps)
(*.f64 eps (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64))) eps) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64))) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) #s(literal 2 binary64)))) (fma.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(/.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 3 binary64)))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (-.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps)) (pow.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) #s(literal 2 binary64))))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 x)) eps (*.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 x) (*.f64 #s(literal 1/24 binary64) (*.f64 (cos.f64 x) eps))) eps) eps))
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(+.f64 (*.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (cos.f64 x)))
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(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))

eval66.0ms (0.6%)

Memory
8.0MiB live, 53.1MiB allocated; 6ms collecting garbage
Compiler

Compiled 19 348 to 2 855 computations (85.2% saved)

prune28.0ms (0.2%)

Memory
33.1MiB live, 33.1MiB allocated; 0ms collecting garbage
Pruning

26 alts after pruning (23 fresh and 3 done)

PrunedKeptTotal
New53321554
Fresh123
Picked235
Done101
Total53726563
Accuracy
100.0%
Counts
563 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
99.6%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
99.7%
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
53.6%
#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)))
99.5%
#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)))
99.8%
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
98.6%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
80.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
79.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))
95.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.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)) (neg.f64 eps))) eps) eps)) eps))
54.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
23.2%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
97.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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))))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
79.0%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
78.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
Compiler

Compiled 1 679 to 1 107 computations (34.1% saved)

series29.0ms (0.2%)

Memory
-28.5MiB live, 18.9MiB allocated; 1ms collecting garbage
Counts
42 → 147
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
(*.f64 (neg.f64 eps) x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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)
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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)))
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))
(fma.f64 (*.f64 x (*.f64 x x)) (-.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)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(-.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))
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) #s(literal 1 binary64))
Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
x
(- (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 (* 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)))))))))
(* -1/2 (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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* 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))))
(pow x 3)
(pow x 2)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)
(* 1/120 (pow x 2))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
1/120
(+ 1/120 (* -1/5040 (pow x 2)))
(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)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(sin (+ x (* 1/2 eps)))
(* x (+ 1 (* 1/2 (/ eps x))))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(sin x)
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 2))
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(sin (- (* 1/2 eps) (* -1 x)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
-1
(- (* 1/6 (pow eps 2)) 1)
(* 1/6 (pow eps 2))
(pow eps 2)
(+ (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 (+ 1/2 (/ 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 2) (- 1/6 (/ 1 (pow eps 2))))
(* eps (+ 1 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(sin (- x (* -1/2 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(- (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))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
8.0ms
x
@0
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
5.0ms
x
@inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
4.0ms
x
@-inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
4.0ms
eps
@inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))
3.0ms
eps
@-inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (* (sin (+ (* 1/2 eps) x)) (sin (* 1/2 eps))) (sin (+ (* 1/2 eps) x)) (+ (* 1/2 eps) x) 1/2 eps x (sin (* 1/2 eps)) (* 1/2 eps) -2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (* (neg eps) x) (neg eps) (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (- (* (* eps eps) 1/6) 1) (* (* eps eps) 1/6) (* eps eps) 1/6 1 (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (* x x) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) (* (+ (* -1/5040 (* x x)) 1/120) x) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (cos (+ x eps)) (+ x eps) (cos x))

simplify144.0ms (1.2%)

Memory
4.8MiB live, 54.1MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04451837
115051783
255671779
082761642
Stop Event
iter limit
node limit
Counts
147 → 145
Calls
Call 1
Inputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(* 1/2 eps)
(+ x (* 1/2 eps))
x
(- (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 (* 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)))))))))
(* -1/2 (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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* 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))))
(pow x 3)
(pow x 2)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)
(* 1/120 (pow x 2))
(* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2))))
(* 1/120 x)
(* x (+ 1/120 (* -1/5040 (pow x 2))))
1/120
(+ 1/120 (* -1/5040 (pow x 2)))
(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)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(sin (+ x (* 1/2 eps)))
(* x (+ 1 (* 1/2 (/ eps x))))
(- (cos (+ eps x)) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(sin x)
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 3))
(* (pow x 3) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* -1/5040 (pow x 2))
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(cos (+ eps x))
(* x (+ 1 (/ eps x)))
(cos x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(sin (- (* 1/2 eps) (* -1 x)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* -1 (* (pow x 3) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(cos (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(* -1 eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 x)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
-1
(- (* 1/6 (pow eps 2)) 1)
(* 1/6 (pow eps 2))
(pow eps 2)
(+ (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 (+ 1/2 (/ 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 2) (- 1/6 (/ 1 (pow eps 2))))
(* eps (+ 1 (/ x eps)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(sin (- x (* -1/2 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(- (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))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(cos (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64) (*.f64 (*.f64 x x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
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(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
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(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (*.f64 #s(literal 1/2 binary64) eps))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(*.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (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)
(* -1 eps)
(neg.f64 eps)
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps)
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(- (* -1/2 (* eps (cos x))) (sin x))
(-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x))
(* -1 x)
(neg.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 (fma.f64 (*.f64 #s(literal 1/6 binary64) eps) x #s(literal -1/2 binary64)) eps (neg.f64 x))
-1
#s(literal -1 binary64)
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(* 1/6 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))
(pow eps 2)
(*.f64 eps eps)
(+ (cos x) (* -1 (* eps (sin x))))
(fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(fma.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/2 binary64)) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.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 (cos.f64 x))
(* eps (+ 1/2 (/ x eps)))
(*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) 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) x) eps)
(* (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 2) (- 1/6 (/ 1 (pow eps 2))))
(*.f64 (*.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) eps) eps)) eps) eps)
(* eps (+ 1 (/ x eps)))
(fma.f64 (/.f64 x eps) eps eps)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 (*.f64 (-.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps)
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 x eps)) (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)))))
(*.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)))
(* (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)
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 x eps))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64)))

rewrite100.0ms (0.9%)

Memory
-11.1MiB live, 34.7MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064419
092409
1357405
02958395
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
42 → 269
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x))
(*.f64 (neg.f64 eps) x)
(neg.f64 eps)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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)
#s(literal 1/6 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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)))
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))
(fma.f64 (*.f64 x (*.f64 x x)) (-.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)
(*.f64 x (*.f64 x x))
(*.f64 x x)
(-.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))
(*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x)
(*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x)
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(cos.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (cos x) #s(literal 1 binary64))
Outputs
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64))
(neg.f64 (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)))
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (neg.f64 (-.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal -2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))
(-.f64 (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))
(+.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))))))
(fma.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (neg.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (neg.f64 x)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps))))))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (neg.f64 x))) (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 (*.f64 #s(literal 1/2 binary64) eps) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (*.f64 eps eps) (*.f64 x (-.f64 x (*.f64 #s(literal 1/2 binary64) eps)))))
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(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps)))) (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 2 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 #s(approx (cos x) #s(literal 1 binary64)) (+.f64 #s(approx (cos x) #s(literal 1 binary64)) (cos.f64 (+.f64 x eps))) (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (sin.f64 eps) (sin.f64 x) #s(approx (cos x) #s(literal 1 binary64))))
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))) (*.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 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))) (fma.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)) (fma.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))))))
(fma.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(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 (+.f64 x eps)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (+.f64 x eps)))
(-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x)))
(cos.f64 (neg.f64 (neg.f64 (+.f64 x eps))))
(cos.f64 (neg.f64 (+.f64 x eps)))
(cos.f64 (+.f64 x eps))
(+.f64 (*.f64 (sin.f64 (+.f64 x eps)) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (+.f64 x eps)) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 x)) (sin.f64 eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.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 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 x eps) (-.f64 eps 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 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps 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 eps #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(+.f64 x eps)
(+.f64 eps x)
#s(approx (cos x) #s(literal 1 binary64))

eval55.0ms (0.5%)

Memory
-5.1MiB live, 40.2MiB allocated; 5ms collecting garbage
Compiler

Compiled 16 229 to 2 290 computations (85.9% saved)

prune24.0ms (0.2%)

Memory
29.2MiB live, 29.2MiB allocated; 0ms collecting garbage
Pruning

27 alts after pruning (22 fresh and 5 done)

PrunedKeptTotal
New42014434
Fresh10818
Picked325
Done033
Total43327460
Accuracy
100.0%
Counts
460 → 27
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
99.8%
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
99.7%
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
53.6%
#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)))
99.5%
#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)))
99.8%
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
80.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
79.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
94.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (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))) eps))
54.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
78.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
54.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
23.2%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.5%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
78.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
Compiler

Compiled 1 886 to 1 202 computations (36.3% saved)

series43.0ms (0.4%)

Memory
-21.3MiB live, 25.4MiB allocated; 2ms collecting garbage
Counts
55 → 190
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos.f64 x)
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)
eps
(*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin.f64 x)
#s(literal -2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
(*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps)
#s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps))
(*.f64 #s(literal -1/2 binary64) eps)
#s(literal -1/2 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(neg.f64 eps)
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
(*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x)))
#s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))
(fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x)
(*.f64 x (*.f64 x x))
#s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)))
(fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64))
#s(literal -1/5040 binary64)
#s(literal 1/120 binary64)
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
(*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x)
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
#s(literal -1/36 binary64)
(*.f64 eps eps)
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
#s(literal 1/4 binary64)
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
#s(literal -1 binary64)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 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)))
x
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
(* x (cos (* 1/2 eps)))
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
(* 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))))
(- (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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* -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 (* -1/6 (pow x 2)))
(pow x 2)
(pow x 3)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)
1/120
(+ 1/120 (* -1/5040 (pow x 2)))
(* 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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))
(* 1/4 (pow eps 2))
(+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* (cos x) (sin (* 1/2 eps)))
(cos x)
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (sin x))
(sin x)
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* -1 (* eps (sin x)))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 2))
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* eps (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* x (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
eps
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x))))))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (sin x)))))))))))))))
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x)))))))
(+ 1 (* -1/8 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))
(* eps (- (* -1/2 (* eps (cos 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)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 eps)
(* 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 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
1/6
(+ 1/6 (* -1/36 (pow eps 2)))
(pow eps 2)
-1
(- (* 1/6 (pow eps 2)) 1)
(cos (* 1/2 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)))))
(* (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 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)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* -1/36 (pow eps 2))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* 1/6 (pow eps 3))
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -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)))
(* -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))))
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))
Calls

6 calls:

TimeVariablePointExpression
12.0ms
eps
@inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2))
7.0ms
x
@inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2))
6.0ms
x
@-inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2))
5.0ms
eps
@-inf
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2))
4.0ms
eps
@0
((* (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) -2) (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (+ (* (* (cos x) (sin (* 1/2 eps))) (sin (* 1/2 eps))) (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps)))) (* (cos x) (sin (* 1/2 eps))) (cos x) x (sin (* 1/2 eps)) (* 1/2 eps) 1/2 eps (* (* (cos (* 1/2 eps)) (sin x)) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)) (cos (* 1/2 eps)) (sin x) -2 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (* -1/2 eps) -1/2 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (neg eps) (sin x) (* (+ (* (* x x) -1/6) 1) x) (+ (* (* x x) -1/6) 1) (* x x) -1/6 1 (- (cos (+ x eps)) (cos x)) (* (neg eps) (sin x)) (sin x) (+ (* (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6)) x) (* x (* x x)) (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (+ (* (+ (* -1/5040 (* x x)) 1/120) (* x x)) -1/6) (+ (* -1/5040 (* x x)) 1/120) -1/5040 1/120 (- (cos (+ x eps)) (cos x)) (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) (* (+ (* -1/36 (* eps eps)) 1/6) x) (+ (* -1/36 (* eps eps)) 1/6) -1/36 (* eps eps) 1/6 (* 1/4 (* eps eps)) 1/4 (* (+ (* (* eps eps) 1/6) -1) eps) (+ (* (* eps eps) 1/6) -1) -1 (* (* eps eps) -1/2))

simplify183.0ms (1.6%)

Memory
-15.3MiB live, 63.0MiB allocated; 66ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06733037
124362889
089412675
Stop Event
iter limit
node limit
Counts
190 → 188
Calls
Call 1
Inputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 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)))
x
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
(* x (cos (* 1/2 eps)))
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
(* 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))))
(- (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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(* -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 (* -1/6 (pow x 2)))
(pow x 2)
(pow x 3)
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)
1/120
(+ 1/120 (* -1/5040 (pow x 2)))
(* 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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))
(* 1/4 (pow eps 2))
(+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
(* (cos x) (sin (* 1/2 eps)))
(cos x)
(* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps))))
(* (cos (* 1/2 eps)) (sin x))
(sin x)
(- (cos (+ eps x)) (cos x))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))
(* -1 (* eps (sin x)))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/5040 (pow x 7))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 7) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* (pow x 7) (- (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 4))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* (pow x 4) (- (* 1/120 (/ 1 (pow x 2))) (+ 1/5040 (/ 1/6 (pow x 4)))))
(* -1/5040 (pow x 2))
(* (pow x 2) (- (* 1/120 (/ 1 (pow x 2))) 1/5040))
(* eps (* (pow x 3) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* (pow x 3) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* eps (* (pow x 2) (+ 1/6 (* -1/36 (pow eps 2)))))
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* (pow x 2) (+ (* 1/4 (/ (pow eps 2) x)) (+ (* eps (+ 1/6 (* -1/36 (pow eps 2)))) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* eps (* x (+ 1/6 (* -1/36 (pow eps 2)))))
(* x (+ (* 1/4 (/ (pow eps 2) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 7) (- 1/5040 (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (* 1/120 (/ 1 (pow x 2))))))
(* -1 (* (pow x 7) (- (+ 1/5040 (/ 1/6 (pow x 4))) (+ (* 1/120 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)))))
(* -1 (* (pow x 3) (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) (* -1/4 (pow eps 2))) x)) (* eps (+ 1/6 (* -1/36 (pow eps 2))))))
(* -1 (* x (+ (* -1 (* eps (+ 1/6 (* -1/36 (pow eps 2))))) (* -1/4 (/ (pow eps 2) x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
eps
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (* 1/384 (sin x))))))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* 1/3840 (sin x)) (+ (* 1/768 (sin x)) (+ (* 1/384 (sin x)) (* (pow eps 2) (+ (* -1/18432 (sin x)) (+ (* -1/30720 (sin x)) (+ (* -1/92160 (sin x)) (* -1/645120 (sin x)))))))))))))))
(+ (sin x) (* -1/8 (* (pow eps 2) (sin x))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* 1/384 (* (pow eps 2) (sin x))))))
(+ (sin x) (* (pow eps 2) (+ (* -1/8 (sin x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (sin x))) (* 1/384 (sin x)))))))
(+ 1 (* -1/8 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))
(* eps (- (* -1/2 (* eps (cos 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)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1 eps)
(* 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 (* eps x))
(* eps (+ (* 1/6 x) (* 1/4 eps)))
(* eps (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x))))))
(* 1/6 x)
(+ (* -1/36 (* (pow eps 2) x)) (* 1/6 x))
1/6
(+ 1/6 (* -1/36 (pow eps 2)))
(pow eps 2)
-1
(- (* 1/6 (pow eps 2)) 1)
(cos (* 1/2 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)))))
(* (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 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)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/6 (/ x (pow eps 2)))))
(* -1/36 (pow eps 2))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* 1/6 (pow eps 3))
(* (pow eps 3) (- 1/6 (/ 1 (pow eps 2))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -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)))
(* -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))))
(* -1 (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6)))
Outputs
(* -2 (pow (sin (* 1/2 eps)) 2))
(*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(*.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 x x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(fma.f64 #s(literal -2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 x x) (fma.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (*.f64 x (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) x (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) (*.f64 x x) (sin.f64 (*.f64 #s(literal 1/2 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 (fma.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 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
x
(* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (*.f64 x (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(* x (+ (* -1/6 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x)
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/120 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))))))
(*.f64 (fma.f64 (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 x x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) x)
(* x (+ (* (cos (* 1/2 eps)) (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/6 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* 1/120 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) x)
(* x (cos (* 1/2 eps)))
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) x)
(* x (+ (cos (* 1/2 eps)) (* -1/6 (* (pow x 2) (cos (* 1/2 eps))))))
(*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) x)
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* 1/120 (* (pow x 2) (cos (* 1/2 eps))))))))
(*.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (*.f64 x x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) x)
(* x (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/120 (cos (* 1/2 eps)))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (*.f64 x x) (*.f64 #s(literal -1/6 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (*.f64 x x) (cos.f64 (*.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)) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #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)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x)
(- (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)) 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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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 x eps) #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 (+ (* 1/4 eps) (* x (+ 1/6 (* -1/36 (pow eps 2))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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))
(* -1 (* eps x))
(*.f64 (neg.f64 x) eps)
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x eps) x) #s(literal 1/6 binary64)) 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 eps) x) (*.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 eps) x) (*.f64 #s(literal -1/120 binary64) eps)) x) x (*.f64 #s(literal 1/6 binary64) eps)) (*.f64 (neg.f64 x) eps))
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow x 2)) 1/6)
(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
(- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))
1/120
#s(literal 1/120 binary64)
(+ 1/120 (* -1/5040 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))
(* 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 (+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))))
(fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))
(* 1/4 (pow eps 2))
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
(+ (* 1/4 (pow eps 2)) (* eps (* x (+ 1/6 (* -1/36 (pow eps 2))))))
(fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
(* x (+ 1/6 (* -1/36 (pow eps 2))))
(*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x)
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
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(+ (* (cos x) (pow (sin (* 1/2 eps)) 2)) (* (cos (* 1/2 eps)) (* (sin x) (sin (* 1/2 eps)))))
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(* (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))))
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rewrite132.0ms (1.1%)

Memory
1.1MiB live, 50.0MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
082721
0126699
1484663
03948648
Stop Event
iter limit
iter limit
node limit
iter limit
Counts
55 → 421
Calls
Call 1
Inputs
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
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(cos.f64 x)
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#s(literal 1/2 binary64)
eps
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#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
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(*.f64 eps eps)
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
#s(literal 1/4 binary64)
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
#s(literal -1 binary64)
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
Outputs
(*.f64 #s(literal -2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -2 binary64))
(neg.f64 (*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(neg.f64 (*.f64 #s(literal 2 binary64) #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
#s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)))) (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(fma.f64 (cos.f64 x) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(-.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))) (/.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 2 binary64)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))))
(-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))))
(-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))))
(-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (neg.f64 (cos.f64 x)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x))) (pow.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) #s(literal 2 binary64)))))
(+.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(+.f64 (*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (*.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 x)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 x))
(*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 x))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 x)))) #s(literal 2 binary64))
(/.f64 (+.f64 (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) eps) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.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)) x) (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (+.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.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 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 eps #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
eps
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 x))
(*.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (sin.f64 x) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))
(*.f64 (sin.f64 x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))
(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 x))
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(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x) eps) (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)))
(+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x) eps))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) x)
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(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) x) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/46656 binary64) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64)) x) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64))))
(/.f64 (*.f64 x (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(/.f64 (*.f64 x (fma.f64 #s(literal -1/46656 binary64) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64))))
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) x (*.f64 #s(literal 1/6 binary64) x))
(fma.f64 #s(literal 1/6 binary64) x (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) x))
(fma.f64 x (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) (*.f64 x #s(literal 1/6 binary64)))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64))))
(+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) x) (*.f64 #s(literal 1/6 binary64) x))
(+.f64 (*.f64 #s(literal 1/6 binary64) x) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) x))
(+.f64 (*.f64 x (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64))) (*.f64 x #s(literal 1/6 binary64)))
(+.f64 (*.f64 x #s(literal 1/6 binary64)) (*.f64 x (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64))))
(/.f64 (-.f64 #s(literal 1/36 binary64) (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64))) (neg.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/46656 binary64) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64)))
(/.f64 (fma.f64 #s(literal -1/46656 binary64) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64)))))
(/.f64 (fma.f64 #s(literal -1/46656 binary64) (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64))))
(fma.f64 (*.f64 #s(literal -1/36 binary64) (fabs.f64 eps)) (fabs.f64 eps) #s(literal 1/6 binary64))
(fma.f64 (*.f64 #s(literal -1/36 binary64) (neg.f64 eps)) (neg.f64 eps) #s(literal 1/6 binary64))
(fma.f64 (*.f64 #s(literal -1/36 binary64) eps) eps #s(literal 1/6 binary64))
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))
(fma.f64 eps (*.f64 #s(literal -1/36 binary64) eps) #s(literal 1/6 binary64))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))))
(-.f64 #s(literal 1/6 binary64) (*.f64 (neg.f64 (*.f64 #s(literal -1/36 binary64) eps)) eps))
(-.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 (neg.f64 eps) eps) #s(literal -1/36 binary64)))
(-.f64 #s(literal 1/6 binary64) (*.f64 #s(literal 1/36 binary64) (*.f64 eps eps)))
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64)))) (/.f64 #s(literal 1/216 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 2 binary64)) #s(literal 1/36 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/216 binary64)))))
(+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)) #s(literal 1/6 binary64))
(+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/36 binary64)))
#s(literal -1/36 binary64)
(*.f64 (neg.f64 (fabs.f64 eps)) (neg.f64 (fabs.f64 eps)))
(*.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)))
(*.f64 (fabs.f64 (fabs.f64 eps)) (fabs.f64 (fabs.f64 eps)))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (pow.f64 eps #s(literal 1 binary64)) eps)
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (fabs.f64 eps) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 eps #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
#s(literal 1/6 binary64)
(*.f64 (*.f64 #s(literal 1/4 binary64) (fabs.f64 eps)) (fabs.f64 eps))
(*.f64 (*.f64 #s(literal 1/4 binary64) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (*.f64 #s(literal 1/4 binary64) eps) eps)
(*.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(*.f64 eps (*.f64 #s(literal 1/4 binary64) eps))
#s(literal 1/4 binary64)
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps)
(*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) eps) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) eps) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) eps (*.f64 #s(literal -1 binary64) eps))
(fma.f64 #s(literal -1 binary64) eps (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) eps))
(fma.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) (*.f64 eps #s(literal -1 binary64)))
(fma.f64 eps #s(literal -1 binary64) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))))
(+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) eps) (*.f64 #s(literal -1 binary64) eps))
(+.f64 (*.f64 #s(literal -1 binary64) eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) eps))
(+.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))) (*.f64 eps #s(literal -1 binary64)))
(+.f64 (*.f64 eps #s(literal -1 binary64)) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(/.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(/.f64 (fma.f64 (pow.f64 (*.f64 eps eps) #s(literal 3 binary64)) #s(literal 1/216 binary64) #s(literal -1 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (fabs.f64 eps)) (fabs.f64 eps) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/6 binary64) (neg.f64 eps)) (neg.f64 eps) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 1/6 binary64) eps) eps #s(literal -1 binary64))
(fma.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 eps eps) #s(literal -1 binary64))
(fma.f64 eps (*.f64 #s(literal 1/6 binary64) eps) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(-.f64 #s(literal -1 binary64) (*.f64 (*.f64 (neg.f64 eps) eps) #s(literal 1/6 binary64)))
(-.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 eps eps)))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 eps) (*.f64 #s(literal 1/6 binary64) eps)))
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)) #s(literal 2 binary64)) #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 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/6 binary64)))
#s(literal -1 binary64)
(*.f64 (*.f64 #s(literal -1/2 binary64) (fabs.f64 eps)) (fabs.f64 eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (fabs.f64 eps) (*.f64 (fabs.f64 eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) eps)
(*.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) eps))

eval98.0ms (0.8%)

Memory
-17.1MiB live, 73.8MiB allocated; 9ms collecting garbage
Compiler

Compiled 41 516 to 4 065 computations (90.2% saved)

prune37.0ms (0.3%)

Memory
-8.6MiB live, 45.4MiB allocated; 4ms collecting garbage
Pruning

26 alts after pruning (19 fresh and 7 done)

PrunedKeptTotal
New7418749
Fresh61117
Picked325
Done055
Total75026776
Accuracy
100.0%
Counts
776 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
53.8%
(-.f64 (cos.f64 (+.f64 x eps)) #s(approx (cos x) #s(literal 1 binary64)))
99.6%
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
99.7%
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
53.6%
#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)))
99.5%
#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)))
99.8%
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
99.7%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
98.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
80.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) (sin.f64 x)))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
79.0%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
53.3%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))) x (*.f64 #s(literal -1/2 binary64) eps))) eps))
54.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
78.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
54.8%
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
97.4%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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)))))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
97.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
79.1%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
78.9%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
78.8%
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
Compiler

Compiled 3 133 to 1 087 computations (65.3% saved)

regimes34.0ms (0.3%)

Memory
21.8MiB live, 21.8MiB allocated; 0ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #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 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)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.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)) (neg.f64 eps))) eps) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) eps) (sin x)) eps) (*.f64 (fma.f64 #s(literal 1/24 binary64) (cos.f64 x) (/.f64 (fma.f64 (sin.f64 x) #s(literal -1/6 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 x) (/.f64 (neg.f64 (sin.f64 x)) eps)) (neg.f64 eps))) (neg.f64 eps))) (pow.f64 eps #s(literal 4 binary64)))))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (fma.f64 (*.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))) #s(literal -2 binary64))
Outputs
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

12.0ms
eps
11.0ms
x
9.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes32.0ms (0.3%)

Memory
20.3MiB live, 20.3MiB allocated; 0ms collecting garbage
Counts
48 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #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 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)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 (*.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)) (neg.f64 eps))) eps) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (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))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

11.0ms
eps
11.0ms
x
8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes31.0ms (0.3%)

Memory
-27.9MiB live, 19.1MiB allocated; 1ms collecting garbage
Counts
45 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) #s(approx (sin (/ (- (+ eps x) x) 2)) (*.f64 (fma.f64 (*.f64 #s(literal -1/48 binary64) eps) eps #s(literal 1/2 binary64)) eps))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 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 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #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 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)))))
Outputs
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
Calls

3 calls:

11.0ms
eps
11.0ms
x
8.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
99.7%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory
17.2MiB live, 17.2MiB allocated; 0ms collecting garbage
Counts
38 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) 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)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) (-.f64 (*.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal 1/6 binary64) eps)) x) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
Calls

3 calls:

9.0ms
x
9.0ms
eps
6.0ms
(-.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)

regimes25.0ms (0.2%)

Memory
-30.6MiB live, 16.9MiB allocated; 1ms collecting garbage
Counts
36 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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)) x) x)) 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)))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
Calls

3 calls:

8.0ms
x
8.0ms
eps
6.0ms
(-.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)

regimes21.0ms (0.2%)

Memory
14.5MiB live, 14.5MiB allocated; 0ms 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 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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:

7.0ms
x
7.0ms
eps
5.0ms
(-.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)

regimes21.0ms (0.2%)

Memory
14.7MiB live, 14.7MiB allocated; 0ms collecting garbage
Counts
30 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64))) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) (-.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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 (-.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)) (*.f64 x x)) x x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (*.f64 (*.f64 eps eps) x) #s(literal 1/4 binary64) (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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 #s(literal -1/2 binary64) eps) eps))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (fma.f64 (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 x x) (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal 1/4 binary64) eps)) x (fma.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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
Calls

3 calls:

7.0ms
eps
7.0ms
x
5.0ms
(-.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)

regimes15.0ms (0.1%)

Memory
10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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) 1/6) (* (cos x) -1/2)) eps) (sin x)) 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)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (fma.f64 (*.f64 x (*.f64 x x)) #s(approx (- (* (* (+ (* -1/5040 (* x x)) 1/120) x) x) 1/6) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 x eps) (fma.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 (* (neg eps) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/120 binary64) (*.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/6 binary64) eps)) x) x (neg.f64 eps)) x)))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) #s(approx (+ (* (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) x) (* (* eps eps) -1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (*.f64 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))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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:

5.0ms
eps
5.0ms
x
4.0ms
(-.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)

regimes9.0ms (0.1%)

Memory
7.7MiB live, 7.7MiB allocated; 0ms collecting garbage
Counts
11 → 1
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) eps) x))))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 #s(literal 1/6 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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))
Calls

3 calls:

3.0ms
x
3.0ms
eps
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.4%1eps
97.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.4%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory
-40.9MiB live, 6.7MiB allocated; 1ms 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 eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (*.f64 #s(literal -1/2 binary64) eps)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) x))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 #s(approx (+ (* (* x x) -1/6) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/6 binary64)) eps) x)))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (neg.f64 eps) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
Outputs
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
Calls

3 calls:

3.0ms
eps
2.0ms
x
2.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
97.4%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
97.4%1x
97.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory
4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Accuracy

Total -15.4b remaining (-113.7%)

Threshold costs -15.4b (-113.7%)

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

3 calls:

1.0ms
eps
1.0ms
x
1.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Results
AccuracySegmentsBranch
78.8%1(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
78.8%1x
78.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify53.0ms (0.5%)

Memory
18.4MiB live, 18.4MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0141509
1243503
2521501
31512494
45756494
Stop Event
node limit
Calls
Call 1
Inputs
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))
Outputs
#s(approx (- (cos (+ x eps)) (cos 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 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal 1/6 binary64) (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) eps) (sin.f64 x)) eps))
(*.f64 #s(approx (* (sin (/ (+ (+ eps x) x) 2)) (sin (/ (- (+ eps x) x) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) #s(literal -2 binary64))
#s(approx (- (cos (+ x eps)) (cos x)) (*.f64 (-.f64 (*.f64 #s(approx (+ (* (+ (* (sin x) 1/6) (* (* (cos x) eps) 1/24)) eps) (* (cos x) -1/2)) (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 eps eps)) #s(literal 1/2 binary64))) eps) (sin.f64 x)) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.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))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 (fma.f64 (fma.f64 (*.f64 (fma.f64 #s(literal -1/36 binary64) (*.f64 eps eps) #s(literal 1/6 binary64)) x) eps (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps))) x (*.f64 (fma.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) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 1/4 (* eps eps))) x) (* (+ (* (* eps eps) 1/6) -1) eps)) (*.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)) x (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) eps) (fma.f64 #s(approx (+ (* (+ (* (* (+ (* -1/36 (* eps eps)) 1/6) x) eps) (* 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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) (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)) (*.f64 #s(approx (- (* (+ (* (* (sin x) eps) 1/6) (* (cos x) -1/2)) eps) (sin x)) #s(approx (+ (* (- (* (* eps eps) 1/6) 1) x) (* -1/2 eps)) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) eps))
#s(approx (- (cos (+ x eps)) (cos x)) #s(approx (* (neg eps) (sin x)) (*.f64 (neg.f64 eps) x)))

derivations486.0ms (4.2%)

Memory
-10.3MiB live, 119.4MiB allocated; 25ms collecting garbage
Stop Event
fuel
Compiler

Compiled 509 to 149 computations (70.7% saved)

preprocess61.0ms (0.5%)

Memory
19.9MiB live, 65.3MiB allocated; 9ms collecting garbage
Compiler

Compiled 1 066 to 340 computations (68.1% saved)

end0.0ms (0%)

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

Profiling

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