2sin (example 3.3)

Time bar (total: 12.5s)

start0.0ms (0%)

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

analyze71.0ms (0.6%)

Memory
-28.8MiB live, 72.1MiB allocated; 57ms 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)

sample7.2s (57.9%)

Memory
-127.7MiB live, 7 668.8MiB allocated; 2.5s collecting garbage
Samples
4.0s25 712×0invalid
1.1s5 041×1valid
385.0ms3 215×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.6s
ival-sin: 913.0ms (25.2% of total)
const: 611.0ms (16.8% of total)
ival-sub: 391.0ms (10.8% of total)
ival-fabs: 327.0ms (9% of total)
ival-add: 284.0ms (7.8% of total)
ival-mult: 277.0ms (7.6% of total)
adjust: 235.0ms (6.5% of total)
ival-<=: 224.0ms (6.2% of total)
ival-<: 211.0ms (5.8% of total)
ival-and: 102.0ms (2.8% of total)
exact: 41.0ms (1.1% of total)
ival-assert: 11.0ms (0.3% of total)
Bogosity

explain96.0ms (0.8%)

Memory
-10.7MiB live, 124.2MiB allocated; 13ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2203(-5.526139394320619e-17 4.1519194956551108e-19)3(1.9851810955919863e-185 2.0315311783046448e-187)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
20-0-(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2206
sin.f64(sin.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2192
-332
Precision
0.9864864864864865
Recall
0.9909502262443439
Confusion?
Predicted +Predicted MaybePredicted -
+21920
-3428
Precision?
0.9692982456140351
Recall?
1.0
Freqs
test
numberfreq
034
1222
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
35.0ms300×1valid
13.0ms212×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-sin: 13.0ms (40.4% of total)
adjust: 9.0ms (28% of total)
ival-sub: 5.0ms (15.5% of total)
ival-add: 4.0ms (12.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess49.0ms (0.4%)

Memory
-9.2MiB live, 43.3MiB allocated; 10ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01843
12243
22943
33743
44943
57143
69343
714743
823143
938543
10101043
11437143
067
0107
1117
0117
Stop Event
iter limit
saturated
iter limit
node limit
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory
3.4MiB live, 3.4MiB allocated; 0ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
01018
11118
01118
Stop Event
iter limit
saturated
iter limit
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(sin.f64 (+.f64 eps x))
(+.f64 x eps)
(+.f64 eps x)
x
eps
(sin.f64 x)

localize29.0ms (0.2%)

Memory
-11.1MiB live, 34.6MiB allocated; 3ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x eps)
accuracy0.0
(sin.f64 x)
accuracy0.1114878714029668
(sin.f64 (+.f64 x eps))
accuracy23.361207239431575
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
16.0ms150×1valid
5.0ms106×0valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-sin: 5.0ms (37.6% of total)
adjust: 4.0ms (30% of total)
ival-add: 2.0ms (15% of total)
ival-sub: 2.0ms (15% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Counts
4 → 31
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)
Outputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
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))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@0
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
1.0ms
eps
@-inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))
0.0ms
x
@inf
((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x))

simplify140.0ms (1.1%)

Memory
36.5MiB live, 124.9MiB allocated; 9ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107303
1366303
21224296
34149296
47986296
08046267
Stop Event
iter limit
node limit
Counts
31 → 29
Calls
Call 1
Inputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
eps
(+ eps x)
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))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 x x)) #s(literal 1/6 binary64))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite203.0ms (1.6%)

Memory
-34.8MiB live, 255.9MiB allocated; 41ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
01016
15116
236516
3445216
0817716
Stop Event
iter limit
node limit
iter limit
Counts
4 → 154
Calls
Call 1
Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
(sin.f64 x)
Outputs
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)))) (fma.f64 (sin.f64 x) (-.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64)) (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (-.f64 (*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x)) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(*.f64 (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))) (/.f64 (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) (fma.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) (+.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))))
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(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 eps x) eps (*.f64 x x)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (+.f64 eps x)) (-.f64 x eps)) (-.f64 x eps)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(neg.f64 (/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (neg.f64 (-.f64 x eps))))
(neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 eps x) eps (*.f64 x x)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (+.f64 eps x) (*.f64 x x)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (/.f64 (*.f64 x x) (*.f64 (-.f64 x eps) (+.f64 eps x))) (+.f64 eps x) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 x x) (*.f64 (-.f64 eps x) eps)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 eps x) eps) (-.f64 (*.f64 (-.f64 eps x) eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (pow.f64 eps #s(literal 3/2 binary64)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (fabs.f64 x) (/.f64 (fabs.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(fma.f64 (*.f64 eps eps) (/.f64 eps (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 eps (/.f64 (*.f64 eps eps) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (*.f64 eps (/.f64 eps (-.f64 x eps))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (-.f64 eps x) eps (*.f64 x x))))
(+.f64 (*.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (*.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)
(sin.f64 x)

eval22.0ms (0.2%)

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

Compiled 5 510 to 734 computations (86.7% saved)

prune21.0ms (0.2%)

Memory
-31.3MiB live, 14.3MiB allocated; 5ms collecting garbage
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1698177
Fresh000
Picked011
Done000
Total1699178
Accuracy
100.0%
Counts
178 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
35.3%
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
36.4%
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
63.5%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
63.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Compiler

Compiled 581 to 198 computations (65.9% saved)

simplify136.0ms (1.1%)

Memory
45.1MiB live, 142.0MiB allocated; 21ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
cost-diff7
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
cost-diff8
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
cost-diff15
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
cost-diff27
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
cost-diff0
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
cost-diff0
(*.f64 (sin.f64 x) eps)
cost-diff0
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff0
(sin.f64 eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff0
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff0
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff1
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042430
075388
1148388
2401354
31495308
46424308
08103308
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(sin.f64 x)
x
(cos.f64 eps)
eps
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
(*.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
(cos.f64 x)
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(+.f64 eps x)
eps
x
#s(literal 2 binary64)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(sin.f64 x)
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(/.f64 eps #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (+.f64 x (/.f64 eps #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(-.f64 (/.f64 eps #s(literal -2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(sin.f64 x)
x
(cos.f64 eps)
eps
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
(*.f64 (sin.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (sin.f64 eps))
(sin.f64 eps)
(cos.f64 x)
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(/.f64 (+.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64))) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))
(pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))
(sin.f64 (+.f64 eps x))
(sin.f64 (+.f64 x eps))
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal 2 binary64)
(+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))
(+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 x)
(*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (fma.f64 (sin.f64 x) (sin.f64 x) (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))

localize168.0ms (1.3%)

Memory
-22.5MiB live, 169.2MiB allocated; 13ms collecting garbage
Localize:

Found 18 expressions of interest:

NewMetricScoreProgram
accuracy11.436489652402313
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
accuracy26.090302292317613
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
accuracy26.11667789100429
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
accuracy27.02548026763016
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
accuracy0.0
(cos.f64 eps)
accuracy0.00390625
(*.f64 (sin.f64 eps) (cos.f64 x))
accuracy0.01953125
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
accuracy23.364584088803664
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
accuracy0.006191259768442017
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
accuracy0.0078125
(*.f64 (sin.f64 x) eps)
accuracy0.015625
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy0.0
(sin.f64 eps)
accuracy1.5909302673869277
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy0.0
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy0.0
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy0.0234375
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.05214346935246515
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
Samples
101.0ms165×1valid
23.0ms88×0valid
7.0ms3valid
Compiler

Compiled 425 to 44 computations (89.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 103.0ms
adjust: 24.0ms (23.4% of total)
ival-mult: 20.0ms (19.5% of total)
ival-sin: 16.0ms (15.6% of total)
ival-add: 12.0ms (11.7% of total)
ival-div: 10.0ms (9.7% of total)
ival-cos: 8.0ms (7.8% of total)
ival-pow2: 7.0ms (6.8% of total)
ival-sub: 5.0ms (4.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series101.0ms (0.8%)

Memory
22.0MiB live, 65.7MiB allocated; 7ms collecting garbage
Counts
23 → 152
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(sin.f64 x)
(cos.f64 eps)
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(*.f64 (sin.f64 eps) (cos.f64 x))
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* 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)))))))
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))))
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))))
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))))
(+ (sin eps) (* x (- (+ 1 (+ (cos eps) (+ (* 4 (cos eps)) (* x (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (+ (* x (- (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (* 2 (/ (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps)))) (sin eps))) (+ (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (pow (sin eps) 2))) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ 1/6 (+ (* -1 (cos eps)) (+ (* -1 (+ 1 (cos eps))) (+ (* -1/3 (cos eps)) (+ (* 2 (- (* -1/6 (cos eps)) 1/6)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (pow (sin eps) 2))) (+ (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 3)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ (* -1/2 (sin eps)) (+ (* 2 (/ (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2)) (sin eps))) (+ (* 4 (/ (pow (cos eps) 2) (sin eps))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps))))))))) (sin eps)) (/ (* (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps))))) (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))))))) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ (* -2 (sin eps)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))) (+ (/ 1 (sin eps)) (+ (/ (* (- (* 2 (cos eps)) (+ 1 (cos eps))) (- (+ 1 (+ (cos eps) (* 4 (cos eps)))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))) (sin eps)) (+ (/ (pow (cos eps) 2) (sin eps)) (/ (pow (+ 1 (cos eps)) 2) (sin eps)))))))))))) (+ (* 2 (cos eps)) (* 2 (+ 1 (cos eps)))))))
(pow (sin eps) 2)
(+ (* x (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))
(+ (* x (- (+ (* 4 (* (cos eps) (sin eps))) (* x (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (+ (* 4 (pow (cos eps) 2)) (* x (- (+ (* 2 (+ (* -1 (* (cos eps) (sin eps))) (* -1/3 (* (cos eps) (sin eps))))) (* 4 (/ (* (cos eps) (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (sin eps)))) (+ (* -1 (* (sin eps) (+ 1 (cos eps)))) (+ (* 2 (* (sin eps) (- (* -1/6 (cos eps)) 1/6))) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (+ (* 2 (+ (* -1 (pow (sin eps) 2)) (pow (cos eps) 2))) (* 4 (pow (cos eps) 2))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2))))) (sin eps))) (/ (* (+ (* -1 (pow (sin eps) 2)) (pow (+ 1 (cos eps)) 2)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))))))))) (+ (* -1 (pow (sin eps) 2)) (+ (* 2 (/ (* (+ 1 (cos eps)) (- (* 4 (* (cos eps) (sin eps))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (sin eps))) (pow (+ 1 (cos eps)) 2)))))) (* 2 (* (sin eps) (+ 1 (cos eps)))))) (pow (sin eps) 2))
(+ (sin eps) (* x (- (* 2 (cos eps)) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (+ (/ (cos eps) (pow (sin eps) 2)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))))) (+ (/ 1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps)))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps)))))
(+ (sin eps) (* x (- (+ (* 2 (cos eps)) (* x (- (+ (* -1 (sin eps)) (+ (* x (- (+ 1/6 (+ (* -1 (cos eps)) (* -1/3 (cos eps)))) (+ (* -1/2 (- (* 2 (cos eps)) (+ 1 (cos eps)))) (+ (* -1/6 (cos eps)) (/ (* (+ 1 (cos eps)) (- (+ (* -1 (sin eps)) (/ (pow (cos eps) 2) (sin eps))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps))))) (sin eps)))))) (/ (pow (cos eps) 2) (sin eps)))) (+ (* -1/2 (sin eps)) (/ (* (+ 1 (cos eps)) (- (* 2 (cos eps)) (+ 1 (cos eps)))) (sin eps)))))) (+ 1 (cos eps)))))
(/ (pow x 2) (sin eps))
(* (pow x 2) (+ (* -1 (* x (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))))
(* (pow x 2) (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))))
(* (pow x 2) (+ (* x (- (* x (- (+ (* 1/2 (/ 1 (sin eps))) (* x (- (* 1/6 (/ 1 (pow (sin eps) 2))) (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (/ (* (+ 1 (cos eps)) (- (* 1/2 (/ 1 (sin eps))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (sin eps))))))) (+ (* -1 (/ (* (+ 1 (cos eps)) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2)))) (sin eps))) (* 1/3 (/ 1 (sin eps)))))) (+ (/ 1 (pow (sin eps) 2)) (/ (cos eps) (pow (sin eps) 2))))) (/ 1 (sin eps))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
(/ (- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))))
(- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2)))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))))
(/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos x) (sin eps))
(/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))
(/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(/ (- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x)))))))
(- (/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2)))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x))))) (/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x))))))
(/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))
(cos (* -1/2 (- eps (* -2 x))))
(/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x)))))
(/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ 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 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 3))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 3)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 3))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x))))))))) (sin x)) (+ (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))) (sin x)) (/ (* (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x)))))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (* (cos x) (sin x)))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2)))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (sin x))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 2)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (sin x))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(+ (sin x) (* eps (- (cos x) (* 1/2 (cos x)))))
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x)))))
(* 1/4 (pow (sin x) 2))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x))))))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 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 (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* 1/2 (sin x))
(+ (* 1/2 (sin x)) (* eps (- (cos x) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/24 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x)))))
(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x)))
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))))
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps)))))
Calls

6 calls:

TimeVariablePointExpression
38.0ms
x
@-inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))
16.0ms
eps
@0
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))
14.0ms
eps
@inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))
11.0ms
x
@0
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))
9.0ms
x
@inf
((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (+ (* (sin x) (cos eps)) (- (* (sin eps) (cos x)) (sin x))) (sin x) (cos eps) (- (* (sin eps) (cos x)) (sin x)) (/ (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (- (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))) (+ (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))) (* (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x))))) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (* (sin eps) (cos x)) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))))

simplify204.0ms (1.6%)

Memory
-15.7MiB live, 207.5MiB allocated; 55ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09317410
132716906
082396495
Stop Event
iter limit
node limit
Counts
152 → 150
Calls
Call 1
Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
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eps
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1
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x
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(pow (sin eps) 2)
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(cos (* -1/2 eps))
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(/ (pow x 2) (sin eps))
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(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(sin x)
(- (* (cos x) (sin eps)) (sin x))
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(- (/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (+ eps x))) 2)))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x)))) (/ (pow (sin (+ eps x)) 2) (+ (sin x) (sin (+ eps x)))))
(/ (pow (sin (+ eps x)) 4) (pow (+ (sin x) (sin (+ eps x))) 2))
(cos (* -1/2 (+ eps (* 2 x))))
(* (cos x) (sin eps))
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(/ (pow (sin x) 2) (+ (sin x) (sin (+ eps x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
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(- (sin (- eps (* -1 x))) (sin x))
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(/ (pow (sin (- eps (* -1 x))) 4) (pow (+ (sin x) (sin (- eps (* -1 x)))) 2))
(cos (* -1/2 (- eps (* -2 x))))
(/ (pow (sin (- eps (* -1 x))) 2) (+ (sin x) (sin (- eps (* -1 x)))))
(/ (pow (sin x) 2) (+ (sin x) (sin (- eps (* -1 x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(cos x)
(+ 1 (* -1/2 (pow eps 2)))
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(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 3))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 3)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 3))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x))))))))) (sin x)) (+ (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))) (sin x)) (/ (* (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x)))))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 3))) (+ (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2)) (+ (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (sin x)) (/ (* (- (cos x) (* 1/2 (cos x))) (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3)))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))))) (sin x))))))))) (+ (/ (* (cos x) (- (cos x) (* 1/2 (cos x)))) (sin x)) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2)))))))
(* eps (* (cos x) (sin x)))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2)))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(* eps (+ (* eps (- (+ (* -1/4 (pow (cos x) 2)) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (sin x))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (sin x))) (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1/3 (pow (cos x) 2)) (+ (* 1/12 (pow (sin x) 2)) (* 1/4 (pow (sin x) 2)))))) (+ (* 4 (* (cos x) (* (sin x) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x))))))) (pow (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) 2))) (pow (sin x) 2)))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (pow (sin x) 2))) (+ (* 1/4 (/ (* (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x)))))) (sin x))))))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x)))) (* (cos x) (sin x))))
(+ (sin x) (* eps (- (cos x) (* 1/2 (cos x)))))
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/12 (cos x)) (+ (* 1/16 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))))) (+ (* -1/4 (sin x)) (+ (* -1/8 (/ (pow (cos x) 2) (sin x))) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))))) (* 1/2 (cos x)))))
(* 1/4 (pow (sin x) 2))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x))))))
(+ (* 1/4 (pow (sin x) 2)) (* eps (- (+ (* eps (- (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (* eps (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x))))) (+ (* 1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2)) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 2))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (sin x))))))) (+ (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (/ (* (cos x) (- (* (cos x) (sin x)) (* 1/4 (* (cos x) (sin x))))) (sin x))))) (* (cos x) (sin x))) (* 1/4 (* (cos x) (sin x))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 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 (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* 1/2 (sin x))
(+ (* 1/2 (sin x)) (* eps (- (cos x) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (+ (cos x) (* eps (- (+ (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (* eps (- (* 1/2 (/ (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))) (sin x))) (+ (* -1/4 (- (cos x) (* 1/4 (cos x)))) (+ (* -1/24 (cos x)) (* 1/2 (/ (* (cos x) (- (* 1/2 (/ (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)) (sin x))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x)))))) (sin x)))))))) (+ (* -1/8 (sin x)) (* 1/2 (/ (* (cos x) (- (cos x) (* 1/4 (cos x)))) (sin x))))))) (* 1/4 (cos x)))))
(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x)))
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(cos eps)
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))))
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps)))))
Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
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(* eps (+ (cos x) (* eps (- (+ (* -1/4 (/ (pow (cos x) 2) (sin x))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))) (* 4 (* (pow (cos x) 2) (pow (sin x) 2)))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (pow (sin x) 2))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (pow (sin x) 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow (sin x) 2) (+ (* -1 (* (cos x) (sin x))) (* -1/3 (* (cos x) (sin x)))))) (* 4 (* (cos x) (* (sin x) (+ (* -1 (pow (sin x) 2)) (pow (cos x) 2)))))) (pow (sin x) 3))) (* eps (- (+ (* -1 (/ (* (cos x) (+ (* -1 (/ (* (cos x) (+ (* -1/4 (pow (cos x) 2)) (* 1/16 (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))))) (sin x))) (+ (* -1/16 (/ (* (cos x) (+ (* -2 (pow (sin x) 2)) (pow (cos x) 2))) (sin x))) (* 1/16 (+ (* -1 (* (cos x) (sin x))) (* -2/3 (* (cos x) (sin x)))))))) (pow (sin x) 2))) (+ (* -1/4 (/ (* (+ (* -2 (pow (sin x) 2)) (pow (cos 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(+ (* -1/4 (* eps (cos x))) (* 1/2 (sin x)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(+ (* 1/2 (sin x)) (* eps (- (* -1 (* eps (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(fma.f64 (fma.f64 (neg.f64 eps) (*.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(+ (* 1/2 (sin x)) (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (cos x) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x))))) (sin x))) (+ (* -1/24 (cos x)) (* 1/16 (cos x)))))) (+ (* -1/8 (sin x)) (* -1/8 (/ (pow (cos x) 2) (sin x)))))) (* 1/4 (cos x)))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x)) (sin.f64 x))) (cos.f64 x)) (sin.f64 x)) #s(literal -1/2 binary64) (*.f64 (cos.f64 x) #s(literal 1/48 binary64)))) eps (*.f64 #s(literal 1/8 binary64) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (sin.f64 x))))) eps (*.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (*.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (*.f64 eps eps))
(* -1/2 (* eps (sin x)))
(*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(cos eps)
(cos.f64 eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(/ (- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))) (+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))))
(/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))) (/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(- (/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)) (/ (pow (sin x) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2)))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))
(+ (/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps))))) (/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/ (pow (sin (- x (* -1 eps))) 4) (pow (+ (sin x) (sin (- x (* -1 eps)))) 2))
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 1/2 binary64)))
(/ (pow (sin (- x (* -1 eps))) 2) (+ (sin x) (sin (- x (* -1 eps)))))
(/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(/ (pow (sin x) 2) (+ (sin x) (sin (- x (* -1 eps)))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))

rewrite243.0ms (1.9%)

Memory
-6.9MiB live, 193.1MiB allocated; 31ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042348
075213
1334203
23024203
08458203
Stop Event
iter limit
node limit
iter limit
Counts
23 → 616
Calls
Call 1
Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(sin.f64 x)
(cos.f64 eps)
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(*.f64 (sin.f64 eps) (cos.f64 x))
(/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
Outputs
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
(/.f64 (-.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (*.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 (fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps)) (*.f64 (-.f64 (*.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64)))
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64)))
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(+.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(sin.f64 eps)
(-.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (sin.f64 eps))))
(+.f64 (*.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (cos.f64 eps)) (*.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps)))
(+.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (cos.f64 eps)) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) eps)
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))) (*.f64 eps eps))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 eps (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)))
(/.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (neg.f64 eps)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (*.f64 eps eps)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (neg.f64 eps)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (sin.f64 x) eps) #s(literal 2 binary64)) (*.f64 (cos.f64 x) (-.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps))))) (*.f64 eps eps)))
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(pow.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1 binary64))
(/.f64 (fabs.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (fabs.f64 (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))) (sqrt.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)))) (sqrt.f64 (neg.f64 (pow.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))))) (sqrt.f64 (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))))
(/.f64 (sqrt.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) (sqrt.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (cos.f64 (/.f64 (-.f64 x (+.f64 x eps)) #s(literal 2 binary64))) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (neg.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fabs.f64 (fabs.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (fabs.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))
(neg.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(sqrt.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 2 binary64)))
(fabs.f64 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(fabs.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(exp.f64 (/.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal 1 binary64)))

eval164.0ms (1.3%)

Memory
4.5MiB live, 232.1MiB allocated; 31ms collecting garbage
Compiler

Compiled 78 434 to 4 100 computations (94.8% saved)

prune29.0ms (0.2%)

Memory
8.9MiB live, 74.2MiB allocated; 6ms collecting garbage
Pruning

18 alts after pruning (16 fresh and 2 done)

PrunedKeptTotal
New1 064141 078
Fresh123
Picked415
Done011
Total1 069181 087
Accuracy
100.0%
Counts
1 087 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
63.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
99.0%
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.7%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.6%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.4%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps)))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
Compiler

Compiled 795 to 565 computations (28.9% saved)

simplify112.0ms (0.9%)

Memory
-12.9MiB live, 122.3MiB allocated; 10ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
cost-diff1
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff1
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff1
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64))
cost-diff2
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
cost-diff0
#s(approx (* (sin x) eps) (*.f64 x eps))
cost-diff0
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff0
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff0
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
cost-diff0
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
cost-diff1
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
cost-diff2
(+.f64 #s(literal 0 binary64) eps)
cost-diff4
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059434
095423
1169414
2485414
31931404
44977404
57693404
08002386
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
x
(PI.f64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps))
#s(literal -1/2 binary64)
(+.f64 x eps)
x
eps
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64))
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
(*.f64 eps eps)
eps
#s(literal 1/1920 binary64)
#s(literal 1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
#s(literal -2 binary64)
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 #s(literal 0 binary64) eps)
eps
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
(/.f64 (-.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(-.f64 (PI.f64) (fma.f64 x #s(literal 2 binary64) eps))
(neg.f64 (fma.f64 x #s(literal 2 binary64) eps))
(fma.f64 x #s(literal 2 binary64) eps)
x
(PI.f64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
(fma.f64 (*.f64 (+.f64 x eps) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps))
(*.f64 (+.f64 x eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(+.f64 x eps)
x
eps
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 x eps)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps)
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64))
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)
(fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))
#s(literal -1/322560 binary64)
(*.f64 eps eps)
eps
#s(literal 1/1920 binary64)
#s(literal 1/24 binary64)
#s(literal 1 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

localize208.0ms (1.7%)

Memory
43.4MiB live, 233.2MiB allocated; 14ms collecting garbage
Localize:

Found 19 expressions of interest:

NewMetricScoreProgram
accuracy0.0234375
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.05214346935246515
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy0.15625
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
accuracy0.17842381862999004
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
accuracy0.006191259768442017
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
accuracy0.015625
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy1.595309492160216
#s(approx (* (sin x) eps) (*.f64 x eps))
accuracy0.0
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
accuracy1.2916828726678498
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
accuracy1.602091357030652
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
accuracy0.0
(PI.f64)
accuracy0.0234375
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
accuracy0.0234375
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
accuracy0.05978930347432946
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
Samples
133.0ms149×1valid
41.0ms107×0valid
Compiler

Compiled 332 to 50 computations (84.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 144.0ms
ival-sin: 35.0ms (24.4% of total)
adjust: 32.0ms (22.3% of total)
ival-mult: 32.0ms (22.3% of total)
ival-add: 14.0ms (9.7% of total)
const: 14.0ms (9.7% of total)
ival-div: 6.0ms (4.2% of total)
ival-cos: 4.0ms (2.8% of total)
ival-sub: 3.0ms (2.1% of total)
ival-pi: 2.0ms (1.4% of total)
exact: 1.0ms (0.7% of total)
ival-neg: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series46.0ms (0.4%)

Memory
-23.9MiB live, 34.0MiB allocated; 15ms collecting garbage
Counts
24 → 126
Calls
Call 1
Inputs
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(PI.f64)
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* 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 (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* -1/2 x))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* eps (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/1920 (pow eps 2))
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 7))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
Calls

6 calls:

TimeVariablePointExpression
24.0ms
x
@0
((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))))
5.0ms
x
@-inf
((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))))
4.0ms
eps
@-inf
((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))))
4.0ms
eps
@inf
((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))))
4.0ms
eps
@0
((sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (+ (neg (+ (* x 2) eps)) (PI)) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (PI) (* -1/2 (+ x eps)) (* (sin (/ (+ 0 eps) 2)) 2) (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))))

simplify146.0ms (1.2%)

Memory
-16.0MiB live, 117.7MiB allocated; 12ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04431757
115901707
258041692
080731564
Stop Event
iter limit
node limit
Counts
126 → 125
Calls
Call 1
Inputs
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* 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 (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* -1/2 x))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* eps (sin x))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 1/1920 (pow eps 2))
(* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 7))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
Outputs
(sin (* 1/2 (- (PI) eps)))
(sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(fma.f64 (neg.f64 x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(- (PI) eps)
(-.f64 (PI.f64) eps)
(- (+ (PI) (* -2 x)) eps)
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(*.f64 #s(literal -2 binary64) (fma.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (*.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
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(cos (* -1/2 eps))
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(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
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(* -2 x)
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(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
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(sin (* 1/2 (- (PI) (* 2 x))))
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(- (PI) (* 2 x))
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(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
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(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
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(* eps (cos x))
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(cos (* -1 x))
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(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(*.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1/2 (* eps x))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(* -1/322560 (pow eps 7))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/322560 binary64))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(*.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -1/1920 binary64) (*.f64 eps eps))) (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64))) (pow.f64 eps #s(literal 7 binary64)))
(* -1/322560 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* eps (- (* -1/2 (/ x eps)) 1/2))
(*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) (neg.f64 eps))))
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2))))))
(*.f64 (neg.f64 (-.f64 #s(literal 1/322560 binary64) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64)))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2))))))
(*.f64 (neg.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))) (pow.f64 eps #s(literal 7 binary64)))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(*.f64 (neg.f64 (pow.f64 eps #s(literal 7 binary64))) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))

rewrite173.0ms (1.4%)

Memory
32.4MiB live, 130.2MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
059338
095324
1348324
22717324
08325318
Stop Event
iter limit
node limit
iter limit
Counts
24 → 422
Calls
Call 1
Inputs
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x))
#s(approx (* (sin x) eps) (*.f64 x eps))
(*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(PI.f64)
(*.f64 #s(literal -1/2 binary64) (+.f64 x eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
(neg.f64 (sin.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (+.f64 (neg.f64 eps) (PI.f64))) #s(literal -2 binary64))))
(fma.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))))
(sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64)))
(-.f64 (*.f64 (cos.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 (+.f64 eps x) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (*.f64 x #s(literal -1 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (*.f64 x #s(literal -1 binary64)))))
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (neg.f64 (*.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 (*.f64 (sin.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (*.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))))
(+.f64 (*.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))))
(+.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 (neg.f64 eps))))
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)))
(*.f64 (sqrt.f64 eps) (sqrt.f64 (-.f64 eps #s(literal 0 binary64))))
(*.f64 (sqrt.f64 eps) (sqrt.f64 eps))
(pow.f64 (neg.f64 eps) #s(literal 1 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 eps)) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 (*.f64 eps eps))))) (*.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (*.f64 (*.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (*.f64 eps eps) (*.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 eps eps))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (*.f64 eps eps)) eps)) (sqrt.f64 (neg.f64 eps)))
(/.f64 (sqrt.f64 (*.f64 eps (neg.f64 (*.f64 eps eps)))) (sqrt.f64 (neg.f64 eps)))
(/.f64 (sqrt.f64 (*.f64 eps (pow.f64 eps #s(literal 3 binary64)))) eps)
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 4 binary64)))) (sqrt.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 0 binary64))) eps)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 0 binary64))) (sqrt.f64 (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 (*.f64 eps eps) #s(literal 0 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 eps eps))))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))) (sqrt.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 (neg.f64 eps))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 (-.f64 eps #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) #s(literal 0 binary64))
(sqrt.f64 (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(fabs.f64 (-.f64 (neg.f64 eps) (/.f64 #s(literal 0 binary64) (neg.f64 eps))))
(fabs.f64 (-.f64 #s(literal 0 binary64) (neg.f64 eps)))
(fabs.f64 (-.f64 eps #s(literal 0 binary64)))
(fabs.f64 (neg.f64 (neg.f64 eps)))
(fabs.f64 (neg.f64 eps))
(fabs.f64 eps)
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
(exp.f64 (-.f64 (*.f64 (log.f64 eps) #s(literal 3 binary64)) (*.f64 (log.f64 eps) #s(literal 2 binary64))))
(exp.f64 (/.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
eps
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(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))
(exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(/.f64 (*.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) #s(literal -1/2 binary64)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1/2 binary64)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps)))))
(fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 x #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (neg.f64 eps) #s(literal -1/2 binary64)))
(-.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) eps))
(+.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 #s(literal -1/2 binary64) x))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps))
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps)
(*.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps))
(*.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)))
(*.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3686400 binary64)) (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) #s(literal 1/1920 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/33560740233216000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/7077888000 binary64)) (*.f64 eps eps)) (fma.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/3686400 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/619315200 binary64)))))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) (-.f64 (*.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/3686400 binary64))) (-.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) #s(literal 1/1920 binary64)))
(/.f64 (*.f64 (*.f64 eps eps) (fma.f64 #s(literal -1/33560740233216000 binary64) (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/7077888000 binary64))) (fma.f64 #s(literal 1/104044953600 binary64) (pow.f64 eps #s(literal 4 binary64)) (-.f64 #s(literal 1/3686400 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/619315200 binary64)))))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (neg.f64 eps)) (neg.f64 eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (neg.f64 eps) (*.f64 (neg.f64 eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64))) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps) (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 eps eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps)))
(fma.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)))
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(fma.f64 (*.f64 eps eps) #s(literal 1/1920 binary64) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64))))
(fma.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps))
(fma.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(fma.f64 eps (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps))
(+.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps)) (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)))
(+.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64)) (*.f64 eps eps)))
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps))
(+.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)))
(+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/322560 binary64))))
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) (*.f64 #s(literal 0 binary64) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps)))
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) #s(literal 0 binary64)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64))) #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/322560 binary64) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)))

eval71.0ms (0.6%)

Memory
11.4MiB live, 100.6MiB allocated; 7ms collecting garbage
Compiler

Compiled 19 074 to 2 647 computations (86.1% saved)

prune43.0ms (0.3%)

Memory
-5.4MiB live, 50.0MiB allocated; 5ms collecting garbage
Pruning

18 alts after pruning (13 fresh and 5 done)

PrunedKeptTotal
New5089517
Fresh7411
Picked235
Done022
Total51718535
Accuracy
100.0%
Counts
535 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
63.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.0%
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
99.7%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
99.4%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
97.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
99.9%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
98.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
Compiler

Compiled 874 to 605 computations (30.8% saved)

simplify147.0ms (1.2%)

Memory
-9.2MiB live, 122.1MiB allocated; 19ms collecting garbage
Algorithm
egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff1
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff1
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
cost-diff2
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
cost-diff0
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
cost-diff0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
cost-diff1
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
cost-diff2
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
cost-diff0
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
cost-diff0
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
cost-diff0
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
cost-diff0
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
cost-diff0
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff0
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
cost-diff1
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079609
0113599
1210593
2600593
32304576
46343576
08110535
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(literal 2 binary64)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
#s(literal -2 binary64)
x
(-.f64 (PI.f64) eps)
(PI.f64)
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(*.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(literal -1/2 binary64)
x
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
#s(literal -2 binary64)
x
(PI.f64)
#s(literal 1/2 binary64)
eps
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
(*.f64 eps eps)
eps
#s(literal 1 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
#s(literal 2 binary64)
x
#s(literal -2 binary64)
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (neg.f64 x))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
#s(literal -2 binary64)
x
(-.f64 (PI.f64) eps)
(PI.f64)
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x eps) #s(literal -1/2 binary64)))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(*.f64 (*.f64 x eps) #s(literal -1/2 binary64))
(*.f64 eps x)
(*.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(fma.f64 (*.f64 x eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(literal -1/2 binary64)
x
(/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))) eps))
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))) eps)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
#s(literal -2 binary64)
x
(PI.f64)
#s(literal 1/2 binary64)
eps
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps))
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) eps)
(fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
#s(literal -1/24 binary64)
(*.f64 eps eps)
eps
#s(literal 1 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x #s(literal 2 binary64) eps)
#s(literal 2 binary64)
x
#s(literal -2 binary64)

localize412.0ms (3.3%)

Memory
-50.0MiB live, 410.4MiB allocated; 111ms collecting garbage
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.0234375
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy0.05214346935246515
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
accuracy0.17842381862999004
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
accuracy0.569230699257536
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
accuracy0.0078125
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
accuracy0.015625
(fma.f64 #s(literal -2 binary64) x (PI.f64))
accuracy0.04502920705492342
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
accuracy0.8026261453645851
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
accuracy0.015625
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
accuracy0.1875
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
accuracy1.2916828726678498
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
accuracy0.0234375
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
accuracy0.6346448248216612
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
accuracy1.2916828726678498
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
accuracy61.781129481028145
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
accuracy0.01171875
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
accuracy0.01171875
(-.f64 (PI.f64) eps)
accuracy0.0234375
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
accuracy0.05978930347432946
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
Samples
234.0ms149×1valid
92.0ms107×0valid
Compiler

Compiled 389 to 73 computations (81.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 257.0ms
ival-sin: 105.0ms (40.9% of total)
ival-mult: 57.0ms (22.2% of total)
adjust: 35.0ms (13.6% of total)
ival-add: 20.0ms (7.8% of total)
const: 14.0ms (5.5% of total)
ival-div: 11.0ms (4.3% of total)
ival-sub: 5.0ms (1.9% of total)
ival-cos: 4.0ms (1.6% of total)
ival-pi: 2.0ms (0.8% of total)
exact: 1.0ms (0.4% of total)
ival-neg: 1.0ms (0.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series46.0ms (0.4%)

Memory
11.3MiB live, 56.1MiB allocated; 5ms collecting garbage
Counts
27 → 156
Calls
Call 1
Inputs
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(-.f64 (PI.f64) eps)
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
Outputs
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* 2 (sin (* 1/2 (- (PI) eps))))
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps)))))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* -1/2 (* eps x))
(PI)
(+ (PI) (* -2 x))
(* -1 x)
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* 2 (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* x (- (* 1/2 (/ (PI) x)) 1))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(sin (* 1/2 (- (PI) (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* x (- (/ (PI) x) 2))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(* 2 (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* eps (sin (* 1/2 (+ (PI) (* -2 x)))))
(sin (* 1/2 (+ (PI) (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* -1 (* x (+ 2 (* -1 (/ (PI) x)))))
(* 1/2 (+ (PI) (* -2 x)))
(+ (* -1/2 eps) (* 1/2 (+ (PI) (* -2 x))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x))))))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x)))))))))))))
(* 2 (sin (* 1/2 (+ (PI) (* -2 x)))))
(+ (* -1 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))))
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/4 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/4 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(+ (PI) (* -1 eps))
(+ (PI) (+ (* -2 x) (* -1 eps)))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 7))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1 eps)
(* eps (- (/ (PI) eps) 1))
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* 2 (sin (* 1/2 eps)))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))))
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps)))))
Calls

6 calls:

TimeVariablePointExpression
21.0ms
eps
@-inf
((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2))
6.0ms
eps
@0
((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2))
5.0ms
eps
@inf
((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2))
4.0ms
x
@inf
((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2))
4.0ms
x
@-inf
((* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ x eps)) x) 1) (* (+ (* -1/2 x) (/ (+ (* (* x x) -1/2) 1) eps)) eps) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (+ (* -2 x) (PI)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* (sin (* (+ (* -2 x) (PI)) 1/2)) eps) (sin (* (+ (* -2 x) (PI)) 1/2)) (* (+ (* (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* eps eps)) 1) eps) (cos (/ (+ (* 2 x) eps) -2)) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (- (PI) eps) (+ (* -2 x) (- (PI) eps)) (* (* eps x) -1/2) (+ (* -2 x) (PI)) (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) (* (sin (/ (+ 0 eps) 2)) 2))

simplify147.0ms (1.2%)

Memory
35.1MiB live, 177.7MiB allocated; 14ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05502318
120422143
271372129
083421993
Stop Event
iter limit
node limit
Counts
156 → 155
Calls
Call 1
Inputs
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* 2 (sin (* 1/2 (- (PI) eps))))
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps)))))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps))))))))))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* -1/2 (* eps x))
(PI)
(+ (PI) (* -2 x))
(* -1 x)
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* 2 (sin (* 1/2 (- (PI) (+ eps (* 2 x))))))
(- (sin (+ eps x)) (sin x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* x (- (* 1/2 (/ (PI) x)) 1))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(sin (* 1/2 (- (PI) (* 2 x))))
(cos (* -1/2 (+ eps (* 2 x))))
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* x (- (/ (PI) x) 2))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(* 2 (sin (* 1/2 (- (+ (PI) (* -2 x)) eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* eps (sin (* 1/2 (+ (PI) (* -2 x)))))
(sin (* 1/2 (+ (PI) (* -2 x))))
(cos (* -1/2 (- eps (* -2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* -1 (* x (+ 2 (* -1 (/ (PI) x)))))
(* 1/2 (+ (PI) (* -2 x)))
(+ (* -1/2 eps) (* 1/2 (+ (PI) (* -2 x))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x))))))))))))
(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x)))))))))))))
(* 2 (sin (* 1/2 (+ (PI) (* -2 x)))))
(+ (* -1 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))))
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/4 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(+ (* 2 (sin (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/4 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(cos x)
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(+ (PI) (* -1 eps))
(+ (PI) (+ (* -2 x) (* -1 eps)))
-1/24
(- (* 1/1920 (pow eps 2)) 1/24)
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/322560 (pow eps 7))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* eps (- (* -1 (/ x eps)) 1/2))
(* -1 eps)
(* eps (- (/ (PI) eps) 1))
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1))
(* -1/322560 (pow eps 4))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(* 2 (sin (* 1/2 eps)))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))))
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* (pow eps 7) (- 1/322560 (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (* 1/1920 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/322560 (/ 1/24 (pow eps 4))) (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps)))))
Outputs
(* 1/2 (- (PI) eps))
(*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
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(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
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(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
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(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x))))))))
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(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x))))))))))))
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(* eps (+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (+ (PI) (* -2 x))))) (* -1/48 (sin (* 1/2 (+ (PI) (* -2 x)))))))))))))
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(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
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(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
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(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))
(fma.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/48 binary64) eps) (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) (*.f64 #s(literal -1/8 binary64) (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))) eps (*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (PI) (* -1 eps))
(-.f64 (PI.f64) eps)
(+ (PI) (+ (* -2 x) (* -1 eps)))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
-1/24
#s(literal -1/24 binary64)
(- (* 1/1920 (pow eps 2)) 1/24)
(-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/1920 binary64)) #s(literal 1/24 binary64))
(- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)
(fma.f64 (*.f64 #s(literal 1/1920 binary64) eps) eps (-.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64)) #s(literal 1/24 binary64)))
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2))
(*.f64 (-.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x) eps) #s(literal 1/2 binary64)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (*.f64 (*.f64 (sin.f64 x) eps) eps) #s(literal -1/2 binary64))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
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(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(* -1/322560 (pow eps 7))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) #s(literal -1/322560 binary64))
(* (pow eps 7) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(*.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (pow.f64 eps #s(literal 7 binary64)))
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(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 7 binary64)))
(* (pow eps 7) (- (+ (* 1/1920 (/ 1 (pow eps 2))) (/ 1 (pow eps 6))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -1/1920 binary64) (*.f64 eps eps))) (+.f64 (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))) #s(literal 1/322560 binary64))) (pow.f64 eps #s(literal 7 binary64)))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (PI) eps) 1))
(*.f64 (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64)) eps)
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps)
(* -1/322560 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/322560 binary64))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) 1/322560))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)))
(* (pow eps 4) (- (* 1/1920 (/ 1 (pow eps 2))) (+ 1/322560 (/ 1/24 (pow eps 4)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/322560 binary64)) (/.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(* 2 (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps)))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x) eps) #s(literal 1/2 binary64)))
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(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))
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(cos (* -1/2 (- (* 2 x) (* -1 eps))))
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(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
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(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))
(sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (PI.f64) eps)))
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(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps)))

rewrite181.0ms (1.4%)

Memory
-14.1MiB live, 221.2MiB allocated; 21ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079497
0113481
1432481
23543481
08398464
Stop Event
iter limit
node limit
iter limit
Counts
27 → 338
Calls
Call 1
Inputs
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
(*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(-.f64 (PI.f64) eps)
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
Outputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))
(*.f64 (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps))
(/.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)))) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps))
(/.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64))))))
(fma.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64) (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64)) (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64))))
(fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) (*.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) #s(literal 2 binary64))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) (-.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 3 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))))
(+.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps)
(*.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (*.f64 eps eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))))
(fma.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(fma.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))))
(fma.f64 eps #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
(+.f64 (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) (*.f64 #s(literal 0 binary64) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))))
(+.f64 (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) #s(literal 0 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))
#s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps)
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) #s(literal 2 binary64))) eps) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) #s(literal 3 binary64))) eps) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) (-.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))) (*.f64 eps eps))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))
(/.f64 (*.f64 eps (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))
(/.f64 (*.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) (-.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) #s(literal 2 binary64))) (neg.f64 (*.f64 eps eps))) (*.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (neg.f64 eps)))
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(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (-.f64 (PI.f64) eps))
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (-.f64 (PI.f64) eps))
(fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(-.f64 (-.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) #s(literal 0 binary64)) eps)
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)) (/.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)) (+.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)) eps)))
(-.f64 (fma.f64 x #s(literal -2 binary64) (PI.f64)) eps)
(-.f64 (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) #s(literal 0 binary64))
(-.f64 (-.f64 (PI.f64) eps) (*.f64 (neg.f64 x) #s(literal -2 binary64)))
(-.f64 (-.f64 (PI.f64) eps) (*.f64 #s(literal 2 binary64) x))
(-.f64 (PI.f64) (fma.f64 #s(literal 2 binary64) x eps))
(+.f64 (/.f64 (pow.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))) (/.f64 (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))))))
(+.f64 (*.f64 x #s(literal -2 binary64)) (-.f64 (PI.f64) eps))
(+.f64 (-.f64 (PI.f64) eps) (*.f64 x #s(literal -2 binary64)))
(+.f64 (PI.f64) (-.f64 (*.f64 x #s(literal -2 binary64)) eps))
(*.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(*.f64 (*.f64 #s(literal -1/2 binary64) x) eps)
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps x))
(*.f64 eps (*.f64 #s(literal -1/2 binary64) x))
(*.f64 x (*.f64 #s(literal -1/2 binary64) eps))
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (*.f64 #s(literal -1/2 binary64) x)) (neg.f64 eps))
(/.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 #s(literal -1/2 binary64) x)) (*.f64 eps eps))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64)))) (neg.f64 (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))))))
(/.f64 (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 (PI.f64)) (PI.f64))) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (*.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64)))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 3 binary64))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64))))))
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64)))
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (PI.f64))
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (PI.f64))
(fma.f64 x #s(literal -2 binary64) (PI.f64))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
(-.f64 (/.f64 (*.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (-.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))))
(-.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(-.f64 (*.f64 x #s(literal -2 binary64)) (*.f64 (neg.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (cbrt.f64 (PI.f64))))
(-.f64 (PI.f64) (*.f64 (neg.f64 x) #s(literal -2 binary64)))
(-.f64 (PI.f64) (*.f64 #s(literal 2 binary64) x))
(+.f64 (/.f64 (pow.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))))) (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (PI.f64) (-.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))))))
(+.f64 (*.f64 x #s(literal -2 binary64)) (PI.f64))
(+.f64 (PI.f64) (*.f64 x #s(literal -2 binary64)))
#s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64))
#s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))

eval75.0ms (0.6%)

Memory
16.0MiB live, 61.8MiB allocated; 3ms collecting garbage
Compiler

Compiled 22 421 to 2 483 computations (88.9% saved)

prune53.0ms (0.4%)

Memory
-5.0MiB live, 41.6MiB allocated; 1ms collecting garbage
Pruning

21 alts after pruning (14 fresh and 7 done)

PrunedKeptTotal
New4697476
Fresh178
Picked325
Done055
Total47321494
Accuracy
100.0%
Counts
494 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.5%
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
63.3%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
99.3%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
99.3%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
99.4%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
98.7%
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
99.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
98.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
98.0%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
97.9%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
97.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
5.1%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
5.7%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
97.5%
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
99.9%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
98.7%
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
Compiler

Compiled 1 907 to 708 computations (62.9% saved)

regimes76.0ms (0.6%)

Memory
-15.9MiB live, 44.4MiB allocated; 14ms collecting garbage
Counts
39 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (sin.f64 x)))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (-.f64 (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))) (*.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))) (*.f64 (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))))))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))) (*.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))) (+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))))
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Calls

3 calls:

56.0ms
x
9.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms
eps
Results
AccuracySegmentsBranch
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes43.0ms (0.3%)

Memory
-8.6MiB live, 37.7MiB allocated; 2ms collecting garbage
Counts
33 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps)))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
Calls

3 calls:

26.0ms
x
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms
eps
Results
AccuracySegmentsBranch
99.9%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory
-12.5MiB live, 33.2MiB allocated; 2ms collecting garbage
Counts
31 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (+.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) eps)))
Outputs
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
Calls

3 calls:

12.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.7%1x
99.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory
28.7MiB live, 28.7MiB allocated; 0ms collecting garbage
Counts
25 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Outputs
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
Calls

3 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
x
6.0ms
eps
Results
AccuracySegmentsBranch
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory
-17.9MiB live, 27.9MiB allocated; 3ms collecting garbage
Counts
24 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 (*.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (sin.f64 (/.f64 (fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64))) #s(literal 2 binary64))))
Outputs
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
Calls

3 calls:

15.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
99.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory
34.1MiB live, 34.1MiB allocated; 0ms collecting garbage
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
Outputs
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
98.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.7%1x
98.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes35.0ms (0.3%)

Memory
-20.5MiB live, 33.6MiB allocated; 4ms collecting garbage
Counts
18 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 #s(approx (* (+ (* -2 x) (PI)) 1/2) (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(approx (* (sin x) eps) (*.f64 eps x)) #s(literal -1/2 binary64)) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
98.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.7%1x
98.7%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes28.0ms (0.2%)

Memory
-28.0MiB live, 19.0MiB allocated; 1ms collecting garbage
Counts
12 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/12 binary64) (*.f64 x eps)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64))))) (neg.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
Calls

3 calls:

20.0ms
eps
3.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
98.0%1eps
98.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
98.0%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory
7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
Calls

3 calls:

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

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0%)

Memory
9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
Calls

3 calls:

2.0ms
x
2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
97.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.5%1x
97.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory
9.2MiB live, 9.2MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
Calls

3 calls:

2.0ms
x
2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
97.5%1x
97.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes5.0ms (0%)

Memory
7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
Accuracy

Total -59.2b remaining (-3719.9%)

Threshold costs -59.2b (-3719.9%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 eps x) #s(literal -1/2 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(approx (+ (* (* -1/2 (+ x eps)) x) 1) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) eps))
Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
Calls

3 calls:

1.0ms
eps
1.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
97.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.5%1x
97.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify51.0ms (0.4%)

Memory
-27.7MiB live, 19.8MiB allocated; 1ms collecting garbage
Algorithm
egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0113345
1178343
2412342
31658342
44745340
56902340
Stop Event
node limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/1920 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(*.f64 #s(approx (* (sin (/ (+ 0 eps) 2)) 2) (*.f64 (fma.f64 #s(approx (- (* (+ (* -1/322560 (* eps eps)) 1/1920) (* eps eps)) 1/24) #s(literal -1/24 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps)) #s(approx (cos (/ (+ (* 2 x) eps) -2)) (cos.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (+.f64 x eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 #s(approx (* -1/2 (+ x eps)) (*.f64 #s(literal -1/2 binary64) x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (sin eps) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64)) eps))

derivations1.2s (9.7%)

Memory
3.0MiB live, 383.3MiB allocated; 16ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09317410
132716906
082396495
042348
075213
1334203
23024203
08458203
05502318
120422143
271372129
083421993
0107303
1366303
21224296
34149296
47986296
08046267
0616
01016
15116
236516
3445216
0817716
04431757
115901707
258041692
080731564
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
Compiler

Compiled 355 to 118 computations (66.8% saved)

preprocess161.0ms (1.3%)

Memory
9.6MiB live, 104.4MiB allocated; 12ms collecting garbage
Compiler

Compiled 754 to 274 computations (63.7% saved)

end0.0ms (0%)

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

Profiling

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