2sin (example 3.3)

Time bar (total: 15.1s)

analyze60.0ms (0.4%)

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%74.7%0%0%0%3
0%0%25.3%74.7%0%0%0%4
0%0%19%81%0%0%0%5
0%0%15.8%84.2%0%0%0%6
0%0%11.1%88.9%0%0%0%7
0%0%8.7%91.3%0%0%0%8
0%0%5.9%94.1%0%0%0%9
0%0%4.5%95.5%0%0%0%10
0%0%3.1%96.9%0%0%0%11
0%0%2.7%97.3%0%0%0%12
Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 35.0ms
ival-sin: 8.0ms (22.8% of total)
...c/correct-round.rkt:119:19: 7.0ms (20% of total)
ival-<=: 4.0ms (11.4% of total)
ival-add: 3.0ms (8.6% of total)
ival-mult: 3.0ms (8.6% of total)
ival-fabs: 3.0ms (8.6% of total)
ival-<: 3.0ms (8.6% of total)
ival-sub: 2.0ms (5.7% of total)
ival-and: 1.0ms (2.9% of total)
const: 1.0ms (2.9% of total)
backward-pass: 0.0ms (0% of total)

sample7.4s (49.3%)

Results
4.2s26557×0precondition
1.1s4475×1valid
535.0ms3781×0valid
Precisions
Click to see histograms. Total time spent on operations: 4.6s
ival-sin: 1.2s (27.1% of total)
...c/correct-round.rkt:119:19: 934.0ms (20.5% of total)
ival-add: 383.0ms (8.4% of total)
ival-<=: 368.0ms (8.1% of total)
ival-<: 359.0ms (7.9% of total)
ival-mult: 355.0ms (7.8% of total)
ival-sub: 340.0ms (7.4% of total)
ival-fabs: 304.0ms (6.7% of total)
ival-and: 133.0ms (2.9% of total)
backward-pass: 104.0ms (2.3% of total)
const: 48.0ms (1.1% of total)
Bogosity

preprocess51.0ms (0.3%)

Algorithm
egg-herbie
Rules
376×fnmadd-define
344×fnmsub-define
344×fmsub-define
320×sum3-define
308×fmm-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02146
14342
29442
319842
450742
591742
6128542
7154842
8168442
9171142
067
197
2147
3217
4317
5637
61227
72107
82957
94017
104797
114857
04857
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Call 2
Inputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(- (sin (+ x (neg eps))) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(neg (- (sin (+ x (neg eps))) (sin x)))
(- (sin (+ eps x)) (sin eps))
Outputs
(- (sin (+ x eps)) (sin x))
(- (sin (+ (neg x) eps)) (sin (neg x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ x (neg eps))) (sin x))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ (neg x) eps)) (sin (neg x))))
(- (sin (- x eps)) (sin x))
(neg (- (sin (+ x (neg eps))) (sin x)))
(+ (sin x) (sin (- eps x)))
(- (sin (+ eps x)) (sin eps))
(- (sin (+ x eps)) (sin eps))

explain96.0ms (0.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2263(-2.3745816446511557e-107 2.300282434976019e-109)3(-1.4921680009134305e-267 2.651260580027058e-269)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
20-0-(sin.f64 (+.f64 x eps))
00-0-x
00-0-(sin.f64 x)
00-0-(+.f64 x eps)
00-0-eps
Results
49.0ms292×1valid
17.0ms216×0valid
1.0ms2valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-sin: 14.0ms (46.3% of total)
ival-add: 7.0ms (23.1% of total)
backward-pass: 5.0ms (16.5% of total)
ival-sub: 4.0ms (13.2% of total)
const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
61.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify13.0ms (0.1%)

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))
Rules
124×fnmadd-define
122×sum3-define
80×fma-lowering-fma.f32
80×fnmsub-define
80×fmsub-define
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32118
43118
56318
612218
721018
829518
940118
1047918
1148518
048518
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
x
eps
(sin x)
Outputs
(- (sin (+ x eps)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin (+ x eps))
(sin.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(sin x)
(sin.f64 x)

localize48.0ms (0.3%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(sin.f64 x)
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy61.7%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Results
29.0ms146×1valid
7.0ms108×0valid
0.0ms2valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-sub: 11.0ms (47.8% of total)
ival-sin: 6.0ms (26.1% of total)
ival-add: 3.0ms (13% of total)
backward-pass: 2.0ms (8.7% of total)
const: 0.0ms (0% of total)

series4.0ms (0%)

Counts
4 → 84
Calls
Call 1
Inputs
#<alt (- (sin (+ x eps)) (sin x))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (sin x)>
Outputs
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
Calls

21 calls:

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

rewrite311.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
2788×*-lowering-*.f32
2788×*-lowering-*.f64
2132×/-lowering-/.f32
2132×/-lowering-/.f64
2068×fma-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
14916
240216
3523216
0830916
Stop Event
iter limit
node limit
Counts
4 → 177
Calls
Call 1
Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
(sin x)
Outputs
(+.f64 (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 x) (sin.f64 (+.f64 x eps))))
(-.f64 (+.f64 (sin.f64 (+.f64 x eps)) #s(literal 0 binary64)) (sin.f64 x))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (sin.f64 (+.f64 x eps)) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))) (/.f64 (sin.f64 (+.f64 x eps)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3/2 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (-.f64 (+.f64 (*.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(fma.f64 (/.f64 (sin.f64 (+.f64 x eps)) #s(literal 2 binary64)) (/.f64 (sin.f64 (+.f64 x eps)) (*.f64 (sin.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))))) (neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64))))) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))))
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(sin.f64 (+.f64 x eps))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (cos.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))
(fma.f64 (sin.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (cos.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))) (neg.f64 (*.f64 (cos.f64 (/.f64 (*.f64 x x) (-.f64 x eps))) (sin.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
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(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(fma.f64 x (/.f64 x (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps))))
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(neg.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
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(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
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(/.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))))
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (-.f64 x eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 x x) (*.f64 eps eps))))))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
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(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
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(/.f64 (*.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) #s(literal 1 binary64)) (-.f64 x eps))
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(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (+.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
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(/.f64 (*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (*.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(*.f64 (+.f64 x eps) (*.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
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(*.f64 (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))))
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(*.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
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(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x)))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))
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(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)))))
(*.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 x x) (*.f64 eps (+.f64 x eps))))
(sin.f64 x)

simplify256.0ms (1.7%)

Algorithm
egg-herbie
Rules
3796×*-lowering-*.f32
3796×*-lowering-*.f64
2064×+-lowering-+.f64
2064×+-lowering-+.f32
1456×fnmadd-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0107488
1327465
2963459
33572459
08267459
Stop Event
iter limit
node limit
Counts
84 → 84
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)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 x (+.f64 (*.f64 x (*.f64 x #s(literal 1/6 binary64))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps))))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(*.f64 eps (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 (*.f64 eps (sin.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (*.f64 x (cos.f64 eps)) (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps)) x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (*.f64 eps (cos.f64 x)) (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (*.f64 (+.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/120 binary64) (*.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

eval29.0ms (0.2%)

Compiler

Compiled 7060 to 730 computations (89.7% saved)

prune34.0ms (0.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New25011261
Fresh000
Picked011
Done000
Total25012262
Accuracy
99.9%
Counts
262 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.7%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
36.4%
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
36.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
61.7%
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
60.1%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
61.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.6%
(-.f64 (sin.f64 eps) (sin.f64 x))
99.7%
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.4%
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
99.3%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
98.6%
(*.f64 eps (cos.f64 x))
96.7%
(sin.f64 eps)
Compiler

Compiled 369 to 218 computations (40.9% saved)

simplify166.0ms (1.1%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 (-.f64 x eps))
cost-diff13184
(/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))
cost-diff13440
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))))
cost-diff13440
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
cost-diff0
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))
cost-diff0
(cos.f64 x)
cost-diff0
(+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
cost-diff0
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff0
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
cost-diff0
(sin.f64 eps)
cost-diff128
(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))
cost-diff128
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
cost-diff128
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff128
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Rules
1676×fma-lowering-fma.f32
1676×fma-lowering-fma.f64
1668×sum5-define
1650×sum3-define
1386×fmm-def
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
036216
185205
2242184
3802182
41506182
53684182
67083182
08102182
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(+ eps 0)
eps
0
2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
(sin eps)
eps
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* x (* x -1/6))))
(+ 1 (* x (* x -1/6)))
1
(* x (* x -1/6))
(* x -1/6)
-1/6
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
eps
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
x
(* -1/2 (* eps (sin x)))
-1/2
(* eps (sin x))
(sin x)
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x))
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))))
1
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))
(sin (- x eps))
(- x eps)
x
eps
(* (sin (+ x eps)) (sin (- x eps)))
(sin (+ x eps))
(+ x eps)
(sin x)
Outputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(sin (/ (+ eps 0) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (+ eps 0) 2)
(/.f64 eps #s(literal 2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
2
#s(literal 2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x 2)
(*.f64 #s(literal 2 binary64) x)
x
(sin eps)
(sin.f64 eps)
eps
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ 1 (* x (* x -1/6))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(+ 1 (* x (* x -1/6)))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))
1
#s(literal 1 binary64)
(* x (* x -1/6))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* x -1/6)
(*.f64 x #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))
eps
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64))))
(cos x)
(cos.f64 x)
x
(* -1/2 (* eps (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(sin x)
(sin.f64 x)
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))))
(sin.f64 (+.f64 eps x))
1
#s(literal 1 binary64)
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(sin (- x eps))
(sin.f64 (-.f64 x eps))
(- x eps)
(-.f64 x eps)
x
eps
(* (sin (+ x eps)) (sin (- x eps)))
(*.f64 (sin.f64 (+.f64 eps x)) (sin.f64 (-.f64 x eps)))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
(sin x)
(sin.f64 x)

localize265.0ms (1.8%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(sin.f64 (-.f64 x eps))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps)))))
accuracy61.7%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
accuracy57.5%
(/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))
accuracy100.0%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
accuracy100.0%
(*.f64 eps (sin.f64 x))
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))
accuracy100.0%
(+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy99.8%
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
accuracy99.5%
(*.f64 x #s(literal -1/6 binary64))
accuracy62.6%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
accuracy100.0%
(sin.f64 eps)
accuracy100.0%
(*.f64 x #s(literal 2 binary64))
accuracy100.0%
(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
accuracy100.0%
(*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
accuracy99.7%
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
Results
145.0ms147×1valid
39.0ms105×0valid
5.0ms2valid
Compiler

Compiled 242 to 37 computations (84.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 112.0ms
ival-mult: 40.0ms (35.8% of total)
ival-sin: 15.0ms (13.4% of total)
ival-div: 13.0ms (11.6% of total)
backward-pass: 11.0ms (9.8% of total)
ival-add: 11.0ms (9.8% of total)
ival-cos: 7.0ms (6.3% of total)
...c/correct-round.rkt:119:19: 7.0ms (6.3% of total)
ival-sub: 6.0ms (5.4% of total)
const: 1.0ms (0.9% of total)

series41.0ms (0.3%)

Counts
22 → 432
Calls
Call 1
Inputs
#<alt (* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (+ eps 0) 2))>
#<alt (/ (+ eps 0) 2)>
#<alt (sin eps)>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (* x (+ 1 (* x (* x -1/6))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (cos x)>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x))>
#<alt (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))))>
#<alt (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))>
#<alt (sin (- x eps))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* x 2)>
#<alt (* x -1/6)>
#<alt (* x (* x -1/6))>
#<alt (* eps (sin x))>
Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (/ 1 (sin eps))>
#<alt (+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (- eps (* -1 x))))>
#<alt (/ 1 (sin (- eps (* -1 x))))>
#<alt (/ 1 (sin (- eps (* -1 x))))>
#<alt (/ 1 (sin (- eps (* -1 x))))>
#<alt (/ 1 (sin x))>
#<alt (+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))>
#<alt (+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))>
#<alt (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (/ 1 (sin (- x (* -1 eps))))>
#<alt (/ 1 (sin (- x (* -1 eps))))>
#<alt (/ 1 (sin (- x (* -1 eps))))>
#<alt (/ 1 (sin (- x (* -1 eps))))>
#<alt (sin (neg eps))>
#<alt (+ (sin (neg eps)) (* x (cos (neg eps))))>
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps)))))))>
#<alt (+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps)))))))))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin (neg (+ eps (* -1 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* -1 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x))))))))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (- x eps))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (sin (+ x (* -1 eps)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
Calls

108 calls:

TimeVariablePointExpression
13.0ms
x
@0
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))
3.0ms
x
@inf
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
1.0ms
x
@-inf
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms
x
@inf
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms
eps
@0
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite430.0ms (2.9%)

Algorithm
batch-egg-rewrite
Rules
5990×*-lowering-*.f32
5990×*-lowering-*.f64
3264×+-lowering-+.f64
3264×+-lowering-+.f32
2992×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036169
1218158
22224132
011117132
Stop Event
iter limit
node limit
Counts
22 → 396
Calls
Call 1
Inputs
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(/ (+ eps 0) 2)
(sin eps)
(- (sin (+ x eps)) (* x (+ 1 (* x (* x -1/6)))))
(sin (+ x eps))
(+ x eps)
(* x (+ 1 (* x (* x -1/6))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(* -1/2 (* eps (sin x)))
(- (/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))) (sin x))
(/ 1 (/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps)))))
(/ (sin (- x eps)) (* (sin (+ x eps)) (sin (- x eps))))
(sin (- x eps))
(cos (/ (+ eps (* x 2)) 2))
(* x 2)
(* x -1/6)
(* x (* x -1/6))
(* eps (sin x))
Outputs
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #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 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #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))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))))
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 1/2 binary64))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) eps)))
(/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 #s(literal 2 binary64) (*.f64 eps eps)))
(/.f64 (*.f64 eps eps) (*.f64 #s(literal 2 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -2 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) #s(literal 2 binary64))
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/2 binary64)) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) eps)
(pow.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 eps #s(literal 2 binary64)))
(*.f64 #s(literal 1/2 binary64) eps)
(*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1/2 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 eps eps)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) 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)))
(-.f64 (*.f64 (sin.f64 eps) #s(literal 1 binary64)) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(-.f64 (*.f64 (sin.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps))) (*.f64 (cos.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps))))
(sin.f64 eps)
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (sin.f64 (+.f64 eps x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) x)) (sin.f64 (+.f64 eps x)))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))))))
(-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps x))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))) (+.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))))
(-.f64 (-.f64 (sin.f64 (+.f64 eps x)) x) (*.f64 x (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(fma.f64 x (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) (sin.f64 (+.f64 eps x)))
(fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) x) (sin.f64 (+.f64 eps x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))))))
(fma.f64 #s(literal -1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) (sin.f64 (+.f64 eps x)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64)))) (sin.f64 (+.f64 eps x)))
(fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))) x (sin.f64 (+.f64 eps x)))
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(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64)) (*.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 eps) (cos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (pow.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) #s(literal 2 binary64))) (sin.f64 (+.f64 eps x)))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 x #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) x)
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(*.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))
(*.f64 #s(literal -1/6 binary64) (*.f64 x x))
(*.f64 (*.f64 x #s(literal -1/6 binary64)) x)
(*.f64 (*.f64 x (*.f64 x #s(literal -1/6 binary64))) #s(literal 1 binary64))
(*.f64 (*.f64 x x) #s(literal -1/6 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/6 binary64))) x)
(+.f64 (*.f64 eps (sin.f64 x)) (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(+.f64 (*.f64 eps (sin.f64 x)) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 eps (sin.f64 x)))
(+.f64 (*.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 eps (sin.f64 x)))
(fma.f64 eps (sin.f64 x) (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(fma.f64 eps (sin.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal 0 binary64) (sin.f64 x) (*.f64 eps (sin.f64 x)))
(fma.f64 (sin.f64 x) eps (*.f64 (sin.f64 x) #s(literal 0 binary64)))
(fma.f64 (sin.f64 x) eps (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 eps (sin.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps eps))) (*.f64 eps eps))
(/.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) eps)
(/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (sin.f64 x)) (*.f64 eps eps))
(/.f64 (*.f64 (*.f64 eps eps) (sin.f64 x)) eps)
(*.f64 eps (sin.f64 x))
(*.f64 (sin.f64 x) eps)

simplify398.0ms (2.6%)

Algorithm
egg-herbie
Rules
4902×*-lowering-*.f32
4902×*-lowering-*.f64
1704×+-lowering-+.f64
1704×+-lowering-+.f32
1510×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04643734
115423404
250233386
081723386
Stop Event
iter limit
node limit
Counts
432 → 432
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 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))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
eps
(* 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))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin 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)))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(sin eps)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
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)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin 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)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(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)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(/ 1 (sin eps))
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin x))
(+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(sin (neg eps))
(+ (sin (neg eps)) (* x (cos (neg eps))))
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* -1/2 (* x (sin (neg eps)))))))
(+ (sin (neg eps)) (* x (+ (cos (neg eps)) (* x (+ (* -1/2 (sin (neg eps))) (* -1/6 (* x (cos (neg eps)))))))))
(sin (- x eps))
(sin (- x eps))
(sin (- x eps))
(sin (- x eps))
(sin (neg (+ eps (* -1 x))))
(sin (neg (+ eps (* -1 x))))
(sin (neg (+ eps (* -1 x))))
(sin (neg (+ eps (* -1 x))))
(sin x)
(+ (sin x) (* -1 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1 (cos x)) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (* -1 (cos x)) (* eps (+ (* -1/2 (sin x)) (* 1/6 (* eps (cos x))))))))
(sin (- x eps))
(sin (- x eps))
(sin (- x eps))
(sin (- x eps))
(sin (+ x (* -1 eps)))
(sin (+ x (* -1 eps)))
(sin (+ x (* -1 eps)))
(sin (+ x (* -1 eps)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* 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)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/24 binary64))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal -2 binary64) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (-.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 x (+.f64 (*.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (*.f64 x (-.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/3 binary64))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* 1/2 (* eps (cos x)))
(*.f64 (*.f64 eps (cos.f64 x)) #s(literal 1/2 binary64))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/12 binary64))) (*.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal 1/2 binary64)) (*.f64 eps (+.f64 (*.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 eps (+.f64 (*.f64 (cos.f64 x) #s(literal -1/12 binary64)) (*.f64 eps (*.f64 (sin.f64 x) #s(literal 1/48 binary64)))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(-.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (-.f64 (*.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal 1/6 binary64))))) (pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64)))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (*.f64 eps (*.f64 eps #s(literal -1/5040 binary64)))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(*.f64 x (*.f64 x #s(literal -1/6 binary64)))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps x)
(*.f64 eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(*.f64 x (+.f64 eps (*.f64 eps (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(*.f64 x (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 eps (*.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(*.f64 x (+.f64 eps (*.f64 (*.f64 x x) (+.f64 (*.f64 eps #s(literal -1/6 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 #s(literal -1/5040 binary64) (*.f64 eps (*.f64 x x))) (*.f64 eps #s(literal 1/120 binary64)))))))))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))

eval109.0ms (0.7%)

Compiler

Compiled 20003 to 2132 computations (89.3% saved)

prune114.0ms (0.8%)

Pruning

26 alts after pruning (23 fresh and 3 done)

PrunedKeptTotal
New94618964
Fresh156
Picked325
Done011
Total95026976
Accuracy
99.9%
Counts
976 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.7%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
36.4%
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
55.1%
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
36.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
60.9%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
61.7%
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
61.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.4%
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
97.7%
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
96.8%
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
99.6%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.6%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.3%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
5.8%
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
99.4%
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
99.4%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
98.6%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
99.3%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
96.8%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
96.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
5.5%
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
98.6%
(*.f64 eps (cos.f64 x))
96.7%
eps
Compiler

Compiled 801 to 507 computations (36.7% saved)

simplify234.0ms (1.6%)

Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 eps (sin.f64 x))
cost-diff0
(*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64)))
cost-diff128
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
cost-diff0
(*.f64 eps (*.f64 x #s(literal -1/2 binary64)))
cost-diff0
(cos.f64 x)
cost-diff0
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
cost-diff0
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
cost-diff0
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
cost-diff0
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
cost-diff0
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))
cost-diff0
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))))
cost-diff0
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
cost-diff0
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Rules
4960×+-lowering-+.f64
4960×+-lowering-+.f32
3668×*-lowering-*.f32
3668×*-lowering-*.f64
2620×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040300
1116272
2369271
31222271
43317271
54686271
65243271
75625271
85654271
95654271
08246271
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
1/2
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(* eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))
-1/48
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(+ 1/3840 (* eps (* eps -1/645120)))
1/3840
(* eps (* eps -1/645120))
(* eps -1/645120)
-1/645120
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
eps
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
eps
(+ 1 (* x (* -1/2 (+ eps x))))
1
(* x (* -1/2 (+ eps x)))
x
(* -1/2 (+ eps x))
-1/2
(+ eps x)
(* eps (+ (cos x) (* eps (* x -1/2))))
eps
(+ (cos x) (* eps (* x -1/2)))
(cos x)
x
(* eps (* x -1/2))
(* x -1/2)
-1/2
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))
(* (* eps (sin x)) (* eps -1/2))
(* eps (sin x))
eps
(sin x)
x
(* eps -1/2)
-1/2
(* eps (cos x))
(cos x)
Outputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
eps
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))
1/2
#s(literal 1/2 binary64)
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))
(* eps eps)
(*.f64 eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))
(+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(+ 1/3840 (* eps (* eps -1/645120)))
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* eps (* eps -1/645120))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* eps -1/645120)
(*.f64 eps #s(literal -1/645120 binary64))
-1/645120
#s(literal -1/645120 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
eps
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
eps
(+ 1 (* x (* -1/2 (+ eps x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
1
#s(literal 1 binary64)
(* x (* -1/2 (+ eps x)))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
x
(* -1/2 (+ eps x))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
-1/2
#s(literal -1/2 binary64)
(+ eps x)
(+.f64 eps x)
(* eps (+ (cos x) (* eps (* x -1/2))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
eps
(+ (cos x) (* eps (* x -1/2)))
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(cos x)
(cos.f64 x)
x
(* eps (* x -1/2))
(*.f64 eps (*.f64 x #s(literal -1/2 binary64)))
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* (* eps (sin x)) (* eps -1/2))
(*.f64 (*.f64 eps eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
eps
(sin x)
(sin.f64 x)
x
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(cos x)
(cos.f64 x)

localize187.0ms (1.2%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 eps (cos.f64 x))
accuracy100.0%
(*.f64 eps (sin.f64 x))
accuracy100.0%
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
accuracy99.9%
(*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64)))
accuracy100.0%
(*.f64 eps (*.f64 x #s(literal -1/2 binary64)))
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
accuracy100.0%
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
accuracy100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
accuracy99.8%
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
accuracy99.8%
(*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))
accuracy99.7%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))
accuracy99.7%
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
accuracy99.7%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64)))))))
Results
134.0ms256×0valid
Compiler

Compiled 304 to 41 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-mult: 32.0ms (49.6% of total)
ival-add: 12.0ms (18.6% of total)
...c/correct-round.rkt:119:19: 10.0ms (15.5% of total)
ival-cos: 5.0ms (7.7% of total)
ival-div: 2.0ms (3.1% of total)
ival-sin: 2.0ms (3.1% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series45.0ms (0.3%)

Counts
21 → 420
Calls
Call 1
Inputs
#<alt (* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))>
#<alt (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))>
#<alt (* eps (+ 1 (* x (* -1/2 (+ eps x)))))>
#<alt (+ 1 (* x (* -1/2 (+ eps x))))>
#<alt (* x (* -1/2 (+ eps x)))>
#<alt (* -1/2 (+ eps x))>
#<alt (* eps (+ (cos x) (* eps (* x -1/2))))>
#<alt (+ (cos x) (* eps (* x -1/2)))>
#<alt (cos x)>
#<alt (* eps (* x -1/2))>
#<alt (+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))>
#<alt (* (* eps (sin x)) (* eps -1/2))>
#<alt (* eps (sin x))>
#<alt (sin x)>
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))>
#<alt (* eps (* eps -1/645120))>
#<alt (* eps (cos x))>
Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* -1/645120 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 7) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/48 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/645120 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/3840 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6)))))))>
#<alt (* -1/645120 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/3840 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/645120 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/48 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* -1/645120 (pow eps 7))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 7) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 7) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 7))>
#<alt (* -1 (* (pow eps 7) (- 1/645120 (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (* 1/3840 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/645120 (/ 1/48 (pow eps 4))) (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/3840 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6)))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2)))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* -1/645120 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 1/3840 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* -1/645120 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* -1/645120 (pow eps 2))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
Calls

105 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))
5.0ms
eps
@-inf
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
3.0ms
x
@0
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
3.0ms
eps
@-inf
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))
2.0ms
x
@inf
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite353.0ms (2.3%)

Algorithm
batch-egg-rewrite
Rules
5474×*-lowering-*.f32
5474×*-lowering-*.f64
3694×/-lowering-/.f32
3694×/-lowering-/.f64
1846×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040230
1224207
21976206
09380206
Stop Event
iter limit
node limit
Counts
21 → 406
Calls
Call 1
Inputs
(* (* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))))
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120)))))))
(* eps (+ 1 (* x (* -1/2 (+ eps x)))))
(+ 1 (* x (* -1/2 (+ eps x))))
(* x (* -1/2 (+ eps x)))
(* -1/2 (+ eps x))
(* eps (+ (cos x) (* eps (* x -1/2))))
(+ (cos x) (* eps (* x -1/2)))
(cos x)
(* eps (* x -1/2))
(+ (* (* eps (sin x)) (* eps -1/2)) (* eps (cos x)))
(* (* eps (sin x)) (* eps -1/2))
(* eps (sin x))
(sin x)
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))))
(cos (/ (+ eps (* x 2)) 2))
(* (* eps eps) (+ 1/3840 (* eps (* eps -1/645120))))
(* eps (* eps -1/645120))
(* eps (cos x))
Outputs
(*.f64 eps (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(*.f64 eps (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(*.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 2 binary64)))
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))) #s(literal 2 binary64))
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(fma.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))
(fma.f64 (*.f64 eps #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps eps)) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))
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(fma.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 eps #s(literal -1/645120 binary64)) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))
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(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(*.f64 #s(literal -1/645120 binary64) (*.f64 eps eps))
(*.f64 (*.f64 eps #s(literal -1/645120 binary64)) eps)
(*.f64 eps (cos.f64 x))
(*.f64 (cos.f64 x) eps)

simplify270.0ms (1.8%)

Algorithm
egg-herbie
Rules
5638×*-lowering-*.f32
5638×*-lowering-*.f64
2114×+-lowering-+.f64
2114×+-lowering-+.f32
1556×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04734972
116884537
261304516
080454516
Stop Event
iter limit
node limit
Counts
420 → 420
Calls
Call 1
Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
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(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
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1/2
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eps
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eps
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1
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eps
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(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/12 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (pow eps 2)) (* 1/10080 (* (pow eps 2) (pow x 2)))))))))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* -1/2 (* (pow eps 2) (sin x)))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* 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)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin 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 x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/24 binary64)) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 #s(literal -1/322560 binary64) (*.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* (pow eps 7) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 4))) (+ (* -1/322560 (cos (* 1/2 (+ eps (* 2 x))))) (+ (* 1/1920 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 6))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (+.f64 (*.f64 #s(literal -1/322560 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 (+.f64 (*.f64 #s(literal 1/1920 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (*.f64 #s(literal -1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))))
(* -1/322560 (* (pow eps 7) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 #s(literal -1/322560 binary64) (*.f64 (pow.f64 eps #s(literal 7 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(*.f64 (pow.f64 eps #s(literal 7 binary64)) (neg.f64 (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4)))))))
(*.f64 (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))) (neg.f64 (pow.f64 eps #s(literal 7 binary64))))
(* -1 (* (pow eps 7) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 6))) (+ (* -1/1920 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (+ (* 1/322560 (cos (* 1/2 (- (* 2 x) (* -1 eps))))) (* 1/24 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 4))))))))
(*.f64 (-.f64 (+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/322560 binary64)) (+.f64 (*.f64 (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/1920 binary64)) (*.f64 #s(literal 1/24 binary64) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 4 binary64)))))) (/.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (pow.f64 eps #s(literal 6 binary64)))) (neg.f64 (pow.f64 eps #s(literal 7 binary64))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (*.f64 (*.f64 eps #s(literal -2 binary64)) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 x (-.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 x (+.f64 (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 x (-.f64 (*.f64 (*.f64 (*.f64 eps #s(literal 1/3 binary64)) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
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(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))
(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (-.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (-.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* -1/645120 (pow eps 6))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (-.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(*.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) (-.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/48 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64))))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (+.f64 (*.f64 (*.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (*.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x (-.f64 (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 1/3840 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* -1/645120 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* -1/645120 (pow eps 4))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -1/645120 binary64))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (*.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+.f64 eps (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (+.f64 (*.f64 eps (*.f64 (*.f64 x x) #s(literal -1/720 binary64))) (*.f64 eps #s(literal 1/24 binary64))))))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))

eval108.0ms (0.7%)

Compiler

Compiled 25271 to 2301 computations (90.9% saved)

prune90.0ms (0.6%)

Pruning

31 alts after pruning (26 fresh and 5 done)

PrunedKeptTotal
New82712839
Fresh41418
Picked325
Done033
Total83431865
Accuracy
99.9%
Counts
865 → 31
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.7%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
36.4%
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
33.9%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
55.1%
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
36.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
60.9%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
61.7%
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
61.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.4%
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
97.7%
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
96.8%
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
99.6%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
99.6%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.5%
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.3%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.6%
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
5.0%
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
97.8%
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
99.4%
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
99.4%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
99.3%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
97.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
96.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
97.3%
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
5.5%
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
5.5%
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
98.6%
(*.f64 eps (cos.f64 x))
96.7%
eps
Compiler

Compiled 1121 to 663 computations (40.9% saved)

simplify178.0ms (1.2%)

Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 (+.f64 eps x))
cost-diff0
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
cost-diff256
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))))
cost-diff256
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
cost-diff0
(cos.f64 x)
cost-diff0
(*.f64 eps (cos.f64 x))
cost-diff0
(*.f64 eps #s(literal -1/2 binary64))
cost-diff256
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))
cost-diff256
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps))))
cost-diff256
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
cost-diff0
(*.f64 x #s(literal -1/2 binary64))
cost-diff0
(*.f64 eps (*.f64 x #s(literal -1/2 binary64)))
cost-diff0
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
cost-diff0
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
cost-diff0
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
cost-diff0
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
Rules
2820×+-lowering-+.f64
2820×+-lowering-+.f32
2538×*-lowering-*.f32
2538×*-lowering-*.f64
1646×sum3-define
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
040270
1119245
2396245
31359245
43704236
55309236
66970236
08096236
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
(* eps 1/2)
eps
1/2
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
-1/48
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(+ 1/3840 (* (* eps eps) -1/645120))
1/3840
(* (* eps eps) -1/645120)
-1/645120
(* eps 2)
2
(* eps (* eps (* x -1/2)))
eps
(* eps (* x -1/2))
(* x -1/2)
x
-1/2
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))
eps
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))
1
(* (* eps -1/2) (+ x (/ (* x x) eps)))
(* eps -1/2)
-1/2
(+ x (/ (* x x) eps))
x
(/ (* x x) eps)
(* x x)
(* eps (cos x))
eps
(cos x)
x
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x))
(/ 1 (/ 1 (sin (+ eps x))))
1
(/ 1 (sin (+ eps x)))
(sin (+ eps x))
(+ eps x)
eps
x
(sin x)
Outputs
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(+ x (* eps 1/2))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))
(* eps eps)
(*.f64 eps eps)
(+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))
(+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))
-1/48
#s(literal -1/48 binary64)
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))
(+ 1/3840 (* (* eps eps) -1/645120))
(+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
1/3840
#s(literal 1/3840 binary64)
(* (* eps eps) -1/645120)
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
-1/645120
#s(literal -1/645120 binary64)
(* eps 2)
(*.f64 eps #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* eps (* eps (* x -1/2)))
(*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 x eps)))
eps
(* eps (* x -1/2))
(*.f64 #s(literal -1/2 binary64) (*.f64 x eps))
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)))))
eps
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))
(+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps))))
1
#s(literal 1 binary64)
(* (* eps -1/2) (+ x (/ (* x x) eps)))
(*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(+ x (/ (* x x) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
x
(/ (* x x) eps)
(/.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(cos x)
(cos.f64 x)
x
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(/ 1 (/ 1 (sin (+ eps x))))
(sin.f64 (+.f64 x eps))
1
#s(literal 1 binary64)
(/ 1 (sin (+ eps x)))
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 x eps)))
(sin (+ eps x))
(sin.f64 (+.f64 x eps))
(+ eps x)
(+.f64 x eps)
eps
x
(sin x)
(sin.f64 x)

localize256.0ms (1.7%)

Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy99.8%
(sin.f64 (+.f64 eps x))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
accuracy99.6%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x))))
accuracy61.7%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(*.f64 eps (cos.f64 x))
accuracy100.0%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
accuracy99.8%
(*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))
accuracy99.6%
(+.f64 x (/.f64 (*.f64 x x) eps))
accuracy57.4%
(/.f64 (*.f64 x x) eps)
accuracy100.0%
(*.f64 x #s(literal -1/2 binary64))
accuracy100.0%
(*.f64 eps (*.f64 x #s(literal -1/2 binary64)))
accuracy99.9%
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
accuracy99.8%
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
accuracy99.7%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
accuracy99.7%
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
accuracy99.7%
(*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))
Results
144.0ms152×1valid
41.0ms101×0valid
4.0ms2valid
Compiler

Compiled 282 to 41 computations (85.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 121.0ms
ival-mult: 51.0ms (42.2% of total)
...c/correct-round.rkt:119:19: 18.0ms (14.9% of total)
ival-add: 14.0ms (11.6% of total)
backward-pass: 11.0ms (9.1% of total)
ival-div: 9.0ms (7.4% of total)
ival-cos: 8.0ms (6.6% of total)
ival-sin: 6.0ms (5% of total)
ival-sub: 2.0ms (1.7% of total)
const: 1.0ms (0.8% of total)

series23.0ms (0.2%)

Counts
22 → 456
Calls
Call 1
Inputs
#<alt (* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))>
#<alt (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (+ x (* eps 1/2))>
#<alt (* eps (* eps (* x -1/2)))>
#<alt (* eps (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))>
#<alt (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))>
#<alt (* (* eps -1/2) (+ x (/ (* x x) eps)))>
#<alt (* eps -1/2)>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (- (/ 1 (/ 1 (sin (+ eps x)))) (sin x))>
#<alt (/ 1 (/ 1 (sin (+ eps x))))>
#<alt (/ 1 (sin (+ eps x)))>
#<alt (sin (+ eps x))>
#<alt (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))>
#<alt (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))>
#<alt (* (* eps eps) -1/645120)>
#<alt (/ (* x x) eps)>
#<alt (+ x (/ (* x x) eps))>
Outputs
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 7) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))))>
#<alt (* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (+ (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (/ (cos (+ x (* 1/2 eps))) (pow eps 6))))))>
#<alt (* -1/322560 (* (pow eps 7) (cos (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/322560 (cos (- x (* -1/2 eps)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4)))))))>
#<alt (* -1 (* (pow eps 7) (+ (* -1 (/ (cos (- x (* -1/2 eps))) (pow eps 6))) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4))))))))>
#<alt (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (+ (* -1 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* -1/2 (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (+ (* x (+ (* -1 (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))) (* 1/6 (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))))) (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))>
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (* 1/2 (cos x))>
#<alt (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x)))>
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))>
#<alt (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* -1/645120 (* (pow eps 6) (cos (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 6) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))>
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))))>
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (+ x (* 1/2 eps)))) (+ (* 1/3840 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (+ x (* 1/2 eps))) (pow eps 6)))))))>
#<alt (* -1/645120 (* (pow eps 6) (cos (- x (* -1/2 eps)))))>
#<alt (* (pow eps 6) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2)))))>
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* (pow eps 6) (+ (* -1/48 (/ (cos (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/645120 (cos (- x (* -1/2 eps)))) (+ (* 1/3840 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/2 (/ (cos (- x (* -1/2 eps))) (pow eps 6)))))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
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#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt (/ (pow x 2) eps)>
#<alt x>
#<alt (* x (+ 1 (/ x eps)))>
#<alt (* x (+ 1 (/ x eps)))>
#<alt (* x (+ 1 (/ x eps)))>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (/ (pow x 2) eps)>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (* (pow x 2) (+ (/ 1 eps) (/ 1 x)))>
#<alt (/ (pow x 2) eps)>
#<alt (/ (+ (* eps x) (pow x 2)) eps)>
#<alt (/ (+ (* eps x) (pow x 2)) eps)>
#<alt (/ (+ (* eps x) (pow x 2)) eps)>
#<alt x>
#<alt (+ x (/ (pow x 2) eps))>
#<alt (+ x (/ (pow x 2) eps))>
#<alt (+ x (/ (pow x 2) eps))>
#<alt x>
#<alt (+ x (/ (pow x 2) eps))>
#<alt (+ x (/ (pow x 2) eps))>
#<alt (+ x (/ (pow x 2) eps))>
Calls

114 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(* (* eps -1/2) (+ x (/ (* x x) eps)))
1.0ms
x
@-inf
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))
1.0ms
x
@inf
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))
1.0ms
eps
@0
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))
1.0ms
eps
@inf
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))

rewrite290.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
3384×*-lowering-*.f32
3384×*-lowering-*.f64
2534×fma-lowering-fma.f32
2534×fma-lowering-fma.f64
2164×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040195
1250176
22203176
08592176
Stop Event
iter limit
node limit
Counts
22 → 446
Calls
Call 1
Inputs
(* (* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120))))))) (* eps 2))
(* (cos (+ x (* eps 1/2))) (+ 1/2 (* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))))
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
(* eps (* eps (* x -1/2)))
(* eps (* x -1/2))
(* x -1/2)
(* eps (+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps)))))
(+ 1 (* (* eps -1/2) (+ x (/ (* x x) eps))))
(* (* eps -1/2) (+ x (/ (* x x) eps)))
(* eps -1/2)
(* eps (cos x))
(cos x)
(- (/ 1 (/ 1 (sin (+ eps x)))) (sin x))
(/ 1 (/ 1 (sin (+ eps x))))
(/ 1 (sin (+ eps x)))
(sin (+ eps x))
(* (* eps eps) (+ -1/48 (* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))))
(* (* eps eps) (+ 1/3840 (* (* eps eps) -1/645120)))
(* (* eps eps) -1/645120)
(/ (* x x) eps)
(+ x (/ (* x x) eps))
Outputs
(+.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal 2 binary64))) (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64))))
(fma.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 eps #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 eps (*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))))
(*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))))
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(*.f64 (*.f64 eps (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))) #s(literal 2 binary64))
(*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))) #s(literal 2 binary64)) eps)
(*.f64 (*.f64 (*.f64 eps #s(literal 2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(+.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(+.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 eps (*.f64 (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(fma.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
(fma.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 eps eps) (*.f64 (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) (*.f64 (*.f64 eps eps) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) eps) (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps)) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (*.f64 eps eps) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 3 binary64)) (pow.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (-.f64 (pow.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (pow.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))
(/.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))))))) (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (-.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) #s(literal 1/2 binary64)))))
(/.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))) (-.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))))
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simplify270.0ms (1.8%)

Algorithm
egg-herbie
Rules
5380×*-lowering-*.f32
5380×*-lowering-*.f64
1868×+-lowering-+.f64
1868×+-lowering-+.f32
1314×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04694646
116134339
254944327
086904327
Stop Event
iter limit
node limit
Counts
456 → 456
Calls
Call 1
Inputs
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
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(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* 2 (* eps (* (cos (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(* eps (cos x))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* -1/322560 (* (pow eps 7) (cos (+ x (* 1/2 eps)))))
(* (pow eps 7) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2)))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))))))
(* (pow eps 7) (+ (* -1/24 (/ (cos (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/322560 (cos (+ x (* 1/2 eps)))) (+ (* 1/1920 (/ (cos (+ x (* 1/2 eps))) (pow eps 2))) (/ (cos (+ x (* 1/2 eps))) (pow eps 6))))))
(* -1/322560 (* (pow eps 7) (cos (- x (* -1/2 eps)))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (* 1/322560 (cos (- x (* -1/2 eps)))))))
(* -1 (* (pow eps 7) (+ (* -1/1920 (/ (cos (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/322560 (cos (- x (* -1/2 eps)))) (* 1/24 (/ (cos (- x (* -1/2 eps))) (pow eps 4)))))))
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(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
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(* -1/645120 (* (pow eps 6) (cos (+ x (* 1/2 eps)))))
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(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 (* eps x))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 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))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* 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 (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(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)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin eps)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(/ 1 (sin x))
(+ (* -1 (/ (* eps (cos x)) (pow (sin x) 2))) (/ 1 (sin x)))
(+ (* eps (- (* eps (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))
(+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1/6 (/ (cos x) (pow (sin x) 2))) (+ (* 1/2 (/ (cos x) (pow (sin x) 2))) (/ (* (cos x) (- (* 1/2 (/ 1 (sin x))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (sin x)))))) (* 1/2 (/ 1 (sin x)))) (* -1 (/ (pow (cos x) 2) (pow (sin x) 3))))) (/ (cos x) (pow (sin x) 2)))) (/ 1 (sin x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin (- x (* -1 eps))))
(/ 1 (sin eps))
(+ (* -1 (/ (* x (cos eps)) (pow (sin eps) 2))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -1/6 (/ (cos eps) (pow (sin eps) 2))) (+ (* 1/2 (/ (cos eps) (pow (sin eps) 2))) (/ (* (cos eps) (- (* 1/2 (/ 1 (sin eps))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (sin eps)))))) (* 1/2 (/ 1 (sin eps)))) (* -1 (/ (pow (cos eps) 2) (pow (sin eps) 3))))) (/ (cos eps) (pow (sin eps) 2)))) (/ 1 (sin eps)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (+ eps x)))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(/ 1 (sin (- eps (* -1 x))))
(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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin eps)
(+ (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))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* -1/645120 (pow eps 6))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
(* 1/3840 (pow eps 2))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 4))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(* -1/645120 (pow eps 2))
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
x
(* x (+ 1 (/ x eps)))
(* x (+ 1 (/ x eps)))
(* x (+ 1 (/ x eps)))
(/ (pow x 2) eps)
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(/ (pow x 2) eps)
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(/ (pow x 2) eps)
(/ (+ (* eps x) (pow x 2)) eps)
(/ (+ (* eps x) (pow x 2)) eps)
(/ (+ (* eps x) (pow x 2)) eps)
x
(+ x (/ (pow x 2) eps))
(+ x (/ (pow x 2) eps))
(+ x (/ (pow x 2) eps))
x
(+ x (/ (pow x 2) eps))
(+ x (/ (pow x 2) eps))
(+ x (/ (pow x 2) eps))
Outputs
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
(*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 #s(literal -2 binary64) (*.f64 eps x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 x (-.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal -2 binary64))) (*.f64 (*.f64 (*.f64 eps x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))))))))
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 x (+.f64 (*.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal -2 binary64))) (*.f64 x (-.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (*.f64 eps x)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))) (*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))))
(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
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(* 2 (* eps (* (cos (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))))
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(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
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(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
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(/ 1 (sin eps))
(/.f64 #s(literal 1 binary64) (sin.f64 eps))
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(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) (/.f64 (*.f64 x (cos.f64 eps)) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))
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(/ 1 (sin (- eps (* -1 x))))
(/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))
(sin x)
(sin.f64 x)
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
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(sin (+ eps x))
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(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1/48 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/48 binary64))
(* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))
(*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))
(*.f64 (*.f64 eps eps) (+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))) #s(literal -1/48 binary64)))
(* -1/645120 (pow eps 6))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* (pow eps 6) (- (* 1/3840 (/ 1 (pow eps 2))) (+ 1/645120 (/ 1/48 (pow eps 4)))))
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(* 1/3840 (pow eps 2))
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(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))
(* -1/645120 (pow eps 4))
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* -1/645120 (pow eps 4))
(*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))
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(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 1/3840 (/ 1 (pow eps 2))) 1/645120))
(*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (+.f64 #s(literal -1/645120 binary64) (/.f64 #s(literal 1/3840 binary64) (*.f64 eps eps))))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
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(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(* -1/645120 (pow eps 2))
(*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))
(/ (pow x 2) eps)
(/.f64 (*.f64 x x) eps)
(/ (pow x 2) eps)
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(/ (pow x 2) eps)
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x
(* x (+ 1 (/ x eps)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* x (+ 1 (/ x eps)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* x (+ 1 (/ x eps)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(/ (pow x 2) eps)
(/.f64 (*.f64 x x) eps)
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
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(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(/ (pow x 2) eps)
(/.f64 (*.f64 x x) eps)
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* (pow x 2) (+ (/ 1 eps) (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(/ (pow x 2) eps)
(/.f64 (*.f64 x x) eps)
(/ (+ (* eps x) (pow x 2)) eps)
(/.f64 (*.f64 x (+.f64 eps x)) eps)
(/ (+ (* eps x) (pow x 2)) eps)
(/.f64 (*.f64 x (+.f64 eps x)) eps)
(/ (+ (* eps x) (pow x 2)) eps)
(/.f64 (*.f64 x (+.f64 eps x)) eps)
x
(+ x (/ (pow x 2) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(+ x (/ (pow x 2) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(+ x (/ (pow x 2) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
x
(+ x (/ (pow x 2) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(+ x (/ (pow x 2) eps))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(+ x (/ (pow x 2) eps))
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eval102.0ms (0.7%)

Compiler

Compiled 22534 to 2242 computations (90.1% saved)

prune97.0ms (0.6%)

Pruning

36 alts after pruning (27 fresh and 9 done)

PrunedKeptTotal
New89012902
Fresh61521
Picked145
Done055
Total89736933
Accuracy
100.0%
Counts
933 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
61.7%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
33.9%
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
55.1%
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
36.5%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
60.9%
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
61.7%
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
61.5%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
99.4%
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
97.7%
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
96.8%
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
99.6%
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
99.8%
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
99.8%
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
99.3%
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
99.6%
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
99.5%
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
99.6%
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
5.0%
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
97.7%
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
97.7%
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
99.4%
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
99.4%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
99.3%
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
97.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
97.6%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
97.5%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
96.7%
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
97.3%
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
5.5%
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
5.5%
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
98.6%
(*.f64 eps (cos.f64 x))
61.5%
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64)))))
96.7%
eps
Compiler

Compiled 1820 to 738 computations (59.5% saved)

regimes47.0ms (0.3%)

Counts
54 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(/.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 2 binary64)) (*.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))))
Outputs
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
Calls

3 calls:

14.0ms
eps
13.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes57.0ms (0.4%)

Counts
51 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
Outputs
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
Calls

3 calls:

24.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms
eps
12.0ms
x
Results
AccuracySegmentsBranch
99.8%1x
99.8%1eps
99.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes44.0ms (0.3%)

Counts
49 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sin.f64 (/.f64 (-.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 x eps) x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))) (*.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (+.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (*.f64 eps (cos.f64 x)) #s(literal -1/6 binary64))))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 x eps)) (*.f64 (sin.f64 (+.f64 x eps)) (sin.f64 (-.f64 x eps))))) (sin.f64 x))
Outputs
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Calls

3 calls:

15.0ms
eps
12.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
12.0ms
x
Results
AccuracySegmentsBranch
99.7%1x
99.7%1eps
99.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes47.0ms (0.3%)

Counts
44 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))))) (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps #s(literal 2 binary64))))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 eps (*.f64 eps #s(literal -1/645120 binary64))))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 (+.f64 eps x)))) (sin.f64 x))
(+.f64 (*.f64 (*.f64 eps (sin.f64 x)) (*.f64 eps #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(/.f64 (*.f64 (+.f64 (cos.f64 x) (*.f64 eps (*.f64 (sin.f64 x) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
Outputs
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
Calls

3 calls:

15.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
11.0ms
eps
11.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
99.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts
33 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 eps (*.f64 eps #s(literal 1/3840 binary64))))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
Calls

2 calls:

9.0ms
eps
8.0ms
x
Results
AccuracySegmentsBranch
99.6%1x
99.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes23.0ms (0.2%)

Counts
30 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
Calls

2 calls:

12.0ms
eps
8.0ms
x
Results
AccuracySegmentsBranch
99.5%1x
99.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes22.0ms (0.1%)

Counts
28 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/6 binary64))))))
Outputs
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
Calls

2 calls:

11.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
99.3%1x
99.3%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts
26 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 eps (+.f64 (cos.f64 x) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
Outputs
(*.f64 eps (cos.f64 x))
Calls

2 calls:

7.0ms
eps
7.0ms
x
Results
AccuracySegmentsBranch
98.6%1x
98.6%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes18.0ms (0.1%)

Counts
23 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(/.f64 (+.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/8 binary64))) (*.f64 (+.f64 eps x) (*.f64 (+.f64 eps x) (+.f64 eps x)))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))) (-.f64 (*.f64 eps eps) (*.f64 (*.f64 eps (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))) eps))))
(*.f64 eps (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (+.f64 x (/.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps)))) (-.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))))
(sin.f64 eps)
Outputs
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
Calls

2 calls:

10.0ms
eps
6.0ms
x
Results
AccuracySegmentsBranch
97.8%1x
97.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts
18 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 eps #s(literal 1/12 binary64)))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
Calls

2 calls:

5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes17.0ms (0.1%)

Counts
15 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (+.f64 x (/.f64 (*.f64 x x) eps)))))
(*.f64 eps (*.f64 eps (+.f64 (/.f64 #s(literal 1 binary64) eps) (*.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 (*.f64 x x) eps))))))
Outputs
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
Calls

2 calls:

4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts
11 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
Calls

2 calls:

4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Counts
10 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps x))))
(+.f64 eps (*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
Calls

2 calls:

3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.5%1x
97.5%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

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

2 calls:

2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
96.8%1x
96.8%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
Outputs
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
Calls

2 calls:

2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
96.7%1x
96.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Accuracy

Total -58.8b remaining (-2820.9%)

Threshold costs -58.8b (-2820.9%)

Counts
4 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 1/6 binary64)))
Outputs
eps
Calls

2 calls:

3.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
96.7%1x
96.7%1eps
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify13.0ms (0.1%)

Algorithm
egg-herbie
Rules
102×*-commutative_binary64
52×+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
097279
1179279
2190279
3195279
4197279
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 x))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
eps
Outputs
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (fma.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (-.f64 (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (*.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))
(*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #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 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64)))))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3840 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/645120 binary64))))))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(*.f64 (*.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))) (*.f64 eps #s(literal 2 binary64)))
(*.f64 (*.f64 eps #s(literal 2 binary64)) (*.f64 (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/48 binary64)))))
(*.f64 (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 eps (cos.f64 x))
(*.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 x x) #s(literal -1/720 binary64))))))) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/24 binary64) (*.f64 x x))))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal 1/24 binary64))))))))
(+.f64 eps (*.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
eps

soundness2.3s (15%)

Rules
5638×*-lowering-*.f32
5638×*-lowering-*.f64
5380×*-lowering-*.f32
5380×*-lowering-*.f64
4902×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040195
1250176
22203176
08592176
0616
14916
240216
3523216
0830916
04694646
116134339
254944327
086904327
04734972
116884537
261304516
080454516
0107488
1327465
2963459
33572459
08267459
04643734
115423404
250233386
081723386
Stop Event
fuel
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
Compiler

Compiled 861 to 486 computations (43.6% saved)

preprocess82.0ms (0.5%)

Compiler

Compiled 612 to 224 computations (63.4% saved)

end0.0ms (0%)

Profiling

Loading profile data...