2sin (example 3.3)

Time bar (total: 15.0s)

analyze48.0ms (0.3%)

Memory
-16.1MiB live, 67.6MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample5.8s (39%)

Memory
-344.2MiB live, 7 850.1MiB allocated
Samples
3.3s26 090×0invalid
632.0ms5 567×0valid
461.0ms2 689×1valid
Precisions
Click to see histograms. Total time spent on operations: 3.1s
const: 622.0ms (20% of total)
ival-sin: 562.0ms (18.1% of total)
ival-mult: 537.0ms (17.3% of total)
ival-add: 287.0ms (9.2% of total)
ival-<=: 261.0ms (8.4% of total)
ival-fabs: 254.0ms (8.2% of total)
ival-sub: 209.0ms (6.7% of total)
ival-<: 164.0ms (5.3% of total)
ival-and: 104.0ms (3.3% of total)
adjust: 48.0ms (1.5% of total)
exact: 48.0ms (1.5% of total)
ival-assert: 14.0ms (0.5% of total)
Bogosity

preprocess27.0ms (0.2%)

Memory
0.7MiB live, 39.5MiB allocated
Algorithm
egg-herbie
Rules
114×sub-neg
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
76×cancel-sign-sub-inv
62×associate--r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02146
14342
29242
318142
432142
539842
648342
752542
853442
067
197
2147
3207
4287
5437
6767
71017
81447
91597
101677
01677
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))

explain121.0ms (0.8%)

Memory
-4.4MiB live, 113.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2223(2.387629466703073e-270 6.323919630425219e-273)4(4.022650708386591e-65 5.599523165333559e-67)(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
31(452.1677815145183 308.6678353255072)1(66.68374274362472 0.00010012846265434226)(sin.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(sin.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))cancellation2218
sin.f64(sin.f64 (+.f64 x eps))sensitivity32
Confusion
Predicted +Predicted -
+2194
-429
Precision
0.9820627802690582
Recall
0.9820627802690582
Confusion?
Predicted +Predicted MaybePredicted -
+21940
-4425
Precision?
0.9653679653679653
Recall?
1.0
Freqs
test
numberfreq
033
1222
21
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
17.0ms344×0valid
15.0ms160×1valid
5.0ms3valid
2.0ms2valid
Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-sin: 15.0ms (62.3% of total)
adjust: 3.0ms (12.5% of total)
ival-add: 3.0ms (12.5% of total)
ival-sub: 3.0ms (12.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
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
80×accelerator-lowering-fma.f32
80×accelerator-lowering-fma.f64
48×*-lowering-*.f32
48×*-lowering-*.f64
36×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
1918
21418
32018
42818
54318
67618
710118
814418
915918
1016718
016718
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)

localize28.0ms (0.2%)

Memory
6.9MiB live, 45.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(+.f64 x eps)
accuracy100.0%
(sin.f64 x)
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy63.2%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Samples
8.0ms172×0valid
7.0ms80×1valid
2.0ms3valid
1.0ms2valid
Compiler

Compiled 20 to 8 computations (60% saved)

Precisions
Click to see histograms. Total time spent on operations: 12.0ms
ival-sin: 8.0ms (64.3% of total)
ival-add: 2.0ms (16.1% of total)
adjust: 1.0ms (8% of total)
ival-sub: 1.0ms (8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory
6.6MiB live, 6.6MiB allocated
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
(- (sin (+ x eps)) (sin x))
0.0ms
x
@0
(sin x)

rewrite341.0ms (2.3%)

Memory
-39.5MiB live, 618.1MiB allocated
Algorithm
batch-egg-rewrite
Rules
4 986×accelerator-lowering-fma.f32
4 986×accelerator-lowering-fma.f64
4 676×*-lowering-*.f32
4 676×*-lowering-*.f64
2 176×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
14916
237616
3476316
0821216
Stop Event
iter limit
node limit
Counts
4 → 214
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)) (fma.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 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(+.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)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)))) #s(literal -1 binary64)))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (-.f64 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64))))
(-.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #s(literal 2 binary64)))))
(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 (fma.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 (fma.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 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (sin.f64 x)))
(fma.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.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 (fma.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 binary64) (cos.f64 (+.f64 x x))) (*.f64 (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #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 (sin.f64 (+.f64 x eps)) (-.f64 (fma.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 (fma.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)) (sin.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(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) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (*.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 (-.f64 eps x))))) (-.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)))
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(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 #s(literal 0 binary64) (-.f64 x eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 x eps) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (-.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps))) (/.f64 (*.f64 x x) (-.f64 x eps))) (*.f64 (*.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))) (/.f64 (*.f64 eps eps) (-.f64 x eps)))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 x x) (-.f64 x eps)) (fma.f64 (/.f64 (*.f64 eps eps) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))))
(/.f64 (-.f64 (*.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)))) (fma.f64 x (/.f64 x (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps))))
(/.f64 (*.f64 (fma.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) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x))))))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))))
(/.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (fma.f64 x x (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 eps x) (*.f64 (+.f64 x eps) (-.f64 eps x))) #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)))
(*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (fma.f64 x x (*.f64 eps (-.f64 eps x)))))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x))))))
(*.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))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(*.f64 (*.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 (*.f64 eps (-.f64 eps x)) (*.f64 eps (-.f64 eps x)))))) (fma.f64 (*.f64 eps (-.f64 eps x)) (-.f64 (*.f64 eps (-.f64 eps x)) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))) (-.f64 (*.f64 x x) (*.f64 eps (-.f64 eps x))))
(*.f64 (/.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))) (fma.f64 eps (+.f64 x eps) (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) (fma.f64 x x (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(*.f64 (pow.f64 (/.f64 (-.f64 x eps) (*.f64 (fma.f64 x x (*.f64 eps eps)) (*.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (fma.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)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) (*.f64 (*.f64 eps (*.f64 eps eps)) (-.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 x (*.f64 x x)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x (*.f64 eps (-.f64 eps x))) (*.f64 (fma.f64 x (*.f64 x x) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 eps (+.f64 x eps) (*.f64 x x)) (-.f64 x eps))))
(exp.f64 (*.f64 (log.f64 (sin.f64 x)) #s(literal 1 binary64)))
(sin.f64 x)
(pow.f64 (sin.f64 x) #s(literal 1 binary64))

simplify701.0ms (4.7%)

Memory
9.3MiB live, 412.2MiB allocated
Algorithm
egg-herbie
Rules
16 678×accelerator-lowering-fma.f32
16 678×accelerator-lowering-fma.f64
4 132×*-lowering-*.f32
4 132×*-lowering-*.f64
2 614×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107496
1314496
2775489
32836489
46173489
08126458
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)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.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 (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (fma.f64 x (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (*.f64 #s(literal 1/6 binary64) (*.f64 x x))) #s(literal 0 binary64))) 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 (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 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 (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 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)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (fma.f64 x (cos.f64 eps) #s(literal 0 binary64)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (*.f64 (cos.f64 eps) (*.f64 x (fma.f64 x (*.f64 x #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 (- 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)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (*.f64 (*.f64 eps (cos.f64 x)) (fma.f64 eps (*.f64 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 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) #s(literal 1 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)

eval98.0ms (0.7%)

Memory
11.7MiB live, 51.7MiB allocated
Compiler

Compiled 7 832 to 845 computations (89.2% saved)

prune83.0ms (0.6%)

Memory
4.5MiB live, 81.7MiB allocated
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2908298
Fresh000
Picked011
Done000
Total2909299
Accuracy
100.0%
Counts
299 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
63.3%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
61.4%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
63.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.7%
(-.f64 (sin.f64 eps) (sin.f64 x))
99.8%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.2%
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
99.1%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
98.5%
(*.f64 eps (cos.f64 x))
96.6%
(sin.f64 eps)
Compiler

Compiled 211 to 142 computations (32.7% saved)

simplify598.0ms (4%)

Memory
-18.6MiB live, 458.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
cost-diff0
(cos.f64 eps)
cost-diff0
(sin.f64 x)
cost-diff6400
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
cost-diff-64
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
cost-diff0
(cos.f64 x)
cost-diff0
(sin.f64 x)
cost-diff0
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
cost-diff0
(fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))
cost-diff0
(+.f64 x eps)
cost-diff0
(sin.f64 (+.f64 x eps))
cost-diff192
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
cost-diff0
(sin.f64 eps)
cost-diff0
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
cost-diff0
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
cost-diff192
(+.f64 eps #s(literal 0 binary64))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
Rules
10 744×accelerator-lowering-fma.f32
10 744×accelerator-lowering-fma.f64
7 680×*-lowering-*.f32
7 680×*-lowering-*.f64
4 974×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036176
184176
2208163
3446163
4961163
52228163
63037163
73538163
83897163
94218163
104370163
115332163
125842163
136028163
146077163
156106163
166128163
176140163
186144163
196144163
206144163
216282163
226342163
236342163
246342163
09703152
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))
(sin (* (+ eps 0) 1/2))
(* (+ eps 0) 1/2)
(+ eps 0)
eps
0
1/2
(cos (* (+ (* x 2) eps) 1/2))
(* (+ (* x 2) eps) 1/2)
(+ (* x 2) eps)
x
2
(sin eps)
eps
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ (* x (* x -1/6)) 1))
(+ (* x (* x -1/6)) 1)
(* x -1/6)
-1/6
1
(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
eps
(+ (* eps (* -1/2 (sin x))) (cos x))
(* -1/2 (sin x))
-1/2
(sin x)
x
(cos x)
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
(sin x)
x
(cos eps)
eps
(- (* (cos x) (sin eps)) (sin x))
(* (cos x) (sin eps))
(cos x)
(sin eps)
Outputs
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
(fma.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))
(fma.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal 0 binary64))
(sin (* (+ eps 0) 1/2))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))
(* (+ eps 0) 1/2)
(fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
1/2
#s(literal 1/2 binary64)
(cos (* (+ (* x 2) eps) 1/2))
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* (+ (* x 2) eps) 1/2)
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ (* x 2) eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
2
#s(literal 2 binary64)
(sin eps)
(sin.f64 eps)
eps
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 0 binary64)) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(sin (+ x eps))
(sin.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ (* x (* x -1/6)) 1))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(+ (* x (* x -1/6)) 1)
(fma.f64 x (fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64)) #s(literal 1 binary64))
(* x -1/6)
(fma.f64 x #s(literal -1/6 binary64) #s(literal 0 binary64))
-1/6
#s(literal -1/6 binary64)
1
#s(literal 1 binary64)
(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
(fma.f64 eps (fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x)) #s(literal 0 binary64))
eps
(+ (* eps (* -1/2 (sin x))) (cos x))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x))
(* -1/2 (sin x))
(fma.f64 #s(literal -1/2 binary64) (sin.f64 x) #s(literal 0 binary64))
-1/2
#s(literal -1/2 binary64)
(sin x)
(sin.f64 x)
x
(cos x)
(cos.f64 x)
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
(fma.f64 (sin.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (fma.f64 (sin.f64 eps) (cos.f64 x) #s(literal 0 binary64)))
(sin x)
(sin.f64 x)
x
(cos eps)
(cos.f64 eps)
eps
(- (* (cos x) (sin eps)) (sin x))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 #s(literal 0 binary64) (sin.f64 x)))
(* (cos x) (sin eps))
(fma.f64 (sin.f64 eps) (cos.f64 x) #s(literal 0 binary64))
(cos x)
(cos.f64 x)
(sin eps)
(sin.f64 eps)

localize164.0ms (1.1%)

Memory
13.9MiB live, 251.4MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(cos.f64 eps)
accuracy100.0%
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
accuracy100.0%
(*.f64 (cos.f64 x) (sin.f64 eps))
accuracy63.3%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
accuracy100.0%
(sin.f64 x)
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
accuracy100.0%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
accuracy100.0%
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))
accuracy99.8%
(sin.f64 (+.f64 x eps))
accuracy99.5%
(*.f64 x #s(literal -1/6 binary64))
accuracy63.8%
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
accuracy100.0%
(sin.f64 eps)
accuracy100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy100.0%
(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy99.8%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
Samples
74.0ms169×0valid
35.0ms81×1valid
8.0ms3valid
3.0ms2valid
Compiler

Compiled 177 to 38 computations (78.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 96.0ms
ival-cos: 38.0ms (39.6% of total)
ival-mult: 23.0ms (23.9% of total)
ival-sin: 14.0ms (14.6% of total)
ival-add: 8.0ms (8.3% of total)
adjust: 5.0ms (5.2% of total)
const: 4.0ms (4.2% of total)
ival-sub: 3.0ms (3.1% of total)
exact: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series32.0ms (0.2%)

Memory
-10.9MiB live, 65.8MiB allocated
Counts
21 → 396
Calls
Call 1
Inputs
#<alt (* (+ (* x 2) eps) 1/2)>
#<alt (+ eps 0)>
#<alt (sin (* (+ eps 0) 1/2))>
#<alt (cos (* (+ (* x 2) eps) 1/2))>
#<alt (sin eps)>
#<alt (- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (* x (* x -1/6)) 1)>
#<alt (+ (* eps (* -1/2 (sin x))) (cos x))>
#<alt (sin x)>
#<alt (cos x)>
#<alt (* eps (+ (* eps (* -1/2 (sin x))) (cos x)))>
#<alt (+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))>
#<alt (cos eps)>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))>
#<alt (* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)>
#<alt (* x -1/6)>
#<alt (* x (+ (* x (* x -1/6)) 1))>
#<alt (* (cos x) (sin eps))>
Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt 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 (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 (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 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 1>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (+ 1 (* -1/6 (pow x 2)))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))>
#<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 (* 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 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>
#<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 (* 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 (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 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (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 (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt (- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* -1 x))>
#<alt (+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))>
#<alt (+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (* -1 (sin x))>
#<alt (- (* eps (cos x)) (sin x))>
#<alt (- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))>
#<alt (- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<alt (- (* (cos x) (sin eps)) (sin x))>
#<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 (* 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 (* -1/6 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 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 (sin eps)>
#<alt (+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))>
#<alt (+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
#<alt (* (cos x) (sin eps))>
Calls

99 calls:

TimeVariablePointExpression
3.0ms
eps
@0
(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
2.0ms
eps
@inf
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
1.0ms
eps
@inf
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))
1.0ms
x
@inf
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
1.0ms
x
@inf
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))

rewrite422.0ms (2.8%)

Memory
14.1MiB live, 728.0MiB allocated
Algorithm
batch-egg-rewrite
Rules
5 448×accelerator-lowering-fma.f32
5 448×accelerator-lowering-fma.f64
5 000×*-lowering-*.f32
5 000×*-lowering-*.f64
4 268×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036136
1185132
21806132
09030123
Stop Event
iter limit
node limit
Counts
21 → 624
Calls
Call 1
Inputs
(* (+ (* x 2) eps) 1/2)
(+ eps 0)
(sin (* (+ eps 0) 1/2))
(cos (* (+ (* x 2) eps) 1/2))
(sin eps)
(- (sin (+ x eps)) (* x (+ (* x (* x -1/6)) 1)))
(sin (+ x eps))
(+ x eps)
(+ (* x (* x -1/6)) 1)
(+ (* eps (* -1/2 (sin x))) (cos x))
(sin x)
(cos x)
(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))
(cos eps)
(- (* (cos x) (sin eps)) (sin x))
(* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2)))
(* (* (sin (* (+ eps 0) 1/2)) (cos (* (+ (* x 2) eps) 1/2))) 2)
(* x -1/6)
(* x (+ (* x (* x -1/6)) 1))
(* (cos x) (sin eps))
Outputs
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(+.f64 (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))
(fma.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 eps #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) eps (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) eps) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64)))) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64))) (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64))) (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64))) (/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1/2 binary64)))
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(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x))
(/.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64))) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(/.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)) x) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)) x) (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64))) (*.f64 x (*.f64 x x)))) (neg.f64 (fma.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) x)))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64)) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/36 binary64) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (fma.f64 x (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/216 binary64))))) (fma.f64 x x (-.f64 (*.f64 (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x))) (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))) (*.f64 x (*.f64 x (*.f64 #s(literal -1/6 binary64) (*.f64 x x)))))))
(*.f64 x (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(/.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 x eps)))) #s(literal -2 binary64))
(*.f64 (sin.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (sin.f64 eps))

simplify450.0ms (3%)

Memory
-4.0MiB live, 514.9MiB allocated
Algorithm
egg-herbie
Rules
14 120×accelerator-lowering-fma.f32
14 120×accelerator-lowering-fma.f64
5 692×*-lowering-*.f32
5 692×*-lowering-*.f64
4 362×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04123565
112603392
234283329
081603043
Stop Event
iter limit
node limit
Counts
396 → 396
Calls
Call 1
Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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))
(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))))
(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))))
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)))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(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 (* 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))))
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
(+ 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) (* -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)))))
(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)))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (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)))))))))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
(- (+ (* (cos eps) (sin x)) (* (cos x) (sin eps))) (sin x))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(sin eps)
(+ (sin eps) (* -1 x))
(+ (sin eps) (* x (- (* -1/2 (* x (sin eps))) 1)))
(+ (sin eps) (* x (- (* x (+ (* -1/2 (sin eps)) (* 1/6 x))) 1)))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(* -1 (sin x))
(- (* eps (cos x)) (sin x))
(- (* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))) (sin x))
(- (* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x))))))) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(- (* (cos x) (sin eps)) (sin x))
(* 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)))
(* 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))))
(* -1/6 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)
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)))))
(sin eps)
(+ (sin eps) (* -1/2 (* (pow x 2) (sin eps))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* 1/24 (* (pow x 2) (sin eps))))))
(+ (sin eps) (* (pow x 2) (+ (* -1/2 (sin eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin eps))) (* 1/24 (sin eps)))))))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* eps (cos x))
(* eps (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* 1/120 (* (pow eps 2) (cos x)))))))
(* eps (+ (cos x) (* (pow eps 2) (+ (* -1/6 (cos x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (cos x))) (* 1/120 (cos x))))))))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
(* (cos x) (sin eps))
Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64)))
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64)))
(* x (+ 1 (* 1/2 (/ eps x))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 1 binary64)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64))))
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/645120 binary64) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 x (-.f64 (*.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) (*.f64 x #s(literal -1/2 binary64))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/8 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/48 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 eps (*.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) #s(literal 1 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)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (cos.f64 eps) (fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps) (-.f64 #s(literal 0 binary64) x)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps)))) (sin.f64 eps))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64)))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64)))))
(* 1/6 (pow x 3))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 (/.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/6 binary64)))))
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 x) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (fma.f64 eps (cos.f64 x) (sin.f64 x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(fma.f64 eps (cos.f64 x) (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 x (cos.f64 eps) (*.f64 (fma.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))))))))
(fma.f64 x (fma.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) (sin.f64 eps))
(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)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (cos.f64 x) (*.f64 (fma.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))))))))
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
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eval132.0ms (0.9%)

Memory
43.1MiB live, 229.9MiB allocated
Compiler

Compiled 30 383 to 2 616 computations (91.4% saved)

prune110.0ms (0.7%)

Memory
-9.2MiB live, 198.1MiB allocated
Pruning

21 alts after pruning (17 fresh and 4 done)

PrunedKeptTotal
New1 066141 080
Fresh033
Picked235
Done011
Total1 068211 089
Accuracy
100.0%
Counts
1 089 → 21
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.6%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
99.2%
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
63.3%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
99.4%
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
99.2%
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))))
96.5%
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
63.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.7%
(-.f64 (sin.f64 eps) (sin.f64 x))
99.2%
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.0%
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
5.9%
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
99.2%
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.7%
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
97.6%
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
99.2%
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
99.1%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
98.6%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x)))
98.5%
(*.f64 eps (cos.f64 x))
96.6%
(sin.f64 eps)
96.6%
eps
Compiler

Compiled 494 to 322 computations (34.8% saved)

simplify317.0ms (2.1%)

Memory
-17.0MiB live, 331.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sin.f64 x)
cost-diff0
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
cost-diff0
(cos.f64 x)
cost-diff448
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))))
cost-diff0
(fma.f64 x #s(literal 2 binary64) eps)
cost-diff0
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
cost-diff320
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))
cost-diff704
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
cost-diff-64
(*.f64 eps (+.f64 eps x))
cost-diff-64
(*.f64 x #s(literal -1/2 binary64))
cost-diff0
(+.f64 eps x)
cost-diff0
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
cost-diff0
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff0
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
cost-diff0
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
cost-diff0
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Rules
9 062×accelerator-lowering-fma.f32
9 062×accelerator-lowering-fma.f64
5 808×*-lowering-*.f32
5 808×*-lowering-*.f64
1 876×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031157
173155
2192151
3403147
4600147
51541147
62424147
73229147
84272147
97791147
08011136
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2)
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))
(sin (* 1/2 eps))
(* 1/2 eps)
1/2
eps
(cos (+ (* 1/2 eps) x))
(+ (* 1/2 eps) x)
x
2
eps
(+ (* (* x -1/2) (* eps (+ eps x))) eps)
(* x -1/2)
x
-1/2
(* eps (+ eps x))
eps
(+ eps x)
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2)))
(* 1/2 eps)
1/2
eps
(cos (* (+ (* x 2) eps) 1/2))
(* (+ (* x 2) eps) 1/2)
(+ (* x 2) eps)
x
2
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))
(cos x)
x
eps
(* (* -1/2 (sin x)) (+ (* eps eps) 0))
(* -1/2 (sin x))
-1/2
(sin x)
(+ (* eps eps) 0)
0
Outputs
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2)
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))) (*.f64 #s(literal 2 binary64) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))))
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))
(*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(sin (* 1/2 eps))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)))
(* 1/2 eps)
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
1/2
#s(literal 1/2 binary64)
eps
(cos (+ (* 1/2 eps) x))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(+ (* 1/2 eps) x)
(fma.f64 #s(literal 1/2 binary64) eps x)
x
2
#s(literal 2 binary64)
eps
(+ (* (* x -1/2) (* eps (+ eps x))) eps)
(fma.f64 eps (fma.f64 x (fma.f64 #s(literal -1/2 binary64) (+.f64 eps x) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(* x -1/2)
(fma.f64 x #s(literal -1/2 binary64) #s(literal 0 binary64))
x
-1/2
#s(literal -1/2 binary64)
(* eps (+ eps x))
(fma.f64 eps (+.f64 eps x) #s(literal 0 binary64))
eps
(+ eps x)
(+.f64 eps x)
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)
(fma.f64 eps (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 0 binary64))
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 0 binary64))
(* 1/2 eps)
(fma.f64 #s(literal 1/2 binary64) eps #s(literal 0 binary64))
1/2
#s(literal 1/2 binary64)
eps
(cos (* (+ (* x 2) eps) 1/2))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* (+ (* x 2) eps) 1/2)
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ (* x 2) eps)
(fma.f64 x #s(literal 2 binary64) eps)
x
2
#s(literal 2 binary64)
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))
(fma.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)) #s(literal 0 binary64))
(cos x)
(cos.f64 x)
x
eps
(* (* -1/2 (sin x)) (+ (* eps eps) 0))
(fma.f64 #s(literal -1/2 binary64) (fma.f64 eps (fma.f64 eps (sin.f64 x) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
-1/2
#s(literal -1/2 binary64)
(sin x)
(sin.f64 x)
(+ (* eps eps) 0)
(fma.f64 eps eps #s(literal 0 binary64))
0
#s(literal 0 binary64)

localize90.0ms (0.6%)

Memory
16.3MiB live, 131.4MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(sin.f64 x)
accuracy100.0%
(cos.f64 x)
accuracy100.0%
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))))
accuracy99.9%
(*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64)))
accuracy100.0%
(*.f64 #s(literal 1/2 binary64) eps)
accuracy100.0%
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
accuracy100.0%
(*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64))))
accuracy99.8%
(cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))
accuracy100.0%
(+.f64 eps x)
accuracy100.0%
(*.f64 x #s(literal -1/2 binary64))
accuracy100.0%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
accuracy99.8%
(*.f64 eps (+.f64 eps x))
accuracy100.0%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
accuracy100.0%
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy100.0%
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
accuracy99.8%
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
Samples
53.0ms255×0valid
1.0ms3valid
Compiler

Compiled 155 to 33 computations (78.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
ival-mult: 22.0ms (57.2% of total)
ival-add: 6.0ms (15.6% of total)
ival-cos: 5.0ms (13% of total)
ival-sin: 4.0ms (10.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series32.0ms (0.2%)

Memory
-9.6MiB live, 39.7MiB allocated
Counts
19 → 384
Calls
Call 1
Inputs
#<alt (* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2)>
#<alt (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))>
#<alt (sin (* 1/2 eps))>
#<alt (cos (+ (* 1/2 eps) x))>
#<alt (+ (* (* x -1/2) (* eps (+ eps x))) eps)>
#<alt (+ eps x)>
#<alt (* x -1/2)>
#<alt (* eps (+ eps x))>
#<alt (* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)>
#<alt (* (+ (* x 2) eps) 1/2)>
#<alt (cos (* (+ (* x 2) eps) 1/2))>
#<alt (+ (* x 2) eps)>
#<alt (+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))>
#<alt (cos x)>
#<alt (* -1/2 (sin x))>
#<alt (sin x)>
#<alt (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (* (* -1/2 (sin x)) (+ (* eps eps) 0))>
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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 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 (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 (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 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 (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<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 (* 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 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<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 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 (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* eps x)>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (* eps x)>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* eps x)>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<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 (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 eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<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 (* 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 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 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (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 (* 1/2 (* 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)) (* -1/16 (* eps (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))>
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<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 (* -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 (* -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)))>
Calls

96 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(sin x)
5.0ms
x
@0
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)
1.0ms
x
@inf
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))
1.0ms
x
@-inf
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))
1.0ms
eps
@0
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)

rewrite496.0ms (3.3%)

Memory
19.3MiB live, 766.9MiB allocated
Algorithm
batch-egg-rewrite
Rules
13 252×accelerator-lowering-fma.f32
13 252×accelerator-lowering-fma.f64
4 580×*-lowering-*.f32
4 580×*-lowering-*.f64
3 264×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031134
1150132
21250130
08591120
Stop Event
iter limit
node limit
Counts
19 → 467
Calls
Call 1
Inputs
(* (* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x))) 2)
(* (sin (* 1/2 eps)) (cos (+ (* 1/2 eps) x)))
(sin (* 1/2 eps))
(cos (+ (* 1/2 eps) x))
(+ (* (* x -1/2) (* eps (+ eps x))) eps)
(+ eps x)
(* x -1/2)
(* eps (+ eps x))
(* (* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2))) 2)
(* (+ (* x 2) eps) 1/2)
(cos (* (+ (* x 2) eps) 1/2))
(+ (* x 2) eps)
(+ (* (cos x) eps) (* (* -1/2 (sin x)) (+ (* eps eps) 0)))
(cos x)
(* -1/2 (sin x))
(sin x)
(* (* 1/2 eps) (cos (* (+ (* x 2) eps) 1/2)))
(* 1/2 eps)
(* (* -1/2 (sin x)) (+ (* eps eps) 0))
Outputs
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(+.f64 (*.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x))) (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(fma.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (cos.f64 x) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))) (*.f64 (*.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (-.f64 #s(literal 0 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 x)))))
(/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x))))) #s(literal 2 binary64))
(/.f64 (*.f64 (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 #s(literal 0 binary64) x)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))))) #s(literal -2 binary64))
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(*.f64 eps (*.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(*.f64 #s(literal -1/2 binary64) (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)))
(*.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)))
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(*.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))
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(*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 3 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 2 binary64))))
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(*.f64 (fma.f64 (sin.f64 x) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal -1/2 binary64))
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(*.f64 (*.f64 (fma.f64 eps eps #s(literal 0 binary64)) #s(literal -1/2 binary64)) (sin.f64 x))
(*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))))
(*.f64 (*.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))))
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(*.f64 (/.f64 (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (sin.f64 x) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(*.f64 (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps))
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(*.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps (fma.f64 eps (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))

simplify515.0ms (3.4%)

Memory
-27.4MiB live, 668.3MiB allocated
Algorithm
egg-herbie
Rules
14 110×accelerator-lowering-fma.f32
14 110×accelerator-lowering-fma.f64
6 608×*-lowering-*.f32
6 608×*-lowering-*.f64
3 672×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03963534
112543441
234713376
083323093
Stop Event
iter limit
node limit
Counts
384 → 384
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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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))
(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 (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 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 (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
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)))
(* 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 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
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)))
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)))
(* -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 x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(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))))
(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))))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ (* -1/2 (* (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))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(+ (* -1/2 (* (pow eps 2) (sin x))) (* eps (cos x)))
(* 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)))
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 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (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)
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 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 (* (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)))
(* -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)))
Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) (cos.f64 x)))
(* 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 (fma.f64 eps (fma.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (*.f64 eps (*.f64 eps #s(literal 1/24 binary64)))) (*.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))) (cos.f64 x)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 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 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 #s(literal 2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 x #s(literal -2 binary64)) (sin.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)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
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(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal 1 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)
(* 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 (fma.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)) (* -1/16 (* eps (cos x)))))))
(*.f64 eps (fma.f64 eps (*.f64 (sin.f64 x) #s(literal -1/4 binary64)) (*.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/16 binary64)) #s(literal 1/2 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/16 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/96 binary64)) #s(literal -1/4 binary64)))) (*.f64 (cos.f64 x) #s(literal 1/2 binary64))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 eps))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(fma.f64 x (*.f64 eps (fma.f64 (*.f64 x (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/4 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(fma.f64 eps (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))) (*.f64 (*.f64 x x) (*.f64 eps (fma.f64 (*.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/12 binary64) (*.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal -1/4 binary64))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(*.f64 (*.f64 eps #s(literal 1/2 binary64)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* 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))
(* -1/2 (* (pow eps 2) x))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))
(*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(*.f64 x (fma.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(* 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)))))))))
(*.f64 x (fma.f64 eps (*.f64 eps #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) (fma.f64 eps (*.f64 eps #s(literal 1/12 binary64)) (*.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal 1/10080 binary64) #s(literal -1/240 binary64)))))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(*.f64 (sin.f64 x) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))

eval180.0ms (1.2%)

Memory
32.3MiB live, 146.1MiB allocated
Compiler

Compiled 19 775 to 1 912 computations (90.3% saved)

prune151.0ms (1%)

Memory
-33.1MiB live, 168.1MiB allocated
Pruning

25 alts after pruning (18 fresh and 7 done)

PrunedKeptTotal
New85213865
Fresh7512
Picked235
Done044
Total86125886
Accuracy
100.0%
Counts
886 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.2%
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x)))
97.6%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
97.6%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
97.4%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
96.5%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
63.3%
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
99.4%
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
98.3%
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
98.5%
(fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))
63.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.7%
(-.f64 (sin.f64 eps) (sin.f64 x))
99.2%
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
53.4%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
99.2%
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
97.4%
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
99.2%
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
99.1%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
5.5%
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
4.9%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
99.0%
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
96.6%
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
98.5%
(*.f64 eps (cos.f64 x))
96.6%
(sin.f64 eps)
96.6%
eps
Compiler

Compiled 571 to 367 computations (35.7% saved)

simplify382.0ms (2.6%)

Memory
23.2MiB live, 304.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
cost-diff0
(fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))
cost-diff0
(*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64)))
cost-diff0
(cos.f64 x)
cost-diff384
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
cost-diff0
(*.f64 eps #s(literal 1/2 binary64))
cost-diff0
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
cost-diff0
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
cost-diff0
(*.f64 eps x)
cost-diff0
(*.f64 x #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
cost-diff-64
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
cost-diff0
(*.f64 x x)
cost-diff0
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
cost-diff0
(sin.f64 x)
cost-diff0
(sin.f64 eps)
cost-diff0
(cos.f64 x)
cost-diff0
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
Rules
10 026×accelerator-lowering-fma.f32
10 026×accelerator-lowering-fma.f64
3 214×*-lowering-*.f32
3 214×*-lowering-*.f64
2 450×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038187
197187
2221185
3452185
41007185
52417185
63020185
73634185
85000185
95693185
106508185
08013172
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps))))
(cos x)
x
(sin eps)
eps
(* (sin x) (+ -1 (cos eps)))
(sin x)
(+ -1 (cos eps))
-1
(cos eps)
(* eps (* -1/2 (* x x)))
eps
(* -1/2 (* x x))
-1/2
(* x x)
x
(+ (* (* x -1/2) (* eps x)) eps)
(* x -1/2)
x
-1/2
(* eps x)
eps
(* eps (cos (* eps 1/2)))
eps
(cos (* eps 1/2))
(* eps 1/2)
1/2
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))
(cos x)
x
eps
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2))
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)
(* x (+ (* x (* x -1/240)) 1/12))
(+ (* x (* x -1/240)) 1/12)
(* x -1/240)
-1/240
1/12
-1/2
(+ (* eps eps) 0)
0
Outputs
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps))))
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) #s(literal 0 binary64)))
(cos x)
(cos.f64 x)
x
(sin eps)
(sin.f64 eps)
eps
(* (sin x) (+ -1 (cos eps)))
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 0 binary64))
(sin x)
(sin.f64 x)
(+ -1 (cos eps))
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
-1
#s(literal -1 binary64)
(cos eps)
(cos.f64 eps)
(* eps (* -1/2 (* x x)))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (*.f64 x eps) #s(literal 0 binary64)))
eps
(* -1/2 (* x x))
(*.f64 x (*.f64 x #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(+ (* (* x -1/2) (* eps x)) eps)
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(* eps x)
(*.f64 x eps)
eps
(* eps (cos (* eps 1/2)))
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
eps
(cos (* eps 1/2))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))
(fma.f64 eps (fma.f64 (*.f64 x eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (cos.f64 x)) #s(literal 0 binary64))
(cos x)
(cos.f64 x)
x
eps
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))
(fma.f64 eps (fma.f64 (*.f64 x eps) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))
(* x (+ (* x (* x -1/240)) 1/12))
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)))
(+ (* x (* x -1/240)) 1/12)
(fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64))
(* x -1/240)
(*.f64 x #s(literal -1/240 binary64))
-1/240
#s(literal -1/240 binary64)
1/12
#s(literal 1/12 binary64)
-1/2
#s(literal -1/2 binary64)
(+ (* eps eps) 0)
(fma.f64 eps eps #s(literal 0 binary64))
0
#s(literal 0 binary64)

localize261.0ms (1.7%)

Memory
-5.3MiB live, 191.6MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
accuracy99.9%
(*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64)))
accuracy99.8%
(*.f64 x #s(literal -1/240 binary64))
accuracy99.6%
(*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)))
accuracy100.0%
(*.f64 eps #s(literal 1/2 binary64))
accuracy100.0%
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
accuracy100.0%
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
accuracy100.0%
(*.f64 x #s(literal -1/2 binary64))
accuracy100.0%
(*.f64 eps x)
accuracy100.0%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
accuracy100.0%
(*.f64 x x)
accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (*.f64 x x))
accuracy99.8%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
accuracy100.0%
(cos.f64 eps)
accuracy100.0%
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
accuracy99.9%
(*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))
accuracy51.6%
(+.f64 #s(literal -1 binary64) (cos.f64 eps))
Samples
162.0ms163×2valid
44.0ms90×1valid
1.0ms0valid
Compiler

Compiled 179 to 40 computations (77.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 144.0ms
ival-mult: 54.0ms (37.6% of total)
ival-cos: 32.0ms (22.3% of total)
adjust: 26.0ms (18.1% of total)
ival-add: 15.0ms (10.4% of total)
const: 10.0ms (7% of total)
ival-sin: 5.0ms (3.5% of total)
exact: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series18.0ms (0.1%)

Memory
17.3MiB live, 17.3MiB allocated
Counts
22 → 348
Calls
Call 1
Inputs
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps))))>
#<alt (cos x)>
#<alt (sin eps)>
#<alt (sin x)>
#<alt (* -1/2 (* x x))>
#<alt (* x x)>
#<alt (* eps (* -1/2 (* x x)))>
#<alt (+ (* (* x -1/2) (* eps x)) eps)>
#<alt (* x -1/2)>
#<alt (* eps x)>
#<alt (* eps (cos (* eps 1/2)))>
#<alt (cos (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))>
#<alt (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2))>
#<alt (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)>
#<alt (+ -1 (cos eps))>
#<alt (* (sin x) (+ -1 (cos eps)))>
#<alt (cos eps)>
#<alt (* x (+ (* x (* x -1/240)) 1/12))>
#<alt (* x -1/240)>
#<alt (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))>
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)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<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 (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<alt (+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))>
#<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 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 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 (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt eps>
#<alt (* eps (+ 1 (* -1/8 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 1/2 eps))>
#<alt (cos (* 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 (* -1/2 (* (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 (* -1/240 (* (pow eps 2) (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))>
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (+ (* 1/12 (/ (pow eps 2) (pow x 2))) (/ (* eps (cos x)) (pow x 5))))))>
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1 (/ (* eps (cos x)) (pow x 5))) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))>
#<alt (* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* -1/240 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* -1/240 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))>
#<alt -1/2>
#<alt (- (* 1/12 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)>
#<alt (* -1/240 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* -1/240 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (* x (- (cos eps) 1))>
#<alt (* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1))>
#<alt (* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt (* (sin x) (- (cos eps) 1))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* 1/12 x)>
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))>
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))>
#<alt (* x (+ 1/12 (* -1/240 (pow x 2))))>
#<alt (* -1/240 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))>
#<alt (* -1/240 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 x)>
#<alt (* -1/240 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) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))>
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))>
#<alt (* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))>
#<alt (* -1/240 (* (pow eps 2) (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
#<alt (* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))>
Calls

87 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))
1.0ms
eps
@0
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))
1.0ms
eps
@0
(* eps (* -1/2 (* x x)))
1.0ms
eps
@-inf
(* eps (cos (* eps 1/2)))
0.0ms
eps
@0
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))

rewrite582.0ms (3.9%)

Memory
-13.5MiB live, 655.5MiB allocated
Algorithm
batch-egg-rewrite
Rules
12 470×accelerator-lowering-fma.f32
12 470×accelerator-lowering-fma.f64
4 378×*-lowering-*.f32
4 378×*-lowering-*.f64
3 280×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
038158
1190158
21541153
08350142
Stop Event
iter limit
node limit
Counts
22 → 494
Calls
Call 1
Inputs
(+ (* (cos x) (sin eps)) (* (sin x) (+ -1 (cos eps))))
(cos x)
(sin eps)
(sin x)
(* -1/2 (* x x))
(* x x)
(* eps (* -1/2 (* x x)))
(+ (* (* x -1/2) (* eps x)) eps)
(* x -1/2)
(* eps x)
(* eps (cos (* eps 1/2)))
(cos (* eps 1/2))
(* eps 1/2)
(+ (* (cos x) eps) (* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0)))
(* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2))
(+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)
(+ -1 (cos eps))
(* (sin x) (+ -1 (cos eps)))
(cos eps)
(* x (+ (* x (* x -1/240)) 1/12))
(* x -1/240)
(* (* x (+ (* x (* x (+ (* x (* x -1/240)) 1/12))) -1/2)) (+ (* eps eps) 0))
Outputs
(+.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))
(+.f64 (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (neg.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))
(+.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))
(-.f64 (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))))
(-.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))) (/.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(fma.f64 (sin.f64 x) #s(literal -1 binary64) (sin.f64 (+.f64 x eps)))
(fma.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 #s(literal -1 binary64) (sin.f64 x) (sin.f64 (+.f64 x eps)))
(fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))) (neg.f64 (/.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))
(fma.f64 (+.f64 (sin.f64 (-.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal 1/2 binary64) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(fma.f64 (+.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (-.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (+.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (*.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (*.f64 (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 eps) (+.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (+.f64 x eps)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))))))
(/.f64 (-.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64))) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (-.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 2 binary64)) (fma.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (*.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))))))))
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(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (*.f64 eps (fma.f64 eps eps #s(literal 0 binary64)))) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) eps))
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)))))
(*.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 (fma.f64 eps eps #s(literal 0 binary64)) (fma.f64 eps eps #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))

simplify461.0ms (3.1%)

Memory
30.6MiB live, 865.9MiB allocated
Algorithm
egg-herbie
Rules
13 948×accelerator-lowering-fma.f32
13 948×accelerator-lowering-fma.f64
5 052×*-lowering-*.f32
5 052×*-lowering-*.f64
4 216×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03003092
18933062
226132976
353932936
082642753
Stop Event
iter limit
node limit
Counts
348 → 348
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)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
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
(* 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)
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)
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
(* -1/2 (* eps (pow x 2)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -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 x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
(* eps x)
eps
(* eps (+ 1 (* -1/8 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8))))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
(* eps (cos (* 1/2 eps)))
1
(+ 1 (* -1/8 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/384 (pow eps 2)) 1/8)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/384 (* -1/46080 (pow eps 2)))) 1/8)))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 1/2 eps))
(cos (* 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 (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (+ (* 1/12 (/ (pow eps 2) (pow x 2))) (/ (* eps (cos x)) (pow x 5))))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* (pow x 5) (+ (* -1 (/ (* eps (cos x)) (pow x 5))) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4))))))))
(* eps (cos x))
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))
(* eps (+ (cos x) (* eps (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) (/ (cos x) eps)))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* -1/240 (pow x 5))
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* (pow x 5) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* -1/240 (pow x 5))
(* -1 (* (pow x 5) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/240 (/ 1/2 (pow x 4))) (* 1/12 (/ 1 (pow x 2))))))
-1/2
(- (* 1/12 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)
(* -1/240 (pow x 4))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* -1/240 (pow x 4))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/12 (/ 1 (pow x 2))) (+ 1/240 (/ 1/2 (pow x 4)))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(* x (- (cos eps) 1))
(* x (- (+ (cos eps) (* -1/6 (* (pow x 2) (- (cos eps) 1)))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* 1/120 (* (pow x 2) (- (cos eps) 1)))))) 1))
(* x (- (+ (cos eps) (* (pow x 2) (+ (* -1/6 (- (cos eps) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (cos eps) 1))) (* 1/120 (- (cos eps) 1))))))) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (sin x))) (* 1/24 (sin x))))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (* (pow eps 2) (+ (* 1/24 (sin x)) (* (pow eps 2) (+ (* -1/720 (sin x)) (* 1/40320 (* (pow eps 2) (sin x)))))))))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
(* (sin x) (- (cos eps) 1))
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(* 1/12 x)
(* x (+ 1/12 (* -1/240 (pow x 2))))
(* x (+ 1/12 (* -1/240 (pow x 2))))
(* x (+ 1/12 (* -1/240 (pow x 2))))
(* -1/240 (pow x 3))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* (pow x 3) (- (* 1/12 (/ 1 (pow x 2))) 1/240))
(* -1/240 (pow x 3))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 x)
(* -1/240 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) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 x (+.f64 (fma.f64 x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (cos.f64 eps)) #s(literal -1 binary64)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (- (cos eps) 1)))))) 1)))
(fma.f64 x (fma.f64 (sin.f64 eps) (*.f64 x #s(literal -1/2 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 (cos.f64 eps) #s(literal -1 binary64)))) (sin.f64 eps))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (+.f64 (cos.f64 eps) #s(literal -1 binary64)) (sin.f64 x)))
(+ (* (cos x) (sin eps)) (* (sin x) (- (cos eps) 1)))
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(*.f64 x (*.f64 (*.f64 x x) #s(literal -1/240 binary64)))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- 1/240 (* 1/12 (/ 1 (pow x 2))))))
(*.f64 (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/240 x)
(*.f64 x #s(literal -1/240 binary64))
(* -1/2 (* (pow eps 2) x))
(*.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2)))))
(*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(*.f64 x (fma.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(* x (+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/240 (* (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))))
(*.f64 x (fma.f64 (*.f64 eps (*.f64 eps (*.f64 x x))) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) (*.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(*.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) eps))
(* (pow x 5) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x)))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* (pow x 5) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/240 (pow eps 2)) (* 1/12 (/ (pow eps 2) (pow x 2))))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* -1/240 (* (pow eps 2) (pow x 5)))
(*.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) eps))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (* 1/240 (pow eps 2)))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/12 binary64) (*.f64 x x)))))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* -1 (* (pow x 5) (+ (* -1/12 (/ (pow eps 2) (pow x 2))) (+ (* 1/240 (pow eps 2)) (* 1/2 (/ (pow eps 2) (pow x 4)))))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 (*.f64 eps eps) (+.f64 #s(literal -1/240 binary64) (+.f64 (/.f64 #s(literal 1/12 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 x x) (*.f64 x x)))))))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* (pow eps 2) (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)))
(*.f64 (*.f64 eps (*.f64 eps x)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))

eval122.0ms (0.8%)

Memory
-1.8MiB live, 279.5MiB allocated
Compiler

Compiled 26 953 to 1 906 computations (92.9% saved)

prune101.0ms (0.7%)

Memory
3.4MiB live, 276.8MiB allocated
Pruning

26 alts after pruning (18 fresh and 8 done)

PrunedKeptTotal
New8478855
Fresh31013
Picked325
Done167
Total85426880
Accuracy
100.0%
Counts
880 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
97.8%
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
97.6%
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
99.4%
(fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
98.3%
(fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps))
99.2%
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x)))
97.4%
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
97.6%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
97.6%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
96.5%
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
99.2%
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
96.6%
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
63.0%
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.7%
(-.f64 (sin.f64 eps) (sin.f64 x))
99.2%
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
99.8%
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
53.4%
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
99.2%
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
99.1%
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
5.5%
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
4.9%
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
99.0%
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
96.6%
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
98.5%
(*.f64 eps (cos.f64 x))
96.6%
(sin.f64 eps)
96.6%
eps
Compiler

Compiled 975 to 407 computations (58.3% saved)

regimes40.0ms (0.3%)

Memory
-14.2MiB live, 103.0MiB allocated
Counts
44 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(fma.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps (*.f64 eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (fma.f64 eps eps #s(literal 0 binary64))))
(*.f64 (*.f64 (sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 eps (fma.f64 (fma.f64 eps (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (*.f64 (*.f64 eps (sin.f64 x)) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (*.f64 eps eps) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)) (*.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x)))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (sin.f64 x) (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(fma.f64 (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

13.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
13.0ms
eps
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)

regimes37.0ms (0.2%)

Memory
-6.5MiB live, 86.8MiB allocated
Counts
33 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(fma.f64 (cos.f64 x) eps (*.f64 x (*.f64 (*.f64 eps eps) (fma.f64 (*.f64 x x) #s(literal 1/12 binary64) #s(literal -1/2 binary64)))))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(fma.f64 (*.f64 (*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64))) eps) eps (*.f64 (cos.f64 x) eps))
(fma.f64 (cos.f64 x) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(-.f64 (sin.f64 eps) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
Outputs
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
Calls

3 calls:

16.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
10.0ms
x
9.0ms
eps
Results
AccuracySegmentsBranch
99.2%1x
99.2%1eps
99.2%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.2%)

Memory
16.3MiB live, 55.8MiB allocated
Counts
25 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps (fma.f64 eps (*.f64 #s(literal -1/2 binary64) x) (cos.f64 x)))
(-.f64 (sin.f64 (+.f64 x eps)) (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) eps) (cos.f64 (*.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))
Outputs
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
Calls

3 calls:

8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms
eps
7.0ms
x
Results
AccuracySegmentsBranch
99.0%1x
99.0%1eps
99.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory
-28.7MiB live, 51.0MiB allocated
Counts
21 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(*.f64 eps (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
Outputs
(*.f64 eps (cos.f64 x))
Calls

3 calls:

8.0ms
x
7.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
98.5%1x
98.5%1eps
98.5%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory
2.2MiB live, 41.5MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(sin.f64 eps)
Outputs
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
Calls

3 calls:

6.0ms
x
6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
eps
Results
AccuracySegmentsBranch
98.0%1x
98.0%1eps
98.0%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory
-2.0MiB live, 37.5MiB allocated
Counts
17 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
Outputs
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
Calls

3 calls:

6.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
97.8%1x
97.8%1eps
97.8%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Memory
-2.8MiB live, 36.9MiB allocated
Counts
16 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) eps)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
Outputs
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
Calls

3 calls:

5.0ms
x
5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms
eps
Results
AccuracySegmentsBranch
97.7%1x
97.7%1eps
97.7%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
27.2MiB live, 27.2MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
Outputs
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
Calls

3 calls:

4.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
4.0ms
eps
Results
AccuracySegmentsBranch
97.6%1eps
97.6%1x
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes12.0ms (0.1%)

Memory
-17.0MiB live, 25.1MiB allocated
Counts
10 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
Outputs
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
Calls

3 calls:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.6%1x
97.6%1eps
97.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory
14.8MiB live, 14.8MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/2 binary64))) eps eps)
Outputs
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
Calls

3 calls:

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

Compiled 15 to 10 computations (33.3% saved)

regimes28.0ms (0.2%)

Memory
-25.8MiB live, 13.9MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
eps
(*.f64 eps (*.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 eps (*.f64 x (*.f64 eps #s(literal -1/2 binary64))))
(*.f64 x (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps eps) eps)
Outputs
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
Calls

3 calls:

22.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.4%1x
97.4%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
97.4%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes7.0ms (0%)

Memory
10.5MiB live, 10.5MiB allocated
Accuracy

Total -58.7b remaining (-2705.7%)

Threshold costs -58.7b (-2705.7%)

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

3 calls:

2.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
96.6%1x
96.6%1(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
96.6%1eps
Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory
9.9MiB live, 9.9MiB allocated
Algorithm
egg-herbie
Rules
46×*-commutative_binary64
+-commutative_binary64
1-exp_binary64
1-exp_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
061159
187159
Stop Event
saturated
Calls
Call 1
Inputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps (cos.f64 x))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
eps
Outputs
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (*.f64 (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (*.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps (cos.f64 x))
(fma.f64 (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(fma.f64 (fma.f64 x (*.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)) eps (*.f64 (*.f64 x (fma.f64 x (*.f64 x (fma.f64 x (*.f64 x #s(literal -1/240 binary64)) #s(literal 1/12 binary64))) #s(literal -1/2 binary64))) (fma.f64 eps eps #s(literal 0 binary64))))
(*.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 eps #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps (+.f64 eps x)) eps)
(*.f64 eps (fma.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 eps x) eps)
(*.f64 eps (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
eps

soundness1.7s (11.3%)

Memory
-83.7MiB live, 1 000.6MiB allocated
Rules
16 678×accelerator-lowering-fma.f32
16 678×accelerator-lowering-fma.f64
14 120×accelerator-lowering-fma.f32
14 120×accelerator-lowering-fma.f64
14 110×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03003092
18933062
226132976
353932936
082642753
0616
14916
237616
3476316
0821216
0107496
1314496
2775489
32836489
46173489
08126458
03963534
112543441
234713376
083323093
04123565
112603392
234283329
081603043
036136
1185132
21806132
09030123
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 569 to 324 computations (43.1% saved)

preprocess109.0ms (0.7%)

Memory
-8.0MiB live, 186.8MiB allocated
Compiler

Compiled 434 to 200 computations (53.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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