Details

Time bar (total: 4.5s)

analyze23.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%25%75%0
0%25%75%1
12.5%12.5%75%2
12.5%12.5%75%3
18.7%6.2%75%4
21.8%3.1%75%5
23.4%1.6%75%6
23.4%1.6%75%7
24.2%0.8%75%8
24.2%0.8%75%9
24.6%0.4%75%10
24.6%0.4%75%11
24.8%0.2%75%12
24.8%0.2%75%13
24.9%0.1%75%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample3.0s (65.2%)

Results
1.5s2078×body1024valid
759.0ms4609×body128valid
461.0ms1044×body512valid
158.0ms520×body256valid
7.0msbody2048valid
Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
fma-def_binary64
+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01017
11715
22315
32615
42715
52615

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
Compiler

Compiled 47 to 28 computations (40.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 v)
0.0b
(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
0.1b
(*.f64 e (sin.f64 v))

series41.0ms (0.9%)

Counts
3 → 32
Calls

3 calls:

31.0ms
(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
8.0ms
(*.f64 e (sin.f64 v))
2.0ms
(sin.f64 v)

rewrite9.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 52
Calls

3 calls:

3.0ms
(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
3.0ms
(*.f64 e (sin.f64 v))
1.0ms
(sin.f64 v)

simplify73.0ms (1.6%)

Algorithm
egg-herbie
Rules
590×associate-/r*_binary64
500×fma-def_binary64
460×fma-neg_binary64
310×cancel-sign-sub-inv_binary64
287×associate-/r/_binary64
Counts
84 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01861794
15021638
219851594
349071594
451781594

prune91.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New87996
Fresh000
Picked101
Done000
Total88997
Error
0.0b
Counts
97 → 9
Alt Table
StatusErrorProgram
1.0b
(/.f64 (*.f64 (*.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
0.5b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
32.1b
(/.f64 (-.f64 (*.f64 v e) (*.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
34.7b
(/.f64 (*.f64 e (exp.f64 (log.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.2b
(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.3b
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
1.2b
(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
0.1b
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
34.2b
(/.f64 (*.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
Compiler

Compiled 2309 to 1232 computations (46.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 v)
0.0b
(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
0.1b
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))

series60.0ms (1.3%)

Counts
2 → 48
Calls

2 calls:

31.0ms
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
28.0ms
(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
19×times-frac_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
2 → 63
Calls

2 calls:

5.0ms
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
2.0ms
(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

simplify99.0ms (2.2%)

Algorithm
egg-herbie
Rules
646×fma-def_binary64
406×fma-neg_binary64
299×cancel-sign-sub-inv_binary64
215×associate-/l/_binary64
174×associate-*r*_binary64
Counts
111 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02433054
16712888
226042844
346302844
450152844

prune131.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1440144
Fresh088
Picked011
Done000
Total1449153
Error
0.0b
Counts
153 → 9
Alt Table
StatusErrorProgram
1.0b
(/.f64 (*.f64 (*.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
0.5b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
32.1b
(/.f64 (-.f64 (*.f64 v e) (*.f64 1/6 (*.f64 (pow.f64 v 3) e))) (fma.f64 e (cos.f64 v) 1))
34.7b
(/.f64 (*.f64 e (exp.f64 (log.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.2b
(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.3b
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
1.2b
(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
0.1b
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
34.2b
(/.f64 (*.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
Compiler

Compiled 3670 to 1976 computations (46.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.1b
(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
0.1b
(expm1.f64 (sin.f64 v))
0.2b
(log1p.f64 (expm1.f64 (sin.f64 v)))

series45.0ms (1%)

Counts
4 → 72
Calls

4 calls:

32.0ms
(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
7.0ms
(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
3.0ms
(log1p.f64 (expm1.f64 (sin.f64 v)))
2.0ms
(expm1.f64 (sin.f64 v))

rewrite9.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
10×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
4 → 65
Calls

4 calls:

3.0ms
(/.f64 (*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
3.0ms
(*.f64 e (log1p.f64 (expm1.f64 (sin.f64 v))))
0.0ms
(expm1.f64 (sin.f64 v))
0.0ms
(log1p.f64 (expm1.f64 (sin.f64 v)))

simplify102.0ms (2.3%)

Algorithm
egg-herbie
Rules
560×fma-def_binary64
509×fma-neg_binary64
348×cancel-sign-sub-inv_binary64
287×associate-/r/_binary64
260×associate-/l/_binary64
Counts
137 → 146
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02102133
15501960
221211905
344661905
449831905
549541905

prune133.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1442146
Fresh167
Picked101
Done011
Total1469155
Error
0.0b
Counts
155 → 9
Alt Table
StatusErrorProgram
0.5b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
31.3b
(/.f64 (*.f64 e (log1p.f64 (fma.f64 1/2 (*.f64 v v) v))) (fma.f64 e (cos.f64 v) 1))
1.0b
(/.f64 (*.f64 (*.f64 e (*.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (cbrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
34.7b
(/.f64 (*.f64 e (exp.f64 (log.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.3b
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
1.2b
(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
0.1b
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
9.0b
(/.f64 (*.f64 e (log1p.f64 (cbrt.f64 (*.f64 (*.f64 (expm1.f64 (sin.f64 v)) (expm1.f64 (sin.f64 v))) (expm1.f64 (sin.f64 v)))))) (fma.f64 e (cos.f64 v) 1))
34.2b
(/.f64 (*.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
Compiler

Compiled 3270 to 1577 computations (51.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sin.f64 v)
0.1b
(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
0.2b
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

series51.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

33.0ms
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
18.0ms
(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
52×*-un-lft-identity_binary64
52×add-sqr-sqrt_binary64
52×add-cube-cbrt_binary64
16×associate-/r*_binary64
Counts
2 → 101
Calls

2 calls:

5.0ms
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
2.0ms
(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

simplify123.0ms (2.7%)

Algorithm
egg-herbie
Rules
565×associate-/r/_binary64
530×fma-def_binary64
425×associate-/l/_binary64
345×fma-neg_binary64
299×cancel-sign-sub-inv_binary64
Counts
149 → 181
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02854112
17113934
225363870
350003870
452073870

prune162.0ms (3.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1962198
Fresh257
Picked011
Done011
Total1989207
Error
0b
Counts
207 → 9
Alt Table
StatusErrorProgram
0.5b
(/.f64 (*.f64 (sqrt.f64 e) (*.f64 (sqrt.f64 e) (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
1.3b
(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
0.5b
(*.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
34.7b
(/.f64 (*.f64 e (exp.f64 (log.f64 (sin.f64 v)))) (fma.f64 e (cos.f64 v) 1))
0.3b
(/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
1.2b
(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))))
0.1b
(*.f64 e (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
9.0b
(/.f64 (*.f64 e (log1p.f64 (cbrt.f64 (*.f64 (*.f64 (expm1.f64 (sin.f64 v)) (expm1.f64 (sin.f64 v))) (expm1.f64 (sin.f64 v)))))) (fma.f64 e (cos.f64 v) 1))
34.2b
(/.f64 (*.f64 (*.f64 e (sqrt.f64 (sin.f64 v))) (sqrt.f64 (sin.f64 v))) (fma.f64 e (cos.f64 v) 1))
Compiler

Compiled 4527 to 2205 computations (51.3% saved)

regimes240.0ms (5.3%)

Accuracy

Total 0.1b remaining (77.7%)

Threshold costs 0.1b (77.7%)

Counts
86 → 1
Compiler

Compiled 4097 to 2750 computations (32.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
11215
21115

end115.0ms (2.5%)

Compiler

Compiled 162 to 105 computations (35.2% saved)

Profiling

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