Details

Time bar (total: 9.9s)

analyze516.0ms (5.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 39 to 31 computations (20.5% saved)

sample106.0ms (1.1%)

Algorithm
1×intervals
Results
38.0ms256×body128valid
9.0ms256×pre128true
0.0ms1×pre128false
Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify16.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
40×fma-neg_binary32
22×sub-neg_binary32
17×cancel-sign-sub-inv_binary32
15×fma-def_binary32
11×*-commutative_binary32
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01422
12621
23821
34621
45621
56721
68221
710621
811921
912521
1014421
1114021
1216721
1318021
1418421
1518521
1616321

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.6b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
13.8b
(*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
Compiler

Compiled 90 to 77 computations (14.4% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
✓0.2b
(sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))
✓0.3b
(*.f32 (*.f32 2 (PI.f32)) u2)
✓0.4b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))

series222.0ms (2.2%)

Counts
4 → 52
Calls

4 calls:

202.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
12.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))
4.0ms
(*.f32 (*.f32 2 (PI.f32)) u2)
4.0ms
(sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))

rewrite18.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
21×sqrt-prod_binary32
18×add-sqr-sqrt_binary32
14×associate-*l*_binary32
13×*-un-lft-identity_binary32
13×add-cube-cbrt_binary32
Counts
4 → 82
Calls

4 calls:

6.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
4.0ms
(*.f32 (*.f32 2 (PI.f32)) u2)
2.0ms
(sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))
2.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))

simplify129.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
553×cancel-sign-sub-inv_binary32
510×fma-neg_binary32
360×times-frac_binary32
236×associate-*l*_binary32
224×fma-def_binary32
Counts
134 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02863674
17753341
225593238
344833212
450793212

prune181.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New14915164
Fresh011
Picked101
Done000
Total15016166
Error
0.1b
Counts
166 → 16
Alt Table
StatusErrorProgram
0.9b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
1.0b
(*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
13.2b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
▶0.6b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
13.8b
(*.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
0.9b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
0.9b
(*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))
0.8b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 u2)) (sqrt.f32 u2))))
1.2b
(*.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
2.3b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (sqrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
2.1b
(*.f32 (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
3.7b
(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
2.0b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))
1.0b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (cbrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))) (cbrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))) (cbrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))
0.8b
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))
2.2b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (sqrt.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))
Compiler

Compiled 5242 to 3229 computations (38.4% saved)

localize66.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f32 (*.f32 u2 u2) u2)
✓0.3b
(*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
✓0.4b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
✓1.0b
(*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

series240.0ms (2.4%)

Counts
4 → 44
Calls

4 calls:

223.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
14.0ms
(*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
3.0ms
(*.f32 (*.f32 u2 u2) u2)
0.0ms
(*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

rewrite129.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
817×pow1_binary32
401×pow-prod-down_binary32
218×add-cbrt-cube_binary32
215×add-exp-log_binary32
213×pow-prod-up_binary32
Counts
4 → 312
Calls

4 calls:

39.0ms
(*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
10.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
5.0ms
(*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))
5.0ms
(*.f32 (*.f32 u2 u2) u2)

simplify239.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
658×fma-def_binary32
486×associate-*l*_binary32
416×associate-*r*_binary32
289×cancel-sign-sub-inv_binary32
246×times-frac_binary32
Counts
356 → 227
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03348080
17095417
227525379
343065370
449315370
549495370

prune281.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2216227
Fresh7815
Picked101
Done000
Total22914243
Error
0.1b
Counts
243 → 14
Alt Table
StatusErrorProgram
0.9b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
1.0b
(*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
2.2b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
0.8b
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))) (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
1.0b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
3.7b
(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.7b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
2.0b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))
1.2b
(*.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
▶0.6b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
2.1b
(*.f32 (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.8b
(*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
13.2b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.9b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
Compiler

Compiled 8928 to 5034 computations (43.6% saved)

localize75.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 (*.f32 u2 u2) u2)
✓0.3b
(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
✓0.4b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
✓1.0b
(*.f32 (PI.f32) (*.f32 (PI.f32) 4))

series216.0ms (2.2%)

Counts
3 → 32
Calls

3 calls:

187.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
29.0ms
(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
0.0ms
(*.f32 (PI.f32) (*.f32 (PI.f32) 4))

rewrite32.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
46×add-cbrt-cube_binary32
46×add-exp-log_binary32
46×pow1_binary32
31×cbrt-unprod_binary32
31×prod-exp_binary32
Counts
3 → 90
Calls

3 calls:

12.0ms
(*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))
7.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
4.0ms
(*.f32 (PI.f32) (*.f32 (PI.f32) 4))

simplify132.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
637×fma-def_binary32
394×associate-*l*_binary32
345×associate-*r*_binary32
289×cancel-sign-sub-inv_binary32
275×fma-neg_binary32
Counts
122 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02804368
16943239
223403110
346923108
449793108

prune212.0ms (2.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1644168
Fresh4913
Picked011
Done000
Total16814182
Error
0.1b
Counts
182 → 14
Alt Table
StatusErrorProgram
0.9b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
1.0b
(*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
3.7b
(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
2.2b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
▶0.7b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
2.0b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))
0.8b
(*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
0.9b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
1.2b
(*.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
✓0.6b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
2.1b
(*.f32 (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.9b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
13.2b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.9b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (*.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
Compiler

Compiled 6664 to 3940 computations (40.9% saved)

localize77.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
✓0.4b
(*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))
✓0.5b
(*.f32 (cbrt.f32 u2) (cbrt.f32 u2))
1.0b
(*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32)))

series244.0ms (2.5%)

Counts
3 → 44
Calls

3 calls:

190.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
39.0ms
(*.f32 (cbrt.f32 u2) (cbrt.f32 u2))
15.0ms
(*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))

rewrite40.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
40×pow1_binary32
30×add-sqr-sqrt_binary32
30×pow1/3_binary32
25×add-exp-log_binary32
24×pow-prod-up_binary32
Counts
3 → 113
Calls

3 calls:

15.0ms
(*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))
9.0ms
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))
5.0ms
(*.f32 (cbrt.f32 u2) (cbrt.f32 u2))

simplify197.0ms (2%)

Algorithm
1×egg-herbie
Rules
651×fma-def_binary32
417×associate-*l*_binary32
358×unswap-sqr_binary32
335×associate-*r*_binary32
285×cancel-sign-sub-inv_binary32
Counts
157 → 182
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02803650
16743057
223582926
345552880
449952880
549402880

prune280.0ms (2.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2161217
Fresh01212
Picked101
Done011
Total21714231
Error
0.1b
Counts
231 → 14
Alt Table
StatusErrorProgram
0.9b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))
1.0b
(*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2))))) (cbrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
3.7b
(exp.f32 (+.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (log.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
2.2b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3))))))) (sqrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
20.2b
(log.f32 (exp.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 2 (PI.f32))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 (*.f32 u2 u2) (*.f32 (cbrt.f32 u2) (cbrt.f32 u2))) (cbrt.f32 u2))))))))
2.0b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (exp.f32 (+.f32 (log.f32 (*.f32 2 (PI.f32))) (log.f32 u2)))))
0.8b
(*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
0.9b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
1.2b
(*.f32 (exp.f32 (log.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))
✓0.6b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2)))))
2.1b
(*.f32 (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))) (sqrt.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.9b
(*.f32 (*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (*.f32 (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 8 (*.f32 (pow.f32 u2 3) (pow.f32 (PI.f32) 3)))))))) (cbrt.f32 (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
13.2b
(*.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (log.f32 (exp.f32 (sin.f32 (*.f32 (*.f32 2 (PI.f32)) u2)))))
0.9b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))))) (*.f32 (cbrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))) (sin.f32 (cbrt.f32 (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) 4)))) (*.f32 2 (PI.f32))) (*.f32 (*.f32 u2 u2) u2))))))
Compiler

Compiled 8796 to 4416 computations (49.8% saved)

regimes3.9s (39.2%)

Accuracy

Total 0.4b remaining (85.8%)

Threshold costs 0.4b (85.8%)

Counts
278 → 1
Compiler

Compiled 84463 to 65685 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
9×*-commutative_binary32
2×+-commutative_binary32
2×sub-neg_binary32
2×neg-sub0_binary32
2×neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02244
13544
23944
34144
44144

end1.0ms (0%)

Compiler

Compiled 28 to 22 computations (21.4% saved)

sample2.3s (23.5%)

Algorithm
1×intervals
Results
1.1s8000×body128valid
309.0ms8000×pre128true
0.0ms4×pre128false
Compiler

Compiled 500 to 375 computations (25% saved)

Profiling

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