Details

Time bar (total: 8.1s)

analyze369.0ms (4.5%)

Algorithm
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 37 to 28 computations (24.3% saved)

sample1.9s (23.2%)

Results
1.8s8256×body128valid
1.0msbody128invalid
Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×sub-neg_binary32
+-commutative_binary32
fma-def_binary32
*-commutative_binary32
div-sub_binary32
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01117
11717
22117
32717
43417
54417
65417
76917
87617
97917
108017
116017

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.3b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 42 to 33 computations (21.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
0.1b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.2b
(/.f32 u1 (-.f32 1 u1))
0.3b
(*.f32 314159265359/50000000000 u2)

series47.0ms (0.6%)

Counts
4 → 40
Calls

4 calls:

32.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
11.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms
(/.f32 u1 (-.f32 1 u1))
2.0ms
(*.f32 314159265359/50000000000 u2)

rewrite33.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt_binary32
69×*-un-lft-identity_binary32
56×times-frac_binary32
50×sqrt-prod_binary32
39×add-cube-cbrt_binary32
Counts
4 → 148
Calls

4 calls:

12.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
5.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
4.0ms
(/.f32 u1 (-.f32 1 u1))
3.0ms
(*.f32 314159265359/50000000000 u2)

simplify125.0ms (1.5%)

Algorithm
egg-herbie
Rules
595×associate-/r*_binary32
481×fma-def_binary32
401×times-frac_binary32
261×associate-/l*_binary32
204×fma-neg_binary32
Counts
188 → 223
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02893681
16353497
218683373
348563373
449243373

prune313.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New21310223
Fresh000
Picked101
Done000
Total21410224
Error
0.0b
Counts
224 → 10
Alt Table
StatusErrorProgram
0.4b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (+.f32 1 (sqrt.f32 u1)))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.3b
(*.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.3b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.3b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.8b
(*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))) (cbrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))))
1.2b
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 u1) (log.f32 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 5119 to 3755 computations (26.6% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
0.2b
(/.f32 u1 (-.f32 1 u1))
0.3b
(*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))
0.4b
(*.f32 314159265359/50000000000 (sqrt.f32 u2))

series46.0ms (0.6%)

Counts
3 → 24
Calls

3 calls:

35.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
7.0ms
(*.f32 314159265359/50000000000 (sqrt.f32 u2))
4.0ms
(*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary32
33×sqrt-prod_binary32
31×associate-*l*_binary32
29×*-un-lft-identity_binary32
20×add-cube-cbrt_binary32
Counts
3 → 94
Calls

3 calls:

11.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
9.0ms
(*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))
4.0ms
(*.f32 314159265359/50000000000 (sqrt.f32 u2))

simplify111.0ms (1.4%)

Algorithm
egg-herbie
Rules
502×fma-neg_binary32
299×*-commutative_binary32
299×associate-/r*_binary32
291×distribute-neg-frac_binary32
280×fma-def_binary32
Counts
118 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02172158
14662055
213281935
334141931
449671931
549891931

prune278.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2132215
Fresh279
Picked101
Done000
Total2169225
Error
0.0b
Counts
225 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (+.f32 1 (sqrt.f32 u1)))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.3b
(*.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.3b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (*.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
1.2b
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 u1) (log.f32 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 5366 to 3562 computations (33.6% saved)

localize48.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f32 u1 (-.f32 1 u1))
0.3b
(*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))
0.6b
(+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))
0.9b
(exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2))))

series44.0ms (0.5%)

Counts
3 → 0
Calls

3 calls:

23.0ms
(*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))
13.0ms
(exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2))))
9.0ms
(+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary32
15×add-sqr-sqrt_binary32
14×pow1_binary32
11×add-cube-cbrt_binary32
log-prod_binary32
Counts
3 → 74
Calls

3 calls:

9.0ms
(*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))
5.0ms
(exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2))))
5.0ms
(+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))

simplify91.0ms (1.1%)

Algorithm
egg-herbie
Rules
1065×fma-def_binary32
765×fma-neg_binary32
496×sub-neg_binary32
310×prod-exp_binary32
291×exp-diff_binary32
Counts
74 → 102
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
087836
1178672
2497670
31059670
41915670
53544670
64987670
75107670

prune220.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1621163
Fresh178
Picked101
Done000
Total1648172
Error
0.0b
Counts
172 → 8
Alt Table
StatusErrorProgram
0.4b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (+.f32 1 (sqrt.f32 u1)))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
0.4b
(*.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.8b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
1.2b
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 u1) (log.f32 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 4285 to 2752 computations (35.8% saved)

localize61.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))
0.3b
(/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))
0.6b
(+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))
0.9b
(exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2))))

series30.0ms (0.4%)

Counts
1 → 1
Calls

1 calls:

30.0ms
(/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))

rewrite54.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
339×times-frac_binary32
313×*-un-lft-identity_binary32
297×add-sqr-sqrt_binary32
113×add-cube-cbrt_binary32
96×sqrt-prod_binary32
Counts
1 → 238
Calls

1 calls:

16.0ms
(/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))

simplify207.0ms (2.6%)

Algorithm
egg-herbie
Rules
518×associate-/r*_binary32
429×associate-/r/_binary32
322×associate-*l/_binary32
310×div-sub_binary32
280×associate-*l*_binary32
Counts
239 → 194
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02108043
15277918
216507905
341687905
450107905

prune381.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2960296
Fresh077
Picked011
Done000
Total2968304
Error
0.0b
Counts
304 → 8
Alt Table
StatusErrorProgram
0.4b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (+.f32 1 (sqrt.f32 u1)))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (sqrt.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 (*.f32 314159265359/50000000000 (sqrt.f32 u2)) (sqrt.f32 u2))))
0.4b
(*.f32 (sqrt.f32 (/.f32 (/.f32 u1 (+.f32 1 (sqrt.f32 u1))) (-.f32 1 (sqrt.f32 u1)))) (cos.f32 (*.f32 (exp.f32 (+.f32 (log.f32 314159265359/50000000000) (log.f32 (sqrt.f32 u2)))) (sqrt.f32 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
0.8b
(*.f32 (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 (cbrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (cos.f32 (*.f32 314159265359/50000000000 u2))))
0.6b
(*.f32 (*.f32 (sqrt.f32 (/.f32 (sqrt.f32 u1) (+.f32 1 (sqrt.f32 u1)))) (sqrt.f32 (/.f32 (sqrt.f32 u1) (-.f32 1 (sqrt.f32 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
1.2b
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (log.f32 u1) (log.f32 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 10542 to 6372 computations (39.6% saved)

regimes3.5s (43.2%)

Accuracy

Total 0.3b remaining (75.3%)

Threshold costs 0.3b (75.3%)

Counts
306 → 1
Compiler

Compiled 61044 to 46370 computations (24% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
11820
22220
32420
42520
52420

end144.0ms (1.8%)

Compiler

Compiled 243 to 184 computations (24.3% saved)

Profiling

Loading profile data...