Details

Time bar (total: 11.2s)

analyze379.0ms (3.4%)

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)

sample84.0ms (0.8%)

Algorithm
intervals
Results
31.0ms256×body128valid
13.0ms256×pre128true
0.0mspre128false
Compiler

Compiled 54 to 42 computations (22.2% saved)

simplify9.0ms (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
0.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.6b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 42 to 33 computations (21.4% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series39.0ms (0.4%)

Counts
4 → 32
Calls

4 calls:

25.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
10.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms
(/.f32 u1 (-.f32 1 u1))
2.0ms
(*.f32 314159265359/50000000000 u2)

rewrite32.0ms (0.3%)

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:

10.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
6.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
4.0ms
(/.f32 u1 (-.f32 1 u1))
3.0ms
(*.f32 314159265359/50000000000 u2)

simplify125.0ms (1.1%)

Algorithm
egg-herbie
Rules
595×associate-/r*_binary32
533×fma-def_binary32
401×times-frac_binary32
260×associate-/l*_binary32
231×fma-neg_binary32
Counts
180 → 222
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02863573
16363380
218873262
349113262
449593262

prune269.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2139222
Fresh000
Picked101
Done000
Total2149223
Error
0.1b
Counts
223 → 9
Alt Table
StatusErrorProgram
0.6b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 (*.f32 1 1) (*.f32 u1 u1)))) (*.f32 (sqrt.f32 (+.f32 1 u1)) (sin.f32 (*.f32 314159265359/50000000000 u2))))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
0.8b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)) (*.f32 (sqrt.f32 314159265359/50000000000) (sqrt.f32 u2)))))
14.4b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.7b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (*.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
0.7b
(*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (*.f32 (sqrt.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
2.9b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 314159265359/50000000000 u2 (*.f32 (pow.f32 u2 3) -31006276680305942139213528068663279/750000000000000000000000000000000)))
0.7b
(/.f32 (*.f32 (sqrt.f32 u1) (sin.f32 (*.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
Compiler

Compiled 4926 to 3597 computations (27% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series52.0ms (0.5%)

Counts
2 → 32
Calls

2 calls:

40.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
11.0ms
(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
33×associate-*l*_binary32
32×add-sqr-sqrt_binary32
29×sqrt-prod_binary32
25×*-un-lft-identity_binary32
19×times-frac_binary32
Counts
2 → 70
Calls

2 calls:

10.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
5.0ms
(*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))

simplify88.0ms (0.8%)

Algorithm
egg-herbie
Rules
493×fma-neg_binary32
367×*-commutative_binary32
334×fma-def_binary32
299×associate-/r*_binary32
259×unswap-sqr_binary32
Counts
102 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02032099
14621958
213791848
335971840
449111840

prune311.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2393242
Fresh268
Picked101
Done000
Total2429251
Error
0.0b
Counts
251 → 9
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))
14.4b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 (*.f32 1 1) (*.f32 u1 u1)))) (*.f32 (sqrt.f32 (+.f32 1 u1)) (sin.f32 (*.f32 314159265359/50000000000 u2))))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
0.8b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (*.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
2.9b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 314159265359/50000000000 u2 (*.f32 (pow.f32 u2 3) -31006276680305942139213528068663279/750000000000000000000000000000000)))
0.7b
(/.f32 (*.f32 (sqrt.f32 u1) (sin.f32 (*.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
0.5b
(*.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
Compiler

Compiled 6131 to 4746 computations (22.6% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
0.2b
(/.f32 u1 (-.f32 1 u1))
0.3b
(*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000)
0.4b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))

series48.0ms (0.4%)

Counts
2 → 32
Calls

2 calls:

45.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))
3.0ms
(*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000)

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary32
39×associate-*l*_binary32
27×*-un-lft-identity_binary32
26×sqrt-prod_binary32
19×times-frac_binary32
Counts
2 → 80
Calls

2 calls:

10.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))
5.0ms
(*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000)

simplify153.0ms (1.4%)

Algorithm
egg-herbie
Rules
479×fma-neg_binary32
456×*-commutative_binary32
353×fma-def_binary32
299×associate-/r*_binary32
211×times-frac_binary32
Counts
112 → 140
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02192623
14732503
215652355
341422331
448772331
549942331
649212331

prune338.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2520252
Fresh088
Picked011
Done000
Total2529261
Error
0.0b
Counts
261 → 9
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))
14.4b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 (*.f32 1 1) (*.f32 u1 u1)))) (*.f32 (sqrt.f32 (+.f32 1 u1)) (sin.f32 (*.f32 314159265359/50000000000 u2))))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
0.8b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (*.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
2.9b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 314159265359/50000000000 u2 (*.f32 (pow.f32 u2 3) -31006276680305942139213528068663279/750000000000000000000000000000000)))
0.7b
(/.f32 (*.f32 (sqrt.f32 u1) (sin.f32 (*.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
0.5b
(*.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
Compiler

Compiled 6254 to 4805 computations (23.2% saved)

localize41.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series45.0ms (0.4%)

Counts
2 → 32
Calls

2 calls:

31.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
14.0ms
(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt_binary32
28×associate-*l*_binary32
26×sqrt-prod_binary32
23×*-un-lft-identity_binary32
19×times-frac_binary32
Counts
2 → 71
Calls

2 calls:

12.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
7.0ms
(*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))

simplify109.0ms (1%)

Algorithm
egg-herbie
Rules
567×fma-neg_binary32
355×fma-def_binary32
347×*-commutative_binary32
299×associate-/r*_binary32
236×sub-neg_binary32
Counts
103 → 123
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01982056
14331923
213091809
335511809
448081809
549321809

prune318.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2332235
Fresh077
Picked011
Done011
Total23311244
Error
0.0b
Counts
244 → 11
Alt Table
StatusErrorProgram
0.6b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 (*.f32 1 1) (*.f32 u1 u1)))) (*.f32 (sqrt.f32 (+.f32 1 u1)) (sin.f32 (*.f32 314159265359/50000000000 u2))))
0.8b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (sin.f32 (*.f32 314159265359/50000000000 u2))) (cbrt.f32 (sin.f32 (*.f32 314159265359/50000000000 u2))))) (cbrt.f32 (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (cbrt.f32 (*.f32 (pow.f32 u2 3) 31006276680305942139213528068663279/125000000000000000000000000000000))))
14.4b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2))))
0.8b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (*.f32 (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))) (cbrt.f32 (sin.f32 (*.f32 u2 314159265359/50000000000))))) (cbrt.f32 (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2)))))
0.7b
(*.f32 (sqrt.f32 (/.f32 (*.f32 (cbrt.f32 u1) (cbrt.f32 u1)) (*.f32 (cbrt.f32 (-.f32 1 u1)) (cbrt.f32 (-.f32 1 u1))))) (*.f32 (sqrt.f32 (/.f32 (cbrt.f32 u1) (cbrt.f32 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2))))
2.9b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (fma.f32 314159265359/50000000000 u2 (*.f32 (pow.f32 u2 3) -31006276680305942139213528068663279/750000000000000000000000000000000)))
0.7b
(/.f32 (*.f32 (sqrt.f32 u1) (sin.f32 (*.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
0.5b
(*.f32 (expm1.f32 (log1p.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 (sqrt.f32 314159265359/50000000000) (*.f32 (sqrt.f32 314159265359/50000000000) u2))))
1.5b
(*.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sqrt.f32 (sin.f32 (*.f32 314159265359/50000000000 u2)))) (sqrt.f32 (sin.f32 (*.f32 (*.f32 (cbrt.f32 314159265359/50000000000) (cbrt.f32 314159265359/50000000000)) (*.f32 (cbrt.f32 314159265359/50000000000) u2)))))
Compiler

Compiled 6372 to 5028 computations (21.1% saved)

regimes6.7s (60.1%)

Accuracy

Total 0.4b remaining (84.6%)

Threshold costs 0.4b (84.6%)

Counts
475 → 1
Compiler

Compiled 104511 to 82985 computations (20.6% saved)

simplify3.0ms (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
01942
12742
23142
33342
43442
53342

end1.0ms (0%)

Compiler

Compiled 30 to 23 computations (23.3% saved)

sample1.8s (16.4%)

Algorithm
intervals
Results
821.0ms8000×body128valid
272.0ms8000×pre128true
0.0mspre128false
Compiler

Compiled 326 to 263 computations (19.3% saved)

Profiling

Loading profile data...