Details

Time bar (total: 7.1s)

analyze393.0ms (5.5%)

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)

sample2.0s (27.7%)

Results
1.9s8256×body128valid
0.0msbody128invalid
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
0.4b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.4b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 42 to 33 computations (21.4% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series45.0ms (0.6%)

Counts
4 → 32
Calls

4 calls:

28.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
13.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms
(/.f32 u1 (-.f32 1 u1))
2.0ms
(*.f32 314159265359/50000000000 u2)

rewrite66.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
532×log-prod_binary32
271×prod-diff_binary32
196×expm1-udef_binary32
195×log1p-udef_binary32
173×log-pow_binary32
Counts
4 → 113
Calls

4 calls:

64.0ms
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
64.0ms
(/.f32 u1 (-.f32 1 u1))
64.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
64.0ms
(*.f32 314159265359/50000000000 u2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01137
122737
2272437
3508537
000
100

simplify58.0ms (0.8%)

Algorithm
egg-herbie
Rules
719×fma-neg_binary32
429×fma-def_binary32
404×associate-/r*_binary32
271×associate-+l+_binary32
227×associate-+r+_binary32
Counts
145 → 148
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01111140
13441066
21151942
34789942
45374942

prune163.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1399148
Fresh000
Picked101
Done000
Total1409149
Error
0.0b
Counts
149 → 9
Alt Table
StatusErrorProgram
15.0b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 2))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
1.8b
(-.f32 (+.f32 (*.f32 314159265359/50000000000 (*.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (*.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (*.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (*.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (*.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
1.8b
(pow.f32 (sqrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 2)
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
0.5b
(*.f32 (*.f32 (sqrt.f32 u1) (sqrt.f32 (/.f32 1 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
1.1b
(*.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.8b
(pow.f32 (cbrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 3)
Compiler

Compiled 3173 to 2467 computations (22.3% saved)

localize42.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series64.0ms (0.9%)

Counts
3 → 40
Calls

3 calls:

52.0ms
(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
9.0ms
(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1)))
2.0ms
(*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))

rewrite79.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
798×prod-diff_binary32
151×add-sqr-sqrt_binary32
144×log1p-expm1-u_binary32
144×expm1-log1p-u_binary32
142×add-log-exp_binary32
Counts
3 → 90
Calls

3 calls:

77.0ms
(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1)))
77.0ms
(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
77.0ms
(*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01460
130633
2379133
3527233
000
100

simplify68.0ms (0.9%)

Algorithm
egg-herbie
Rules
740×fma-neg_binary32
421×fma-def_binary32
406×associate-/r*_binary32
274×associate-+l+_binary32
227×associate-+r+_binary32
Counts
130 → 128
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01141438
13501296
211651162
348141162
454201162

prune127.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1422144
Fresh088
Picked101
Done000
Total14310153
Error
0.0b
Counts
153 → 10
Alt Table
StatusErrorProgram
15.0b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 2))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
1.8b
(-.f32 (+.f32 (*.f32 314159265359/50000000000 (*.f32 u2 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 3060196847853821555298148281676017575122444629042460390799/37500000000000000000000000000000000000000000000000000000 (*.f32 (pow.f32 u2 5) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))) (+.f32 (*.f32 302029322777818351566783844332719832329455959975176141755859165754785028165295919/3937500000000000000000000000000000000000000000000000000000000000000000000000000 (*.f32 (pow.f32 u2 7) (sqrt.f32 (/.f32 u1 (-.f32 1 u1))))) (*.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (*.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 u1 (-.f32 1 u1)))))))
1.8b
(pow.f32 (sqrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 2)
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
0.5b
(*.f32 (*.f32 (sqrt.f32 u1) (sqrt.f32 (/.f32 1 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(*.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
6.1b
(*.f32 314159265359/50000000000 (*.f32 u2 (sqrt.f32 (/.f32 (fma.f32 u1 u1 u1) (-.f32 1 (*.f32 u1 u1))))))
1.1b
(*.f32 (sqrt.f32 (exp.f32 (log.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.8b
(pow.f32 (cbrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 3)
Compiler

Compiled 3506 to 2559 computations (27% saved)

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series60.0ms (0.8%)

Counts
3 → 44
Calls

3 calls:

54.0ms
(*.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
3.0ms
(/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1)))
2.0ms
(/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))

rewrite76.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
266×expm1-udef_binary32
265×log1p-udef_binary32
232×fma-neg_binary32
154×add-sqr-sqrt_binary32
147×log1p-expm1-u_binary32
Counts
3 → 116
Calls

3 calls:

73.0ms
(/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1)))
73.0ms
(/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))
73.0ms
(*.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01464
131252
2397552
3489452
000
100

simplify54.0ms (0.8%)

Algorithm
egg-herbie
Rules
609×fma-neg_binary32
326×fma-def_binary32
279×sub-neg_binary32
268×distribute-neg-in_binary32
228×associate-/r*_binary32
Counts
160 → 150
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0911197
12681067
2882939
33310939
44961939

prune186.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1615166
Fresh549
Picked101
Done000
Total1679176
Error
0.0b
Counts
176 → 9
Alt Table
StatusErrorProgram
0.6b
(*.f32 (sqrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 (/.f32 (-.f32 1 (*.f32 u1 u1)) (fma.f32 u1 u1 u1))) 3))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
3.4b
(-.f32 (*.f32 314159265359/50000000000 (*.f32 u2 (sqrt.f32 (/.f32 (+.f32 (pow.f32 u1 2) u1) (-.f32 1 (pow.f32 u1 2)))))) (*.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (*.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 (+.f32 (pow.f32 u1 2) u1) (-.f32 1 (pow.f32 u1 2)))))))
1.8b
(pow.f32 (sqrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 2)
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
15.0b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(*.f32 (*.f32 (sqrt.f32 u1) (sqrt.f32 (/.f32 1 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(/.f32 (sin.f32 (*.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (-.f32 1 (*.f32 u1 u1)) (fma.f32 u1 u1 u1))))
0.6b
(*.f32 (sqrt.f32 (/.f32 1 (*.f32 (/.f32 1 (pow.f32 (cbrt.f32 (fma.f32 u1 u1 u1)) 2)) (/.f32 (-.f32 1 (*.f32 u1 u1)) (cbrt.f32 (fma.f32 u1 u1 u1)))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.7b
(*.f32 (sqrt.f32 (/.f32 1 (/.f32 (-.f32 1 (*.f32 u1 u1)) (+.f32 u1 (*.f32 u1 u1))))) (sin.f32 (pow.f32 (sqrt.f32 (*.f32 314159265359/50000000000 u2)) 2)))
Compiler

Compiled 4430 to 2765 computations (37.6% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
0.1b
(/.f32 u1 (-.f32 1 u1))
0.3b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
0.4b
(*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2))

series29.0ms (0.4%)

Counts
2 → 32
Calls

2 calls:

26.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
3.0ms
(*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2))

rewrite95.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
450×prod-diff_binary32
222×expm1-udef_binary32
221×log1p-udef_binary32
202×log-pow_binary32
132×fma-def_binary32
Counts
2 → 31
Calls

2 calls:

94.0ms
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
94.0ms
(*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01329
126924
2312624
3491724
4509924
000
100

simplify67.0ms (0.9%)

Algorithm
egg-herbie
Rules
960×fma-neg_binary32
282×fma-def_binary32
274×distribute-rgt-neg-in_binary32
228×sub-neg_binary32
224×distribute-neg-in_binary32
Counts
63 → 52
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
080900
1227856
2713742
32907742
44849742
55176742

prune152.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1491150
Fresh178
Picked011
Done000
Total1509159
Error
0.0b
Counts
159 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (pow.f32 (*.f32 9740909103402808085817682884085781839780052161/6250000000000000000000000000000000000000000 (pow.f32 u2 4)) 1/2))))
0.5b
(*.f32 (*.f32 (sqrt.f32 u1) (sqrt.f32 (/.f32 1 (-.f32 1 u1)))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.6b
(*.f32 (sqrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 (/.f32 (-.f32 1 (*.f32 u1 u1)) (fma.f32 u1 u1 u1))) 3))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
3.4b
(-.f32 (*.f32 314159265359/50000000000 (*.f32 u2 (sqrt.f32 (/.f32 (+.f32 (pow.f32 u1 2) u1) (-.f32 1 (pow.f32 u1 2)))))) (*.f32 31006276680305942139213528068663279/750000000000000000000000000000000 (*.f32 (pow.f32 u2 3) (sqrt.f32 (/.f32 (+.f32 (pow.f32 u1 2) u1) (-.f32 1 (pow.f32 u1 2)))))))
1.8b
(pow.f32 (sqrt.f32 (*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (*.f32 314159265359/50000000000 u2)))) 2)
0.5b
(*.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (sin.f32 (sqrt.f32 (*.f32 98696044010906577398881/2500000000000000000000 (*.f32 u2 u2)))))
15.0b
(*.f32 (sqrt.f32 (log.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
0.5b
(/.f32 (sin.f32 (*.f32 314159265359/50000000000 u2)) (sqrt.f32 (/.f32 (-.f32 1 (*.f32 u1 u1)) (fma.f32 u1 u1 u1))))
0.6b
(*.f32 (sqrt.f32 (/.f32 1 (*.f32 (/.f32 1 (pow.f32 (cbrt.f32 (fma.f32 u1 u1 u1)) 2)) (/.f32 (-.f32 1 (*.f32 u1 u1)) (cbrt.f32 (fma.f32 u1 u1 u1)))))) (sin.f32 (*.f32 314159265359/50000000000 u2)))
Compiler

Compiled 3257 to 2376 computations (27% saved)

regimes3.1s (43.1%)

Accuracy

Total 0.4b remaining (81.1%)

Threshold costs 0.4b (81.1%)

Counts
258 → 1
Compiler

Compiled 51176 to 39201 computations (23.4% 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
01625
12225
22625
32825
42925
52825

end139.0ms (1.9%)

Compiler

Compiled 237 to 184 computations (22.4% saved)

Profiling

Loading profile data...