Details

Time bar (total: 6.8s)

analyze112.0ms (1.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%1.5%98.5%0
0%1.5%98.5%1
0%1.5%98.5%2
0.8%0.8%98.5%3
0.8%0.8%98.5%4
1.2%0.4%98.5%5
1.2%0.4%98.5%6
1.4%0.2%98.5%7
1.4%0.2%98.5%8
1.4%0.1%98.5%9
1.4%0.1%98.5%10
1.5%0%98.5%11
1.5%0%98.5%12
1.5%0%98.5%13
1.5%0%98.5%14
Compiler

Compiled 27 to 21 computations (22.2% saved)

sample2.0s (30%)

Results
1.6s8256×body128valid
Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify23.0ms (0.3%)

Algorithm
egg-herbie
Rules
175×fma-neg_binary32
156×fma-def_binary32
46×cancel-sign-sub-inv_binary32
46×sub-neg_binary32
29×distribute-rgt-in_binary32
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01014
12411
23811
36411
48311
511011
614411
719411
824411
929111
1031911
1136211
1240111
1347811
1449111
1544311

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
12.5b
(*.f32 s (log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

localize19.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))

series323.0ms (4.7%)

Counts
1 → 24
Calls

1 calls:

323.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×associate-*r*_binary32
add-sqr-sqrt_binary32
*-un-lft-identity_binary32
add-cube-cbrt_binary32
distribute-lft-neg-in_binary32
Counts
1 → 28
Calls

1 calls:

4.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify67.0ms (1%)

Algorithm
egg-herbie
Rules
600×fma-neg_binary32
472×unsub-neg_binary32
440×fma-def_binary32
293×times-frac_binary32
224×associate-*l/_binary32
Counts
52 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0120895
1325806
2988779
32281765
44285761
54957761

prune51.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New58664
Fresh101
Picked011
Done000
Total59766
Error
0.0b
Counts
66 → 7
Alt Table
StatusErrorProgram
2.0b
(+.f32 (*.f32 8 (*.f32 s (pow.f32 u 2))) (+.f32 (*.f32 64/3 (*.f32 s (pow.f32 u 3))) (+.f32 (*.f32 64 (*.f32 s (pow.f32 u 4))) (*.f32 4 (*.f32 s u)))))
0.7b
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.7b
(*.f32 (*.f32 (cbrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (cbrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))) (cbrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.5b
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 1195 to 850 computations (28.9% saved)

localize52.0ms (0.8%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))
0.3b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))

series323.0ms (4.7%)

Counts
2 → 32
Calls

2 calls:

301.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
22.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary32
12×associate-*l*_binary32
11×associate-*r*_binary32
*-un-lft-identity_binary32
add-cube-cbrt_binary32
Counts
2 → 56
Calls

2 calls:

6.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
5.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify78.0ms (1.1%)

Algorithm
egg-herbie
Rules
915×fma-def_binary32
715×times-frac_binary32
366×fma-neg_binary32
252×associate-+l+_binary32
224×associate-*r*_binary32
Counts
88 → 128
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01861744
15411595
217211526
344531526
455621526

prune89.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1262128
Fresh325
Picked011
Done011
Total1296135
Error
0.0b
Counts
135 → 6
Alt Table
StatusErrorProgram
1.9b
(fma.f32 s (*.f32 (*.f32 u u) 8) (fma.f32 s (*.f32 (pow.f32 u 3) 64/3) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64 (pow.f32 u 4))))))
0.7b
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.6b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 2528 to 1521 computations (39.8% saved)

localize36.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f32 (sqrt.f32 s))
0.3b
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))
0.3b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.4b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))

series584.0ms (8.5%)

Counts
3 → 48
Calls

3 calls:

332.0ms
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
233.0ms
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
18.0ms
(sqrt.f32 (sqrt.f32 s))

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
28×sqrt-prod_binary32
19×pow1_binary32
18×associate-*l*_binary32
17×add-cbrt-cube_binary32
17×add-exp-log_binary32
Counts
3 → 78
Calls

3 calls:

12.0ms
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
7.0ms
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
1.0ms
(sqrt.f32 (sqrt.f32 s))

simplify127.0ms (1.9%)

Algorithm
egg-herbie
Rules
897×fma-def_binary32
346×times-frac_binary32
292×distribute-rgt-neg-out_binary32
268×associate-*r*_binary32
214×associate-*l*_binary32
Counts
126 → 154
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02072685
15892232
218632129
345832127
452172127

prune167.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2421243
Fresh033
Picked011
Done022
Total2427249
Error
0b
Counts
249 → 7
Alt Table
StatusErrorProgram
1.9b
(fma.f32 s (*.f32 (*.f32 u u) 8) (fma.f32 s (*.f32 (pow.f32 u 3) 64/3) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64 (pow.f32 u 4))))))
0.7b
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.6b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
14.5b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (log1p.f32 (*.f32 u -4)) (neg.f32 (pow.f32 (pow.f32 s 3) 1/4))))
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 5824 to 3159 computations (45.8% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(cbrt.f32 (log1p.f32 (*.f32 u -4)))
0.3b
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.3b
(*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.5b
(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

series1.4s (20.5%)

Counts
4 → 72
Calls

4 calls:

920.0ms
(*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
358.0ms
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
102.0ms
(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
22.0ms
(cbrt.f32 (log1p.f32 (*.f32 u -4)))

rewrite31.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary32
25×cbrt-prod_binary32
25×pow1_binary32
23×associate-*r*_binary32
20×add-exp-log_binary32
Counts
4 → 113
Calls

4 calls:

9.0ms
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
8.0ms
(*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
5.0ms
(*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
1.0ms
(cbrt.f32 (log1p.f32 (*.f32 u -4)))

simplify216.0ms (3.2%)

Algorithm
egg-herbie
Rules
871×fma-def_binary32
530×times-frac_binary32
284×*-commutative_binary32
272×associate-/l*_binary32
157×+-commutative_binary32
Counts
185 → 243
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
07199106
123478130
248798019
350008019
449648019

prune416.0ms (6.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New3210321
Fresh033
Picked011
Done033
Total3217328
Error
0b
Counts
328 → 7
Alt Table
StatusErrorProgram
1.9b
(fma.f32 s (*.f32 (*.f32 u u) 8) (fma.f32 s (*.f32 (pow.f32 u 3) 64/3) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64 (pow.f32 u 4))))))
0.7b
(*.f32 (*.f32 s (*.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))) (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))
0.6b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
14.5b
(*.f32 (sqrt.f32 (sqrt.f32 s)) (*.f32 (log1p.f32 (*.f32 u -4)) (neg.f32 (pow.f32 (pow.f32 s 3) 1/4))))
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 16302 to 13284 computations (18.5% saved)

regimes496.0ms (7.3%)

Accuracy

Total 0.2b remaining (88%)

Threshold costs 0.2b (88%)

Counts
73 → 1
Compiler

Compiled 9836 to 7266 computations (26.1% 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
0811
11611
22311
32911
43211
53311
63311

end88.0ms (1.3%)

Compiler

Compiled 140 to 102 computations (27.1% saved)

Profiling

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