Details

Time bar (total: 6.0s)

analyze509.0ms (8.4%)

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)

sample44.0ms (0.7%)

Algorithm
intervals
Results
20.0ms256×body128valid
7.0ms256×pre128true
Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify23.0ms (0.4%)

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
11.9b
(*.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)

localize18.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (*.f32 u -4))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))

series334.0ms (5.5%)

Counts
2 → 36
Calls

2 calls:

331.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
3.0ms
(log1p.f32 (*.f32 u -4))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×associate-*r*_binary32
add-sqr-sqrt_binary32
*-un-lft-identity_binary32
add-cube-cbrt_binary32
add-cbrt-cube_binary32
Counts
2 → 39
Calls

2 calls:

4.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.0ms
(log1p.f32 (*.f32 u -4))

simplify67.0ms (1.1%)

Algorithm
egg-herbie
Rules
715×fma-neg_binary32
622×fma-def_binary32
409×unsub-neg_binary32
304×times-frac_binary32
234×associate-+l+_binary32
Counts
75 → 100
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01571231
14411117
214151071
336451067
451071067

prune78.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New937100
Fresh101
Picked011
Done000
Total948102
Error
0.0b
Counts
102 → 8
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.5b
(+.f32 (*.f32 s (*.f32 u (+.f32 4 (*.f32 u 8)))) (*.f32 s (fma.f32 64/3 (pow.f32 u 3) (*.f32 64 (pow.f32 u 4)))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.5b
(+.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (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 (*.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))))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 1776 to 1295 computations (27.1% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (*.f32 u -4))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.4b
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.9b
(sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))

series173.0ms (2.9%)

Counts
2 → 20
Calls

2 calls:

139.0ms
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
34.0ms
(sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
54×pow1_binary32
30×sqrt-pow1_binary32
21×pow-prod-down_binary32
11×pow1/2_binary32
10×pow-prod-up_binary32
Counts
2 → 64
Calls

2 calls:

9.0ms
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
2.0ms
(sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))

simplify58.0ms (1%)

Algorithm
egg-herbie
Rules
661×associate-/l*_binary32
645×associate-/r*_binary32
460×fma-def_binary32
185×unswap-sqr_binary32
117×associate-*r*_binary32
Counts
84 → 112
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01642084
14161805
215981589
353411589

prune326.0ms (5.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3453348
Fresh156
Picked011
Done011
Total34610356
Error
0.0b
Counts
356 → 10
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (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)))))
2.5b
(+.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)))))
0.5b
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.6b
(*.f32 (sqrt.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))) (*.f32 (sqrt.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.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))))))
0.2b
(*.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 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (log1p.f32 (*.f32 u -4)) (neg.f32 (cbrt.f32 s))))))
Compiler

Compiled 9904 to 7480 computations (24.5% saved)

localize48.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.3b
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.3b
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s))
0.9b
(sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))

series267.0ms (4.4%)

Counts
2 → 16
Calls

2 calls:

182.0ms
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
85.0ms
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
21×pow1_binary32
19×associate-*r*_binary32
15×sqrt-prod_binary32
15×pow-prod-down_binary32
13×add-sqr-sqrt_binary32
Counts
2 → 63
Calls

2 calls:

9.0ms
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
6.0ms
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s))

simplify123.0ms (2%)

Algorithm
egg-herbie
Rules
392×cancel-sign-sub-inv_binary32
354×fma-def_binary32
322×associate-*l*_binary32
294×*-commutative_binary32
273×associate-*r*_binary32
Counts
79 → 126
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03675319
110754851
242114792
352284792

prune315.0ms (5.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New2251226
Fresh077
Picked011
Done022
Total22511236
Error
0b
Counts
236 → 11
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (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)))))
2.5b
(+.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)))))
0.5b
(*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.6b
(*.f32 (sqrt.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))) (*.f32 (sqrt.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.8b
(*.f32 (*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s))) (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)))) (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)))) (sqrt.f32 (neg.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))))))
0.2b
(*.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 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (log1p.f32 (*.f32 u -4)) (neg.f32 (cbrt.f32 s))))))
Compiler

Compiled 10656 to 8077 computations (24.2% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (*.f32 u -4))
0.1b
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))
0.3b
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.3b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

series742.0ms (12.3%)

Counts
3 → 48
Calls

3 calls:

367.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
362.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
14.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite18.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
31×sqrt-prod_binary32
26×associate-*r*_binary32
20×add-sqr-sqrt_binary32
15×*-un-lft-identity_binary32
15×add-cube-cbrt_binary32
Counts
3 → 83
Calls

3 calls:

7.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
5.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
1.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify111.0ms (1.8%)

Algorithm
egg-herbie
Rules
435×times-frac_binary32
418×fma-neg_binary32
366×cancel-sign-sub-inv_binary32
291×associate-/r*_binary32
291×associate-/l*_binary32
Counts
131 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02583444
17372979
223592881
347012859
449462859

prune285.0ms (4.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New2551256
Fresh167
Picked011
Done033
Total25611267
Error
0b
Counts
267 → 11
Alt Table
StatusErrorProgram
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)) (sqrt.f32 (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)))))
2.5b
(+.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.8b
(*.f32 (*.f32 (*.f32 (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s))) (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)))) (cbrt.f32 (*.f32 (sqrt.f32 (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 s)))) (sqrt.f32 (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 (*.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))))))
0.2b
(*.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 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (log1p.f32 (*.f32 u -4)) (neg.f32 (cbrt.f32 s))))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (*.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))))))
Compiler

Compiled 7582 to 6081 computations (19.8% saved)

regimes852.0ms (14.1%)

Accuracy

Total 0.2b remaining (94.5%)

Threshold costs 0.2b (94.5%)

Counts
114 → 1
Compiler

Compiled 16466 to 12988 computations (21.1% 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
0811
11611
22311
32911
43211
53311
63311

end0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (25.6%)

Algorithm
intervals
Results
705.0ms8000×body128valid
209.0ms8000×pre128true
Compiler

Compiled 289 to 220 computations (23.9% saved)

Profiling

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