Details

Time bar (total: 6.6s)

analyze146.0ms (2.2%)

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)

sample2.4s (36.2%)

Results
2.0s8256×body128valid
Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify24.0ms (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
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
12.2b
(*.f32 s (log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u)))))
Compiler

Compiled 61 to 49 computations (19.7% saved)

localize19.0ms (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))))

series274.0ms (4.2%)

Counts
2 → 36
Calls

2 calls:

271.0ms
(*.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))

simplify68.0ms (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

prune103.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New955100
Fresh101
Picked011
Done000
Total966102
Error
0.0b
Counts
102 → 6
Alt Table
StatusErrorProgram
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.1b
(+.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)))))
2.1b
(+.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)))))
Compiler

Compiled 1694 to 1237 computations (27% saved)

localize27.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series204.0ms (3.1%)

Counts
2 → 32
Calls

2 calls:

187.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
17.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite23.0ms (0.4%)

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:

13.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))
7.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))

simplify84.0ms (1.3%)

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 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01861744
15411595
217211526
344531526
455621526

prune119.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1530153
Fresh044
Picked011
Done011
Total1536159
Error
0.0b
Counts
159 → 6
Alt Table
StatusErrorProgram
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.1b
(+.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)))))
2.1b
(+.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)))))
Compiler

Compiled 3076 to 1914 computations (37.8% saved)

localize27.0ms (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))))
0.2b
(*.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)))))

series558.0ms (8.5%)

Counts
3 → 48
Calls

3 calls:

277.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
272.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
8.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite20.0ms (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 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
7.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify118.0ms (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

prune239.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2551256
Fresh033
Picked011
Done022
Total2557262
Error
0b
Counts
262 → 7
Alt Table
StatusErrorProgram
2.1b
(+.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)))))
0.5b
(*.f32 (*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.1b
(+.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)))))
Compiler

Compiled 7564 to 6073 computations (19.7% saved)

localize72.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.2b
(*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2))
0.2b
(*.f32 (*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.4b
(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)

series627.0ms (9.6%)

Counts
4 → 56
Calls

4 calls:

314.0ms
(*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2))
274.0ms
(*.f32 (*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
21.0ms
(sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
18.0ms
(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)

rewrite30.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod_binary32
33×associate-*r*_binary32
33×add-sqr-sqrt_binary32
28×unpow-prod-down_binary32
24×*-un-lft-identity_binary32
Counts
4 → 132
Calls

4 calls:

8.0ms
(*.f32 (*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
8.0ms
(*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2))
3.0ms
(pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)
2.0ms
(sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))

simplify138.0ms (2.1%)

Algorithm
egg-herbie
Rules
933×times-frac_binary32
344×associate-*l*_binary32
339×associate-*r*_binary32
295×fma-def_binary32
256×*-commutative_binary32
Counts
188 → 221
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03905849
111025278
237865220
352905220

prune260.0ms (4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New2210221
Fresh033
Picked011
Done033
Total2217228
Error
0b
Counts
228 → 7
Alt Table
StatusErrorProgram
2.1b
(+.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)))))
0.5b
(*.f32 (*.f32 s (pow.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))) 3/2)) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.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)))))
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.4b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
2.1b
(+.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)))))
Compiler

Compiled 7813 to 6469 computations (17.2% saved)

regimes889.0ms (13.6%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

Counts
111 → 1
Compiler

Compiled 15248 to 11770 computations (22.8% 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

end101.0ms (1.5%)

Compiler

Compiled 154 to 120 computations (22.1% saved)

Profiling

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