Details

Time bar (total: 5.9s)

analyze102.0ms (1.7%)

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)

sample452.0ms (7.6%)

Algorithm
intervals
Results
24.0ms256×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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 37 to 29 computations (21.6% saved)

localize17.0ms (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))))

series314.0ms (5.3%)

Counts
2 → 36
Calls

2 calls:

311.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
3.0ms
(log1p.f32 (*.f32 u -4))

rewrite7.0ms (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:

5.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.0ms
(log1p.f32 (*.f32 u -4))

simplify60.0ms (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

prune81.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New946100
Fresh000
Picked011
Done000
Total947101
Error
0b
Counts
101 → 7
Alt Table
StatusErrorProgram
0.5b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (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)))))
3.1b
(fma.f32 s (*.f32 64/3 (pow.f32 u 3)) (*.f32 s (*.f32 u (+.f32 4 (*.f32 u 8)))))
0.2b
(*.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)))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
0.8b
(*.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))))))
Compiler

Compiled 1726 to 1255 computations (27.3% saved)

localize28.0ms (0.5%)

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))))

series240.0ms (4%)

Counts
2 → 32
Calls

2 calls:

219.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
21.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite13.0ms (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 (1.3%)

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

prune99.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1521153
Fresh145
Picked011
Done011
Total1537160
Error
0b
Counts
160 → 7
Alt Table
StatusErrorProgram
3.1b
(fma.f32 s (*.f32 64/3 (pow.f32 u 3)) (*.f32 s (*.f32 u (+.f32 4 (*.f32 u 8)))))
0.2b
(*.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)))))
0.5b
(*.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)))))
3.0b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
0.8b
(*.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))))))
Compiler

Compiled 3086 to 1914 computations (38% saved)

localize25.0ms (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)))))

series663.0ms (11.2%)

Counts
3 → 48
Calls

3 calls:

332.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
318.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
12.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite24.0ms (0.4%)

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:

11.0ms
(*.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))))

simplify105.0ms (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

prune227.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2551256
Fresh134
Picked011
Done022
Total2567263
Error
0b
Counts
263 → 7
Alt Table
StatusErrorProgram
3.1b
(fma.f32 s (*.f32 64/3 (pow.f32 u 3)) (*.f32 s (*.f32 u (+.f32 4 (*.f32 u 8)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.7b
(*.f32 (*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (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)))))
0.5b
(*.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)))))
3.0b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
Compiler

Compiled 7530 to 6039 computations (19.8% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series704.0ms (11.9%)

Counts
2 → 40
Calls

2 calls:

368.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
336.0ms
(*.f32 (*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))

rewrite110.0ms (1.9%)

Algorithm
rewrite-expression-head
Rules
46×sqrt-prod_binary32
32×associate-*r*_binary32
16×add-cbrt-cube_binary32
16×add-exp-log_binary32
16×pow1_binary32
Counts
2 → 69
Calls

2 calls:

42.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
13.0ms
(*.f32 (*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))

simplify108.0ms (1.8%)

Algorithm
egg-herbie
Rules
691×fma-def_binary32
333×associate-*l*_binary32
262×times-frac_binary32
242×associate-*r*_binary32
228×cancel-sign-sub-inv_binary32
Counts
109 → 125
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02303697
16532692
221452608
349132608
449952608

prune338.0ms (5.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New2910291
Fresh033
Picked011
Done033
Total2917298
Error
0b
Counts
298 → 7
Alt Table
StatusErrorProgram
3.1b
(fma.f32 s (*.f32 64/3 (pow.f32 u 3)) (*.f32 s (*.f32 u (+.f32 4 (*.f32 u 8)))))
0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
0.7b
(*.f32 (*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))) (sqrt.f32 (sqrt.f32 (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)))))
0.5b
(*.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)))))
3.0b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
Compiler

Compiled 11776 to 9705 computations (17.6% saved)

regimes442.0ms (7.5%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Counts
59 → 1
Compiler

Compiled 7524 to 5765 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
0811
11611
22311
32911
43211
53311
63311

end0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.6s (27.6%)

Algorithm
intervals
Results
657.0ms8000×body128valid
214.0ms8000×pre128true
Compiler

Compiled 157 to 119 computations (24.2% saved)

Profiling

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