Details

Time bar (total: 10.2s)

analyze247.0ms (2.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%24.7%75.3%0
0%24.7%75.3%1
0%24.7%75.3%2
12.4%12.4%75.3%3
12.4%12.4%75.3%4
18.5%6.2%75.3%5
18.5%6.2%75.3%6
21.6%3.1%75.3%7
21.6%3.1%75.3%8
23.2%1.5%75.3%9
23.2%1.5%75.3%10
23.9%0.8%75.3%11
23.9%0.8%75.3%12
24.3%0.4%75.3%13
24.3%0.4%75.3%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample60.0ms (0.6%)

Algorithm
intervals
Results
27.0ms256×body128valid
7.0ms256×pre128true
Compiler

Compiled 28 to 23 computations (17.9% saved)

simplify78.0ms (0.8%)

Algorithm
egg-herbie
Rules
944×fma-neg_binary32
518×unswap-sqr_binary32
432×exp-prod_binary32
340×times-frac_binary32
333×associate-*l*_binary32
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11714
22714
33614
45014
57914
614714
726114
852814
9167614
10316014
11412114
12485014

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.0b
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
Compiler

Compiled 33 to 27 computations (18.2% saved)

localize45.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
0.0b
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
0.0b
(exp.f32 (/.f32 (neg.f32 x) s))

rewrite82.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
29×add-cube-cbrt_binary32
13×pow1_binary32
13×add-cbrt-cube_binary32
12×add-sqr-sqrt_binary32
11×add-log-exp_binary32
Counts
3 → 132
Calls

3 calls:

25.0ms
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
24.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
21.0ms
(exp.f32 (/.f32 (neg.f32 x) s))

series76.0ms (0.7%)

Counts
3 → 72
Calls

3 calls:

58.0ms
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
10.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
9.0ms
(exp.f32 (/.f32 (neg.f32 x) s))

simplify255.0ms (2.5%)

Algorithm
egg-herbie
Rules
771×fma-neg_binary32
364×times-frac_binary32
251×associate-*l*_binary32
241×fma-def_binary32
236×associate-*r*_binary32
Counts
204 → 343
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01522722
13182485
28902408
335832322
446102322
549992322
648702322

prune293.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3403343
Fresh000
Picked101
Done000
Total3413344
Error
0b
Counts
344 → 3
Alt Table
StatusErrorProgram
0.2b
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)
0.0b
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
23.9b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
Compiler

Compiled 3168 to 1652 computations (47.9% saved)

localize61.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))
0.0b
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
0.0b
(exp.f32 (/.f32 (neg.f32 x) s))
1.6b
(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

rewrite70.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
26×add-cube-cbrt_binary32
13×add-cbrt-cube_binary32
12×pow1_binary32
12×add-sqr-sqrt_binary32
10×add-exp-log_binary32
Counts
3 → 114
Calls

3 calls:

26.0ms
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
17.0ms
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))
17.0ms
(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

series2.7s (26.8%)

Counts
3 → 72
Calls

3 calls:

970.0ms
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
888.0ms
(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))
872.0ms
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))

simplify199.0ms (1.9%)

Algorithm
egg-herbie
Rules
595×times-frac_binary32
505×fma-def_binary32
366×associate-/l*_binary32
362×fma-neg_binary32
283×associate-/r*_binary32
Counts
186 → 322
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01692644
13732354
211882246
345972237
449012237

prune276.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New4230423
Fresh022
Picked011
Done000
Total4233426
Error
0b
Counts
426 → 3
Alt Table
StatusErrorProgram
0.2b
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)
0.0b
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
23.9b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
Compiler

Compiled 4089 to 2030 computations (50.4% saved)

localize78.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
0.0b
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
0.0b
(exp.f32 (/.f32 (neg.f32 x) s))
0.2b
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)

rewrite40.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
add-cube-cbrt_binary32
cube-div_binary32
cbrt-div_binary32
cube-mult_binary32
pow-to-exp_binary32
Counts
1 → 49
Calls

1 calls:

31.0ms
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)

series1.2s (11.6%)

Counts
1 → 24
Calls

1 calls:

1.2s
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)

simplify183.0ms (1.8%)

Algorithm
egg-herbie
Rules
898×fma-def_binary32
427×associate-*l*_binary32
408×associate-*r*_binary32
211×exp-prod_binary32
210×fma-neg_binary32
Counts
73 → 128
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0811207
11721074
25641017
33167987
44919987
54981987

prune353.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New5720572
Fresh011
Picked011
Done011
Total5723575
Error
0b
Counts
575 → 3
Alt Table
StatusErrorProgram
0.2b
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)
0.0b
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
23.9b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
Compiler

Compiled 4777 to 2857 computations (40.2% saved)

localize55.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(fma.f32 (/.f32 x s) 1/4 1/2)
0.2b
(pow.f32 (/.f32 x s) 3)
5.3b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))

rewrite78.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
17×add-cube-cbrt_binary32
12×add-sqr-sqrt_binary32
11×pow1_binary32
10×add-cbrt-cube_binary32
10×fma-udef_binary32
Counts
3 → 116
Calls

3 calls:

28.0ms
(pow.f32 (/.f32 x s) 3)
20.0ms
(fma.f32 (/.f32 x s) 1/4 1/2)
20.0ms
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))

series178.0ms (1.7%)

Counts
3 → 72
Calls

3 calls:

87.0ms
(pow.f32 (/.f32 x s) 3)
55.0ms
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
35.0ms
(fma.f32 (/.f32 x s) 1/4 1/2)

simplify166.0ms (1.6%)

Algorithm
egg-herbie
Rules
475×associate-*l/_binary32
391×associate-*r/_binary32
281×fma-neg_binary32
243×fma-def_binary32
192×cancel-sign-sub-inv_binary32
Counts
188 → 307
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01141923
12681829
210041810
348551810
449661810

prune148.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3070307
Fresh000
Picked011
Done022
Total3073310
Error
0b
Counts
310 → 3
Alt Table
StatusErrorProgram
0.2b
(pow.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) 3)
0.0b
(/.f32 1 (+.f32 1 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))
23.9b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
Compiler

Compiled 2752 to 1625 computations (41% saved)

regimes1.2s (11.4%)

Accuracy

Total 0.0b remaining (28.7%)

Threshold costs 0.0b (28.7%)

Compiler

Compiled 9868 to 8332 computations (15.6% saved)

simplify7.0ms (0.1%)

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
0914
11714
22314
32714
42814
52814

end1.0ms (0%)

Compiler

Compiled 10 to 8 computations (20% saved)

sample2.1s (20.5%)

Algorithm
intervals
Results
889.0ms8000×body128valid
236.0ms8000×pre128true
Compiler

Compiled 69 to 55 computations (20.3% saved)

Profiling

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