Details

Time bar (total: 6.0s)

analyze97.0ms (1.6%)

Algorithm
1×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)

sample451.0ms (7.5%)

Algorithm
1×intervals
Results
20.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify23.0ms (0.4%)

Algorithm
1×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

prune5.0ms (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
12.6b
(*.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))))

series312.0ms (5.2%)

Counts
2 → 36
Calls

2 calls:

308.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
3.0ms
(log1p.f32 (*.f32 u -4))

rewrite9.0ms (0.1%)

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

2 calls:

4.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
3.0ms
(log1p.f32 (*.f32 u -4))

simplify62.0ms (1%)

Algorithm
1×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

prune80.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New946100
Fresh011
Picked011
Done000
Total948102
Error
0.0b
Counts
102 → 8
Alt Table
StatusErrorProgram
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)))))
2.3b
(+.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)))))
✓0.2b
(*.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)))))
0.7b
(*.f32 (*.f32 (sqrt.f32 s) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (*.f32 (sqrt.f32 s) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
12.6b
(*.f32 s (log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u)))))
Compiler

Compiled 1744 to 1273 computations (27% 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))))

series245.0ms (4.1%)

Counts
2 → 32
Calls

2 calls:

225.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
19.0ms
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite15.0ms (0.3%)

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

2 calls:

7.0ms
(*.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))))

simplify85.0ms (1.4%)

Algorithm
1×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

prune111.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1512153
Fresh156
Picked101
Done011
Total1538161
Error
0b
Counts
161 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f32 (*.f32 (sqrt.f32 s) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (*.f32 (sqrt.f32 s) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))))
2.8b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
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 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
✓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)))))
0.7b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (cbrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
12.6b
(*.f32 s (log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u)))))
Compiler

Compiled 3133 to 1951 computations (37.7% saved)

localize28.0ms (0.5%)

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)))))

series658.0ms (11%)

Counts
3 → 48
Calls

3 calls:

327.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
319.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
12.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

rewrite19.0ms (0.3%)

Algorithm
1×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)))))
3.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify106.0ms (1.8%)

Algorithm
1×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

prune295.0ms (4.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2542256
Fresh246
Picked011
Done011
Total2568264
Error
0b
Counts
264 → 8
Alt Table
StatusErrorProgram
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 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
✓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)))))
11.2b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log.f32 (fma.f32 u -4 1))))) (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)))))
2.8b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
0.6b
(*.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))))))
Compiler

Compiled 7591 to 6088 computations (19.8% saved)

localize51.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
✓0.3b
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4)))))
✓0.4b
(*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))
✓0.5b
(*.f32 (cbrt.f32 s) (cbrt.f32 s))

series650.0ms (10.9%)

Counts
4 → 68
Calls

4 calls:

354.0ms
(*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))
238.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
36.0ms
(*.f32 (cbrt.f32 s) (cbrt.f32 s))
21.0ms
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4)))))

rewrite42.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
35×add-sqr-sqrt_binary32
27×pow1_binary32
25×associate-*l*_binary32
22×add-exp-log_binary32
21×*-un-lft-identity_binary32
Counts
4 → 127
Calls

4 calls:

13.0ms
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
9.0ms
(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4)))))
7.0ms
(*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))
4.0ms
(*.f32 (cbrt.f32 s) (cbrt.f32 s))

simplify185.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
381×associate-*r*_binary32
343×distribute-rgt-neg-out_binary32
328×associate-*l*_binary32
291×fma-neg_binary32
263×fma-def_binary32
Counts
195 → 257
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03154293
18813592
227023497
345813488
449873488
549993488
650343488

prune222.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2570257
Fresh055
Picked011
Done022
Total2578265
Error
0b
Counts
265 → 8
Alt Table
StatusErrorProgram
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 (sqrt.f32 s) (*.f32 (sqrt.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (*.f32 (sqrt.f32 (cbrt.f32 s)) (neg.f32 (log1p.f32 (*.f32 u -4))))))
✓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)))))
11.2b
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log.f32 (fma.f32 u -4 1))))) (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)))))
2.8b
(fma.f32 s (*.f32 (*.f32 u u) 8) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64/3 (pow.f32 u 3)))))
0.6b
(*.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))))))
Compiler

Compiled 6665 to 3284 computations (50.7% saved)

regimes836.0ms (14%)

Accuracy

Total 0.2b remaining (90.8%)

Threshold costs 0.2b (90.8%)

Counts
120 → 1
Compiler

Compiled 14189 to 10817 computations (23.8% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
6×*-commutative_binary32
3×+-commutative_binary32
3×sub-neg_binary32
3×neg-sub0_binary32
3×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)

sample1.3s (22.5%)

Algorithm
1×intervals
Results
598.0ms8000×body128valid
213.0ms8000×pre128true
Compiler

Compiled 181 to 139 computations (23.2% saved)

Profiling

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