Details

Time bar (total: 6.2s)

analyze110.0ms (1.8%)

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)

sample2.2s (35.9%)

Results
1.8s8256×body128valid
Compiler

Compiled 66 to 52 computations (21.2% 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

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
13.1b
(*.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)

localize21.0ms (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))))

series338.0ms (5.4%)

Counts
2 → 36
Calls

2 calls:

335.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
3.0ms
(log1p.f32 (*.f32 u -4))

rewrite5.0ms (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))))
0.0ms
(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

prune82.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New937100
Fresh101
Picked101
Done000
Total957102
Error
0.0b
Counts
102 → 7
Alt Table
StatusErrorProgram
▶0.3b
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
0.8b
(*.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)))))
0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
1.5b
(+.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)))))
1.6b
(+.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)))))
0.7b
(*.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))))))
Compiler

Compiled 1763 to 1292 computations (26.7% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (*.f32 u -4))
✓0.2b
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
✓0.4b
(log1p.f32 (log1p.f32 (*.f32 u -4)))
✓0.4b
(expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))

series305.0ms (4.9%)

Counts
3 → 48
Calls

3 calls:

293.0ms
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
8.0ms
(log1p.f32 (log1p.f32 (*.f32 u -4)))
3.0ms
(expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
10×associate-*r*_binary32
9×add-sqr-sqrt_binary32
7×*-un-lft-identity_binary32
7×add-cube-cbrt_binary32
5×add-cbrt-cube_binary32
Counts
3 → 50
Calls

3 calls:

4.0ms
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
0.0ms
(log1p.f32 (log1p.f32 (*.f32 u -4)))
0.0ms
(expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))

simplify61.0ms (1%)

Algorithm
1×egg-herbie
Rules
932×fma-def_binary32
522×distribute-rgt-in_binary32
195×distribute-neg-in_binary32
187×sub-neg_binary32
174×cancel-sign-sub-inv_binary32
Counts
98 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02462044
17001865
224201808
354321808

prune206.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1881189
Fresh156
Picked011
Done000
Total1897196
Error
0b
Counts
196 → 7
Alt Table
StatusErrorProgram
✓0.3b
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
0.8b
(*.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)))))
▶0.5b
(*.f32 (sqrt.f32 s) (*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4)))))
1.6b
(+.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)))))
0.7b
(*.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))))))
3.9b
(*.f32 s (neg.f32 (expm1.f32 (neg.f32 (+.f32 (*.f32 16 (pow.f32 u 2)) (*.f32 4 u))))))
Compiler

Compiled 3900 to 3072 computations (21.2% saved)

localize26.0ms (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)))))
✓0.4b
(*.f32 (sqrt.f32 s) (neg.f32 (log1p.f32 (*.f32 u -4))))

series234.0ms (3.8%)

Counts
2 → 32
Calls

2 calls:

215.0ms
(*.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))))

rewrite13.0ms (0.2%)

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:

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))))

simplify76.0ms (1.2%)

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

prune119.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1521153
Fresh145
Picked011
Done011
Total1537160
Error
0b
Counts
160 → 7
Alt Table
StatusErrorProgram
✓0.3b
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
0.8b
(*.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)))))
1.5b
(fma.f32 s (*.f32 (*.f32 u u) 8) (fma.f32 s (*.f32 (pow.f32 u 3) 64/3) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64 (pow.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 (*.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))))))
3.9b
(*.f32 s (neg.f32 (expm1.f32 (neg.f32 (+.f32 (*.f32 16 (pow.f32 u 2)) (*.f32 4 u))))))
Compiler

Compiled 3110 to 1942 computations (37.6% 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)))))

series662.0ms (10.7%)

Counts
3 → 48
Calls

3 calls:

328.0ms
(*.f32 (*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
321.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
13.0ms
(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)))))
6.0ms
(*.f32 s (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
1.0ms
(sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4))))

simplify108.0ms (1.7%)

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

prune242.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2551256
Fresh134
Picked011
Done022
Total2567263
Error
0b
Counts
263 → 7
Alt Table
StatusErrorProgram
✓0.3b
(*.f32 s (neg.f32 (expm1.f32 (log1p.f32 (log1p.f32 (*.f32 u -4))))))
0.8b
(*.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)))))
1.5b
(fma.f32 s (*.f32 (*.f32 u u) 8) (fma.f32 s (*.f32 (pow.f32 u 3) 64/3) (*.f32 s (+.f32 (*.f32 4 u) (*.f32 64 (pow.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 (*.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))))))
0.6b
(*.f32 (*.f32 s (*.f32 (fabs.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) (sqrt.f32 (neg.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))))))) (sqrt.f32 (neg.f32 (log1p.f32 (*.f32 u -4)))))
Compiler

Compiled 7474 to 6003 computations (19.7% saved)

regimes1.1s (17.6%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Counts
169 → 1
Compiler

Compiled 20470 to 15788 computations (22.9% saved)

simplify2.0ms (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
01116
11916
22616
33216
43516
53616
63616

end105.0ms (1.7%)

Compiler

Compiled 167 to 132 computations (21% saved)

Profiling

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