Details

Time bar (total: 5.0s)

analyze103.0ms (2.1%)

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)

sample2.0s (39.1%)

Results
1.5s8256×body128valid
Compiler

Compiled 66 to 52 computations (21.2% saved)

simplify23.0ms (0.5%)

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

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)

localize18.0ms (0.4%)

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))))

series253.0ms (5.1%)

Counts
2 → 36
Calls

2 calls:

251.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
2.0ms
(log1p.f32 (*.f32 u -4))

rewrite98.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
591×expm1-log1p-u_binary32
590×log1p-expm1-u_binary32
334×log-prod_binary32
311×fma-def_binary32
143×prod-diff_binary32
Counts
2 → 56
Calls

2 calls:

97.0ms
(log1p.f32 (*.f32 u -4))
97.0ms
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0817
116215
2158315
3485315
4506215

simplify78.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
836×fma-neg_binary32
530×fma-def_binary32
369×sub-neg_binary32
321×unsub-neg_binary32
219×associate-+l+_binary32
Counts
92 → 105
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0106726
1335675
2998632
32998621
44495618
54993618
64943618

prune72.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New987105
Fresh000
Picked011
Done000
Total988106
Error
0.0b
Counts
106 → 8
Alt Table
StatusErrorProgram
2.7b
(+.f32 (*.f32 8 (*.f32 s (pow.f32 u 2))) (+.f32 (*.f32 64/3 (*.f32 s (pow.f32 u 3))) (*.f32 4 (*.f32 s u))))
2.2b
(+.f32 (*.f32 (*.f32 s u) (+.f32 4 (*.f32 u 8))) (*.f32 s (*.f32 (pow.f32 u 3) (-.f32 64/3 (*.f32 -64 u)))))
▶0.7b
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
2.0b
(*.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (*.f32 u -8)) (*.f32 (pow.f32 u 3) (-.f32 -64/3 (*.f32 64 u))))))
13.0b
(*.f32 s (neg.f32 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (*.f32 u -4)))) 1)))
12.4b
(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓0.2b
(*.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 1772 to 1335 computations (24.7% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (*.f32 u -4))
✓0.1b
(cbrt.f32 (log1p.f32 (*.f32 u -4)))
✓0.2b
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
✓0.8b
(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)

series283.0ms (5.7%)

Counts
3 → 48
Calls

3 calls:

236.0ms
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
35.0ms
(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
12.0ms
(cbrt.f32 (log1p.f32 (*.f32 u -4)))

rewrite51.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
759×expm1-log1p-u_binary32
758×log1p-expm1-u_binary32
155×log1p-udef_binary32
143×prod-diff_binary32
99×add-sqr-sqrt_binary32
Counts
3 → 77
Calls

3 calls:

50.0ms
(cbrt.f32 (log1p.f32 (*.f32 u -4)))
50.0ms
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
50.0ms
(pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01125
121023
2202623
3494723

simplify111.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
372×fma-def_binary32
275×associate-+r+_binary32
227×+-commutative_binary32
224×sub-neg_binary32
222×associate-/r*_binary32
Counts
125 → 150
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03052700
110292419
238202407
349142305
449852305
549372305

prune162.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2052207
Fresh156
Picked011
Done011
Total2069215
Error
0.0b
Counts
215 → 9
Alt Table
StatusErrorProgram
▶1.2b
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.2b
(+.f32 (*.f32 (*.f32 s u) (+.f32 4 (*.f32 u 8))) (*.f32 s (*.f32 (pow.f32 u 3) (-.f32 64/3 (*.f32 -64 u)))))
✓0.7b
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
2.0b
(*.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (*.f32 u -8)) (*.f32 (pow.f32 u 3) (-.f32 -64/3 (*.f32 64 u))))))
2.7b
(fma.f32 8 (*.f32 u (*.f32 u s)) (fma.f32 4 (*.f32 u s) (*.f32 64/3 (*.f32 (pow.f32 u 3) s))))
13.0b
(*.f32 s (neg.f32 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (*.f32 u -4)))) 1)))
12.4b
(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓0.2b
(*.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 5736 to 4572 computations (20.3% saved)

localize44.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
✓0.4b
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
✓0.5b
(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
✓0.7b
(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)

series285.0ms (5.7%)

Counts
4 → 60
Calls

4 calls:

234.0ms
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
29.0ms
(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)
19.0ms
(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
3.0ms
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

rewrite57.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
527×log-prod_binary32
282×pow2_binary32
200×expm1-udef_binary32
200×log1p-udef_binary32
196×pow1/3_binary32
Counts
4 → 106
Calls

4 calls:

55.0ms
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
55.0ms
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
55.0ms
(pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2)
55.0ms
(pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01577
130939
2261339
3487639

simplify76.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
566×times-frac_binary32
338×cancel-sign-sub-inv_binary32
323×fma-def_binary32
263×distribute-neg-in_binary32
210×sub-neg_binary32
Counts
166 → 201
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02813168
19122902
230252896
350232896

prune170.0ms (3.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2001201
Fresh156
Picked011
Done022
Total2019210
Error
0.0b
Counts
210 → 9
Alt Table
StatusErrorProgram
✓1.2b
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.2b
(+.f32 (*.f32 (*.f32 s u) (+.f32 4 (*.f32 u 8))) (*.f32 s (*.f32 (pow.f32 u 3) (-.f32 64/3 (*.f32 -64 u)))))
✓0.7b
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
2.0b
(*.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (*.f32 u -8)) (*.f32 (pow.f32 u 3) (-.f32 -64/3 (*.f32 64 u))))))
▶0.4b
(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.7b
(fma.f32 8 (*.f32 u (*.f32 u s)) (fma.f32 4 (*.f32 u s) (*.f32 64/3 (*.f32 (pow.f32 u 3) s))))
13.0b
(*.f32 s (neg.f32 (-.f32 (exp.f32 (log1p.f32 (log1p.f32 (*.f32 u -4)))) 1)))
12.4b
(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 6222 to 5092 computations (18.2% saved)

localize36.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))
✓0.2b
(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
✓0.4b
(pow.f32 (log1p.f32 (*.f32 u -4)) 2)
✓0.4b
(*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

series296.0ms (5.9%)

Counts
4 → 60
Calls

4 calls:

238.0ms
(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
50.0ms
(cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))
5.0ms
(pow.f32 (log1p.f32 (*.f32 u -4)) 2)
3.0ms
(*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))

rewrite54.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
834×expm1-log1p-u_binary32
833×log1p-expm1-u_binary32
143×prod-diff_binary32
113×add-sqr-sqrt_binary32
107×add-cbrt-cube_binary32
Counts
4 → 93
Calls

4 calls:

52.0ms
(cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2))
52.0ms
(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
52.0ms
(pow.f32 (log1p.f32 (*.f32 u -4)) 2)
52.0ms
(*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01337
124635
2223035
3519735

simplify70.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
625×fma-def_binary32
288×associate-+l+_binary32
247×associate-*r*_binary32
207×associate-*l*_binary32
202×times-frac_binary32
Counts
153 → 188
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04233818
114463523
251403523

prune182.0ms (3.6%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New1871188
Fresh145
Picked011
Done033
Total1889197
Error
0.0b
Counts
197 → 9
Alt Table
StatusErrorProgram
1.0b
(*.f32 s (neg.f32 (*.f32 (exp.f32 (log.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)))) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.0b
(*.f32 s (neg.f32 (fma.f32 u (+.f32 -4 (*.f32 u -8)) (*.f32 (pow.f32 u 3) (-.f32 -64/3 (*.f32 64 u))))))
✓1.2b
(*.f32 s (neg.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4)))) 2) 3) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.2b
(+.f32 (*.f32 (*.f32 s u) (+.f32 4 (*.f32 u 8))) (*.f32 s (*.f32 (pow.f32 u 3) (-.f32 64/3 (*.f32 -64 u)))))
✓0.7b
(*.f32 s (neg.f32 (pow.f32 (cbrt.f32 (log1p.f32 (*.f32 u -4))) 3)))
✓0.4b
(*.f32 s (neg.f32 (*.f32 (cbrt.f32 (pow.f32 (log1p.f32 (*.f32 u -4)) 2)) (cbrt.f32 (log1p.f32 (*.f32 u -4))))))
2.7b
(fma.f32 8 (*.f32 u (*.f32 u s)) (fma.f32 4 (*.f32 u s) (*.f32 64/3 (*.f32 (pow.f32 u 3) s))))
12.4b
(*.f32 s (neg.f32 (log.f32 (fma.f32 u -4 1))))
✓0.2b
(*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4))))
Compiler

Compiled 7007 to 5645 computations (19.4% saved)

regimes306.0ms (6.1%)

Accuracy

Total 0.1b remaining (69.1%)

Threshold costs 0.1b (69.1%)

Counts
46 → 1
Compiler

Compiled 5385 to 4137 computations (23.2% 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
0811
11611
22311
32911
43211
53311
63311

end181.0ms (3.6%)

Compiler

Compiled 173 to 135 computations (22% saved)

Profiling

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