Details

analyze108.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0.1%	0.1%	99.8%	3
0.1%	0.1%	99.8%	4
0.1%	0%	99.8%	5
0.1%	0%	99.8%	6
0.1%	0%	99.8%	7
0.1%	0%	99.8%	8
0.2%	0%	99.8%	9
0.2%	0%	99.8%	10
0.2%	0%	99.8%	11
0.2%	0%	99.8%	12
0.2%	0%	99.8%	13
0.2%	0%	99.8%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.7s (45.7%)

Alt Table

Status	Error	Program
▶	15.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 85 to 62 computations (27.1% saved)

localize25.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
✓	15.5b	(log.f32 (-.f32 1 u0))

series227.0ms (6%)

Counts

2 → 36

Calls

2 calls:

224.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
3.0ms	(log.f32 (-.f32 1 u0))

rewrite44.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

716×	`log1p-expm1-u_binary32`
716×	`expm1-log1p-u_binary32`
138×	`expm1-udef_binary32`
138×	`log1p-udef_binary32`
132×	`prod-diff_binary32`

Counts

2 → 37

Calls

2 calls:

43.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
43.0ms	(log.f32 (-.f32 1 u0))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	183	16
2	1850	16
3	4979	16
0	0	0
1	0	0

prune64.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	8	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	8	74

Error

0.1b

Counts

74 → 8

Alt Table

Status	Error	Program
	0.8b	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
	0.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
	1.1b	(.f32 (.f32 (neg.f32 alpha) alpha) (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log1p.f32 (fma.f32 u0 u0 u0))))
	16.2b	(.f32 (.f32 (neg.f32 alpha) alpha) (+.f32 (log.f32 (sqrt.f32 (-.f32 1 u0))) (log.f32 (sqrt.f32 (-.f32 1 u0)))))
▶	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))
	1.7b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	7.0b	(*.f32 u0 (pow.f32 alpha 2))
	1.7b	(.f32 (.f32 (neg.f32 alpha) alpha) (neg.f32 (+.f32 u0 (+.f32 (.f32 1/3 (pow.f32 u0 3)) (+.f32 (.f32 1/4 (pow.f32 u0 4)) (*.f32 1/2 (pow.f32 u0 2)))))))

Compiler

Compiled 1331 to 830 computations (37.6% saved)

localize22.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))

series213.0ms (5.6%)

Counts

2 → 36

Calls

2 calls:

210.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite50.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

522×	`expm1-log1p-u_binary32`
521×	`log1p-expm1-u_binary32`
450×	`unpow-prod-down_binary32`
318×	`log-prod_binary32`
153×	`pow2_binary32`

Counts

2 → 48

Calls

2 calls:

49.0ms	(log1p.f32 (neg.f32 u0))
49.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	163	12
2	1402	12
3	5265	12
0	0	0
1	0	0

prune43.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Error

0.1b

Counts

92 → 9

Alt Table

Status	Error	Program
▶	0.8b	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
	0.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
	1.1b	(.f32 (.f32 (neg.f32 alpha) alpha) (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log1p.f32 (fma.f32 u0 u0 u0))))
	16.2b	(.f32 (.f32 (neg.f32 alpha) alpha) (+.f32 (log.f32 (sqrt.f32 (-.f32 1 u0))) (log.f32 (sqrt.f32 (-.f32 1 u0)))))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))
	1.7b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	1.7b	(.f32 (.f32 (neg.f32 alpha) alpha) (neg.f32 (+.f32 u0 (+.f32 (.f32 1/3 (pow.f32 u0 3)) (+.f32 (.f32 1/4 (pow.f32 u0 4)) (*.f32 1/2 (pow.f32 u0 2)))))))
	7.7b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	7.8b	(pow.f32 (cbrt.f32 (.f32 (.f32 alpha alpha) (log1p.f32 u0))) 3)

Compiler

Compiled 1489 to 917 computations (38.4% saved)

localize30.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.1b	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
✓	0.7b	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3)

series286.0ms (7.5%)

Counts

4 → 60

Calls

4 calls:

227.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
40.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3)
17.0ms	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite105.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

693×	`expm1-log1p-u_binary32`
692×	`log1p-expm1-u_binary32`
148×	`fma-def_binary32`
138×	`expm1-udef_binary32`
138×	`log1p-udef_binary32`

Counts

4 → 84

Calls

4 calls:

103.0ms	(log1p.f32 (neg.f32 u0))
103.0ms	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
103.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
103.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	211	20
2	1852	20
3	4912	20
4	4989	20
5	4918	20
0	0	0
1	0	0

prune96.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	143	10	153

Error

0.1b

Counts

153 → 10

Alt Table

Status	Error	Program
✓	0.8b	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
▶	0.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
	1.1b	(.f32 (.f32 (neg.f32 alpha) alpha) (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log1p.f32 (fma.f32 u0 u0 u0))))
	10.2b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u0) 3) (pow.f32 (.f32 alpha alpha) 3)))
	16.2b	(.f32 (.f32 (neg.f32 alpha) alpha) (+.f32 (log.f32 (sqrt.f32 (-.f32 1 u0))) (log.f32 (sqrt.f32 (-.f32 1 u0)))))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))
	1.7b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	1.7b	(.f32 (.f32 (neg.f32 alpha) alpha) (neg.f32 (+.f32 u0 (+.f32 (.f32 1/3 (pow.f32 u0 3)) (+.f32 (.f32 1/4 (pow.f32 u0 4)) (*.f32 1/2 (pow.f32 u0 2)))))))
	7.7b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	7.8b	(pow.f32 (cbrt.f32 (.f32 (.f32 alpha alpha) (log1p.f32 u0))) 3)

Compiler

Compiled 3524 to 2380 computations (32.5% saved)

localize39.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
✓	0.3b	(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2))
✓	0.5b	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)

series257.0ms (6.8%)

Counts

4 → 60

Calls

4 calls:

215.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
23.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)
15.0ms	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
3.0ms	(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2))

rewrite60.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

733×	`expm1-log1p-u_binary32`
732×	`log1p-expm1-u_binary32`
148×	`expm1-udef_binary32`
148×	`log1p-udef_binary32`
110×	`associate-r_binary32`

Counts

4 → 69

Calls

4 calls:

58.0ms	(cbrt.f32 (log1p.f32 (neg.f32 u0)))
58.0ms	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
58.0ms	(*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2))
58.0ms	(pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	228	23
2	1965	23
3	4924	23
0	0	0
1	0	0

prune99.0ms (2.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	163	11	174

Error

0.1b

Counts

174 → 11

Alt Table

Status	Error	Program
	7.6b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (log1p.f32 u0))) 3) 2)))
	1.7b	(.f32 (.f32 (neg.f32 alpha) alpha) (neg.f32 (+.f32 u0 (+.f32 (.f32 1/3 (pow.f32 u0 3)) (+.f32 (.f32 1/4 (pow.f32 u0 4)) (*.f32 1/2 (pow.f32 u0 2)))))))
✓	0.8b	(.f32 (.f32 (neg.f32 alpha) alpha) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 3))
✓	0.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (*.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (pow.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) 2)))
	1.1b	(.f32 (.f32 (neg.f32 alpha) alpha) (-.f32 (log.f32 (-.f32 1 (pow.f32 u0 3))) (log1p.f32 (fma.f32 u0 u0 u0))))
	10.2b	(cbrt.f32 (.f32 (pow.f32 (log1p.f32 u0) 3) (pow.f32 (.f32 alpha alpha) 3)))
	16.2b	(.f32 (.f32 (neg.f32 alpha) alpha) (+.f32 (log.f32 (sqrt.f32 (-.f32 1 u0))) (log.f32 (sqrt.f32 (-.f32 1 u0)))))
✓	0.3b	(.f32 (.f32 (neg.f32 alpha) alpha) (log1p.f32 (neg.f32 u0)))
	1.7b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	7.7b	(pow.f32 (*.f32 alpha (sqrt.f32 (log1p.f32 u0))) 2)
	7.8b	(pow.f32 (cbrt.f32 (.f32 (.f32 alpha alpha) (log1p.f32 u0))) 3)

Compiler

Compiled 4412 to 2781 computations (37% saved)

regimes153.0ms (4%)

Accuracy

Total 0.2b remaining (66.7%)

Threshold costs 0.2b (66.7%)

Counts

21 → 1

Compiler

Compiled 2268 to 1718 computations (24.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	28	13
3	36	13
4	41	13
5	44	13
6	45	13
7	45	13

end132.0ms (3.5%)

Compiler: Compiled 215 to 160 computations (25.6% saved)

Details

analyze108.0ms (2.9%)

sample1.7s (45.7%)

localize25.0ms (0.7%)

series227.0ms (6%)

rewrite44.0ms (1.2%)

prune64.0ms (1.7%)

localize22.0ms (0.6%)

series213.0ms (5.6%)

rewrite50.0ms (1.3%)

prune43.0ms (1.1%)

localize30.0ms (0.8%)

series286.0ms (7.5%)

rewrite105.0ms (2.8%)

prune96.0ms (2.5%)

localize39.0ms (1%)

series257.0ms (6.8%)

rewrite60.0ms (1.6%)

prune99.0ms (2.6%)

regimes153.0ms (4%)

simplify3.0ms (0.1%)

end132.0ms (3.5%)

Profiling