Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample4.5s (72.6%)

Alt Table

Status	Error	Program
▶	58.7b	(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Results

2.4s	4116×	body	1024	valid
805.0ms	2084×	body	512	valid
481.0ms	408×	body	2048	valid
253.0ms	1063×	body	256	valid
77.0ms	585×	body	128	valid

Compiler

Compiled 67 to 57 computations (14.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 x) (-.f64 1 x))
✓	4.7b	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
3.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

rewrite52.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

786×	`log1p-expm1-u_binary64`
786×	`expm1-log1p-u_binary64`
187×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
73×	`egg-rr`

Counts

2 → 73

Calls

2 calls:

50.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))
50.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	150	20
2	1974	20
3	5211	20
0	0	0
1	0	0

prune52.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

Counts

98 → 3

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)))
▶	0.0b	(*.f64 (/.f64 1 2) (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
	40.1b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))))

Compiler

Compiled 1958 to 1289 computations (34.2% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

rewrite85.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

874×	`log1p-udef_binary64`
484×	`expm1-log1p-u_binary64`
482×	`log1p-expm1-u_binary64`
391×	`prod-diff_binary64`
300×	`unpow-prod-down_binary64`

Counts

1 → 94

Calls

1 calls:

82.0ms

(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	130	8
2	1224	8
3	4990	8
4	6467	8
0	0	0
1	0	0

prune42.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
▶	1.6b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)))
✓	0.0b	(*.f64 (/.f64 1 2) (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
	40.1b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))))

Compiler

Compiled 2143 to 1112 computations (48.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)
✓	0.7b	(cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

series39.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

19.0ms	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)
12.0ms	(cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
4.0ms	(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2))
3.0ms	(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))

rewrite123.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

672×	`expm1-log1p-u_binary64`
670×	`log1p-expm1-u_binary64`
391×	`prod-diff_binary64`
300×	`fma-udef_binary64`
233×	`egg-rr`

Counts

4 → 233

Calls

4 calls:

117.0ms	(-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))
117.0ms	(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2))
117.0ms	(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)
117.0ms	(cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	193	37
2	1732	37
3	4945	37
4	4738	37
5	4926	37
0	0	0
1	0	0

prune208.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	430	0	430
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	430	3	433

Error

Counts

433 → 3

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)))
✓	0.0b	(*.f64 (/.f64 1 2) (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
▶	40.1b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))))

Compiler

Compiled 13109 to 6155 computations (53% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (log1p.f64 x) (log1p.f64 x))
✓	0.0b	(pow.f64 (log1p.f64 (neg.f64 x)) 3)
✓	4.7b	(+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
✓	39.6b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (*.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))))

series538.0ms (8.7%)

Counts

4 → 48

Calls

4 calls:

492.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (*.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))))
26.0ms	(*.f64 (log1p.f64 x) (log1p.f64 x))
11.0ms	(pow.f64 (log1p.f64 (neg.f64 x)) 3)
9.0ms	(+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

rewrite100.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

592×	`fma-def_binary64`
291×	`fma-neg_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
212×	`egg-rr`

Counts

4 → 212

Calls

4 calls:

94.0ms	(*.f64 (log1p.f64 x) (log1p.f64 x))
94.0ms	(pow.f64 (log1p.f64 (neg.f64 x)) 3)
94.0ms	(+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
93.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (*.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	350	31
2	3434	31
3	4872	31
0	0	0
1	0	0

prune295.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	260	3	263

Error

Counts

263 → 3

Alt Table

Status	Error	Program
✓	1.6b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))) 2)))
✓	0.0b	(*.f64 (/.f64 1 2) (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
✓	40.1b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log1p.f64 (neg.f64 x)) 3)) (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x))) (.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))))

Compiler

Compiled 15912 to 10342 computations (35% saved)

regimes39.0ms (0.6%)

Accuracy

Total 0.0b remaining (55%)

Threshold costs 0.0b (55%)

Counts

9 → 1

Compiler

Compiled 780 to 550 computations (29.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	19	13
2	24	13
3	27	13
4	28	13
5	26	13

end67.0ms (1.1%)

Compiler: Compiled 87 to 55 computations (36.8% saved)

Details

analyze5.0ms (0.1%)

sample4.5s (72.6%)

localize8.0ms (0.1%)

series6.0ms (0.1%)

rewrite52.0ms (0.8%)

prune52.0ms (0.8%)

localize7.0ms (0.1%)

series3.0ms (0.1%)

rewrite85.0ms (1.4%)

prune42.0ms (0.7%)

localize11.0ms (0.2%)

series39.0ms (0.6%)

rewrite123.0ms (2%)

prune208.0ms (3.4%)

localize16.0ms (0.3%)

series538.0ms (8.7%)

rewrite100.0ms (1.6%)

prune295.0ms (4.8%)

regimes39.0ms (0.6%)

simplify2.0ms (0%)

end67.0ms (1.1%)

Profiling