Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.7s (44.9%)

Results

491.0ms	1390×	body	1024	valid
470.0ms	4578×	body	128	valid
402.0ms	1551×	body	512	valid
136.0ms	737×	body	256	valid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
597×	`fma-neg_binary64`
564×	`rules-21_binary64`
376×	`rules-15-rev_binary64`
303×	`rules-13_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	30	22
2	74	22
3	225	22
4	1206	22
5	4473	22
6	4873	22
7	4959	22

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series41.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

32.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))

rewrite96.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

938×	`prod-diff_binary64`
196×	`egg-rr`
123×	`add-sqr-sqrt_binary64`
121×	`log1p-expm1-u_binary64`
121×	`expm1-log1p-u_binary64`

Counts

4 → 196

Calls

4 calls:

92.0ms	(/.f64 1 (-.f64 x 1))
92.0ms	(/.f64 1 (+.f64 x 1))
92.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
92.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	281	49
2	3773	49
3	5612	49
0	0	0
1	0	0

simplify98.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

788×	`rules-15-rev_binary64`
666×	`rules-21_binary64`
333×	`fma-def_binary64`
290×	`rules-13_binary64`
274×	`rules-14-rev_binary64`

Counts

244 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	752
1	247	736
2	1025	618
3	3574	615
4	5647	615

prune226.0ms (6.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	246	3	249
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	247	3	250

Error

0.6b

Counts

250 → 3

Alt Table

Status	Error	Program
▶	13.2b	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
	32.5b	(/.f64 2 (pow.f64 x 3))
	17.7b	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)

Compiler

Compiled 5859 to 4732 computations (19.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
✓	0.1b	(*.f64 (+.f64 1 x) (/.f64 2 x))
✓	0.1b	(*.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))
✓	7.7b	(-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x)))

series14.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(*.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))
4.0ms	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
4.0ms	(-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x)))
2.0ms	(*.f64 (+.f64 1 x) (/.f64 2 x))

rewrite109.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
174×	`egg-rr`
145×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`

Counts

4 → 174

Calls

4 calls:

106.0ms	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
106.0ms	(*.f64 (+.f64 1 x) (/.f64 2 x))
106.0ms	(*.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))
106.0ms	(-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	79
1	327	64
2	4428	64
3	5096	64
0	0	0
1	0	0

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
551×	`rules-13_binary64`
446×	`rules-14-rev_binary64`
376×	`rules-21_binary64`
258×	`fma-neg_binary64`

Counts

222 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	656
1	254	635
2	1215	601
3	4279	583
4	4988	583
5	4968	583

prune196.0ms (5.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	218	5	223

Error

0.0b

Counts

223 → 5

Alt Table

Status	Error	Program
✓	13.2b	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
	32.5b	(/.f64 2 (pow.f64 x 3))
	32.5b	(/.f64 (/.f64 (fma.f64 x 2 2) (pow.f64 x 3)) (+.f64 1 x))
	32.0b	(/.f64 (+.f64 (.f64 2 (/.f64 1 (pow.f64 x 3))) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 x))
▶	17.7b	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)

Compiler

Compiled 5980 to 4778 computations (20.1% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)
✓	0.1b	(*.f64 (/.f64 1 (-.f64 1 x)) x)
✓	0.1b	(fma.f64 (/.f64 1 (+.f64 1 x)) x -2)
✓	8.0b	(-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x))

series15.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)
4.0ms	(-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x))
2.0ms	(*.f64 (/.f64 1 (-.f64 1 x)) x)
2.0ms	(fma.f64 (/.f64 1 (+.f64 1 x)) x -2)

rewrite86.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

229×	`log-div_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
200×	`log-pow_binary64`
153×	`egg-rr`

Counts

4 → 153

Calls

4 calls:

83.0ms	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)
83.0ms	(*.f64 (/.f64 1 (-.f64 1 x)) x)
83.0ms	(fma.f64 (/.f64 1 (+.f64 1 x)) x -2)
83.0ms	(-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	67
1	290	61
2	3715	61
3	4886	61
0	0	0
1	0	0

simplify77.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
567×	`fma-def_binary64`
483×	`rules-13_binary64`
429×	`rules-14-rev_binary64`
383×	`rules-21_binary64`

Counts

201 → 205

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	727
1	321	704
2	1339	659
3	4407	657
4	4897	657
5	5138	657

prune164.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	205	5	210

Error

0.0b

Counts

210 → 5

Alt Table

Status	Error	Program
✓	13.2b	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
	32.5b	(/.f64 2 (pow.f64 x 3))
	32.5b	(/.f64 (/.f64 (fma.f64 x 2 2) (pow.f64 x 3)) (+.f64 1 x))
✓	17.7b	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)
▶	32.0b	(/.f64 (/.f64 2 (pow.f64 x 2)) x)

Compiler

Compiled 4698 to 3464 computations (26.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (pow.f64 x 2)) x)
✓	0.3b	(/.f64 2 (pow.f64 x 2))

series5.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(/.f64 (/.f64 2 (pow.f64 x 2)) x)
2.0ms	(/.f64 2 (pow.f64 x 2))

rewrite55.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

518×	`log1p-expm1-u_binary64`
518×	`expm1-log1p-u_binary64`
374×	`fma-neg_binary64`
243×	`log-prod_binary64`
193×	`fma-def_binary64`

Counts

2 → 65

Calls

2 calls:

54.0ms	(/.f64 (/.f64 2 (pow.f64 x 2)) x)
54.0ms	(/.f64 2 (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	139	14
2	1560	14
3	4996	14
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

9×	`rules-6_binary64`
2×	`rules-20_binary64`
1×	`rules-1_binary64`
1×	`rules-6-rev_binary64`
1×	`rules-22_binary64`

Counts

77 → 66

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	9	84
2	14	84
3	19	84
4	26	84
5	29	84
6	30	84
7	30	84

prune53.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	63	8	71

Error

0.0b

Counts

71 → 8

Alt Table

Status	Error	Program
✓	13.2b	(/.f64 (-.f64 (-.f64 1 (.f64 (+.f64 1 x) (/.f64 2 x))) (.f64 (/.f64 1 (-.f64 1 x)) (+.f64 1 x))) (+.f64 1 x))
	32.5b	(/.f64 2 (pow.f64 x 3))
	32.5b	(/.f64 (/.f64 (fma.f64 x 2 2) (pow.f64 x 3)) (+.f64 1 x))
	32.0b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 2) x) 2) x)
	32.1b	(/.f64 (.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) 2)) x)
✓	17.7b	(/.f64 (-.f64 (fma.f64 (/.f64 1 (+.f64 1 x)) x -2) (*.f64 (/.f64 1 (-.f64 1 x)) x)) x)
	32.1b	(.f64 (pow.f64 (cbrt.f64 (/.f64 2 (.f64 x x))) 2) (/.f64 (cbrt.f64 (/.f64 2 (*.f64 x x))) x))
	32.0b	(.f64 (/.f64 2 (.f64 x x)) (/.f64 1 x))

Compiler

Compiled 824 to 590 computations (28.4% saved)

regimes434.0ms (11.8%)

Accuracy

Total 0.4b remaining (73.7%)

Threshold costs 0.4b (73.7%)

Counts

129 → 3

Compiler

Compiled 4140 to 3278 computations (20.8% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	122
1	34	122
2	33	122

end169.0ms (4.6%)

Compiler: Compiled 281 to 212 computations (24.6% saved)

Details

analyze8.0ms (0.2%)

sample1.7s (44.9%)

simplify64.0ms (1.7%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series41.0ms (1.1%)

rewrite96.0ms (2.6%)

simplify98.0ms (2.7%)

prune226.0ms (6.1%)

localize11.0ms (0.3%)

series14.0ms (0.4%)

rewrite109.0ms (3%)

simplify70.0ms (1.9%)

prune196.0ms (5.3%)

localize13.0ms (0.4%)

series15.0ms (0.4%)

rewrite86.0ms (2.3%)

simplify77.0ms (2.1%)

prune164.0ms (4.5%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite55.0ms (1.5%)

simplify10.0ms (0.3%)

prune53.0ms (1.4%)

regimes434.0ms (11.8%)

bsearch5.0ms (0.1%)

simplify2.0ms (0.1%)

end169.0ms (4.6%)

Profiling