Details

analyze467.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.0s (18%)

Results

877.0ms	8256×	body	128	valid
27.0ms	224×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	17.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	1.1b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series67.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

54.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
13.0ms	(/.f64 v (+.f64 t1 u))

rewrite64.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

646×	`prod-diff_binary64`
223×	`log1p-udef_binary64`
123×	`add-sqr-sqrt_binary64`
117×	`log1p-expm1-u_binary64`
117×	`expm1-log1p-u_binary64`

Counts

2 → 77

Calls

2 calls:

62.0ms	(/.f64 v (+.f64 t1 u))
62.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	234	23
2	3505	23
3	5206	23
0	0	0
1	0	0

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1006×	`fma-neg_binary64`
403×	`times-frac_binary64`
343×	`distribute-rgt-neg-in_binary64`
280×	`distribute-neg-frac_binary64`
277×	`associate-/l*_binary64`

Counts

137 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	1599
1	221	1571
2	706	1511
3	3176	1511
4	4983	1511
5	5083	1511

prune91.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Error

0.0b

Counts

113 → 7

Alt Table

Status	Error	Program
	1.8b	(/.f64 (pow.f64 (cbrt.f64 (/.f64 v (+.f64 t1 u))) 3) (-.f64 -1 (/.f64 u t1)))
	1.8b	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
✓	1.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	1.9b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
	17.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	1.2b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.8b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 2277 to 1052 computations (53.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.2b	(*.f64 v (/.f64 1 (+.f64 t1 u)))
✓	1.1b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

series75.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

53.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
13.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
8.0ms	(/.f64 1 (+.f64 t1 u))

rewrite68.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

649×	`prod-diff_binary64`
136×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`
128×	`expm1-log1p-u_binary64`
126×	`add-cbrt-cube_binary64`

Counts

3 → 96

Calls

3 calls:

67.0ms	(/.f64 1 (+.f64 t1 u))
67.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
67.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	269	30
2	3700	30
3	4992	30
0	0	0
1	0	0

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-neg_binary64`
435×	`times-frac_binary64`
309×	`associate-/l*_binary64`
244×	`sub-neg_binary64`
237×	`fma-def_binary64`

Counts

192 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	2157
1	261	2129
2	842	2021
3	3641	2021
4	4997	2021
5	5013	2021

prune107.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	144	7	151

Error

0.0b

Counts

151 → 7

Alt Table

Status	Error	Program
	1.8b	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
✓	1.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	1.9b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
	17.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	3.8b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))
▶	0.8b	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
✓	1.2b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 2856 to 1405 computations (50.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 t1 u))
✓	0.7b	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
✓	2.3b	(/.f64 v (-.f64 -1 (/.f64 u t1)))

series76.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

53.0ms	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
23.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

rewrite69.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

637×	`prod-diff_binary64`
138×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`
130×	`expm1-log1p-u_binary64`
128×	`add-cbrt-cube_binary64`

Counts

2 → 89

Calls

2 calls:

67.0ms	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
67.0ms	(/.f64 v (-.f64 -1 (/.f64 u t1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	272	26
2	3774	26
3	5028	26
0	0	0
1	0	0

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

960×	`fma-neg_binary64`
564×	`times-frac_binary64`
392×	`associate-/l*_binary64`
258×	`associate-/r*_binary64`
177×	`fma-def_binary64`

Counts

161 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1755
1	247	1727
2	814	1628
3	3730	1613
4	4983	1613
5	4990	1613

prune170.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	167	6	173

Error

Counts

173 → 6

Alt Table

Status	Error	Program
▶	1.9b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
	17.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	1.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	1.2b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
✓	0.8b	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
	1.9b	(/.f64 1 (*.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) v) (+.f64 u t1)))

Compiler

Compiled 3139 to 1617 computations (48.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
	1.1b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	21.4b	(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

series2.2s (38.6%)

Counts

2 → 72

Calls

2 calls:

1.2s	(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))
990.0ms	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)

rewrite71.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

646×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
133×	`add-cbrt-cube_binary64`

Counts

2 → 100

Calls

2 calls:

69.0ms	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
69.0ms	(cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	282	34
2	3944	34
3	5170	34
0	0	0
1	0	0

simplify167.0ms (3%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
405×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`
245×	`associate-r_binary64`
223×	`times-frac_binary64`

Counts

172 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	4460
1	921	3904
2	3161	3530
3	4991	3530
4	4951	3530

prune259.0ms (4.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	311	6	317

Error

Counts

317 → 6

Alt Table

Status	Error	Program
✓	1.9b	(pow.f64 (cbrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 3)
	17.9b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	1.2b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
✓	1.2b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
✓	0.8b	(*.f64 (/.f64 v (-.f64 -1 (/.f64 u t1))) (/.f64 1 (+.f64 t1 u)))
	1.9b	(/.f64 1 (*.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) v) (+.f64 u t1)))

Compiler

Compiled 8558 to 4919 computations (42.5% saved)

regimes234.0ms (4.2%)

Accuracy

Total 1.1b remaining (83.9%)

Threshold costs 0b (0%)

Counts

66 → 1

Compiler

Compiled 4154 to 2818 computations (32.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end80.0ms (1.4%)

Compiler: Compiled 122 to 80 computations (34.4% saved)

Details

analyze467.0ms (8.4%)

sample1.0s (18%)

simplify71.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series67.0ms (1.2%)

rewrite64.0ms (1.1%)

simplify77.0ms (1.4%)

prune91.0ms (1.6%)

localize8.0ms (0.1%)

series75.0ms (1.3%)

rewrite68.0ms (1.2%)

simplify89.0ms (1.6%)

prune107.0ms (1.9%)

localize8.0ms (0.1%)

series76.0ms (1.4%)

rewrite69.0ms (1.2%)

simplify79.0ms (1.4%)

prune170.0ms (3.1%)

localize9.0ms (0.2%)

series2.2s (38.6%)

rewrite71.0ms (1.3%)

simplify167.0ms (3%)

prune259.0ms (4.6%)

regimes234.0ms (4.2%)

simplify2.0ms (0%)

end80.0ms (1.4%)

Profiling