Details

analyze386.0ms (9%)

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)

sample1.2s (27.1%)

Results

1.0s	8256×	body	128	valid
29.0ms	276×	body	128	invalid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify70.0ms (1.6%)

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

prune4.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	0.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series80.0ms (1.9%)

Counts

2 → 60

Calls

2 calls:

64.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
16.0ms	(/.f64 v (+.f64 t1 u))

rewrite64.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

77× egg-rr

Counts

2 → 77

Calls

2 calls:

63.0ms	((/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1))) (/.f64 v (+.f64 t1 u)))
0.0ms	()

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

simplify82.0ms (1.9%)

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

prune103.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Error

0.3b

Counts

113 → 8

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	3.9b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	1.6b	(pow.f64 (*.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 (+.f64 t1 u) v)) -1)
	23.7b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
✓	0.9b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	24.5b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 v (+.f64 t1 u))) 2) (-.f64 -1 (/.f64 u t1)))
	2.0b	(*.f64 (/.f64 v (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 2)) (/.f64 (/.f64 1 (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 2329 to 1088 computations (53.3% saved)

localize8.0ms (0.2%)

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)))
✓	0.9b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))

series87.0ms (2%)

Counts

3 → 96

Calls

3 calls:

62.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
17.0ms	(*.f64 v (/.f64 1 (+.f64 t1 u)))
8.0ms	(/.f64 1 (+.f64 t1 u))

rewrite69.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

96× egg-rr

Counts

3 → 96

Calls

2 calls:

67.0ms	((/.f64 (.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1))) (.f64 v (/.f64 1 (+.f64 t1 u))) (/.f64 1 (+.f64 t1 u)))
0.0ms	()

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

simplify93.0ms (2.2%)

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

prune114.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	145	7	152

Error

0.3b

Counts

152 → 7

Alt Table

Status	Error	Program
▶	1.8b	(pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1)
	3.9b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (*.f64 v (/.f64 1 (+.f64 t1 u))) (-.f64 -1 (/.f64 u t1)))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	23.7b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))) 2)
	24.5b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 v (+.f64 t1 u))) 2) (-.f64 -1 (/.f64 u t1)))
	2.0b	(*.f64 (/.f64 v (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 2)) (/.f64 (/.f64 1 (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 2896 to 1434 computations (50.5% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.9b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))
✓	1.1b	(pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1)

series93.0ms (2.2%)

Counts

2 → 72

Calls

2 calls:

70.0ms	(pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1)
23.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u)))

rewrite120.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

234× egg-rr

Counts

2 → 234

Calls

2 calls:

109.0ms	((pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1) (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	264	32
2	3908	32
3	5571	32
0	0	0
1	0	0

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

892×	`cancel-sign-sub-inv_binary64`
611×	`fma-neg_binary64`
412×	`times-frac_binary64`
297×	`associate-/l*_binary64`
216×	`associate-/r*_binary64`

Counts

306 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	1713
1	238	1663
2	771	1573
3	3221	1573
4	5290	1573

prune395.0ms (9.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	315	2	317
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	317	7	324

Error

0.1b

Counts

324 → 7

Alt Table

Status	Error	Program
✓	1.8b	(pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1)
	3.9b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))
	20.7b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	23.4b	(pow.f64 (+.f64 (fma.f64 -1 (/.f64 (+.f64 u t1) v) (neg.f64 (.f64 (/.f64 (/.f64 1 t1) (/.f64 v (+.f64 u t1))) (/.f64 u 1)))) (fma.f64 (neg.f64 (/.f64 (/.f64 1 t1) (/.f64 v (+.f64 u t1)))) (/.f64 u 1) (.f64 (/.f64 (/.f64 1 t1) (/.f64 v (+.f64 u t1))) (/.f64 u 1)))) -1)
▶	1.7b	(/.f64 (/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v)) (+.f64 u t1))
	24.5b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 v (+.f64 t1 u))) 2) (-.f64 -1 (/.f64 u t1)))
	2.0b	(*.f64 (/.f64 v (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 2)) (/.f64 (/.f64 1 (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 12924 to 4432 computations (65.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v))
✓	1.0b	(/.f64 (/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v)) (+.f64 u t1))
✓	3.8b	(/.f64 (-.f64 -1 (/.f64 u t1)) v)

series106.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

65.0ms	(/.f64 (/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v)) (+.f64 u t1))
25.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v))
16.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) v)

rewrite92.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

177× egg-rr

Counts

3 → 177

Calls

2 calls:

87.0ms	((/.f64 (-.f64 -1 (/.f64 u t1)) v) (/.f64 (/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v)) (+.f64 u t1)) (/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) v)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	277	36
2	3951	36
3	5454	36
0	0	0
1	0	0

simplify128.0ms (3%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-neg_binary64`
570×	`times-frac_binary64`
400×	`associate-/l*_binary64`
264×	`associate-/r*_binary64`
189×	`sub-neg_binary64`

Counts

285 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	2208
1	269	2144
2	873	2033
3	3848	2012
4	4980	2012

prune294.0ms (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	223	6	229

Error

Counts

229 → 6

Alt Table

Status	Error	Program
✓	1.8b	(pow.f64 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 t1 u))) -1)
	3.9b	(.f64 v (/.f64 1 (.f64 (+.f64 t1 u) (-.f64 -1 (/.f64 u t1)))))
	1.0b	(.f64 (/.f64 1 (-.f64 -1 (/.f64 u t1))) (.f64 v (/.f64 1 (+.f64 u t1))))
	5.8b	(/.f64 (/.f64 1 (-.f64 (/.f64 -1 v) (/.f64 u (*.f64 v t1)))) (+.f64 u t1))
	24.5b	(/.f64 (pow.f64 (sqrt.f64 (/.f64 v (+.f64 t1 u))) 2) (-.f64 -1 (/.f64 u t1)))
	2.0b	(*.f64 (/.f64 v (pow.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) 2)) (/.f64 (/.f64 1 (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))

Compiler

Compiled 6351 to 2756 computations (56.6% saved)

regimes473.0ms (11.1%)

Accuracy

Total 1.3b remaining (98%)

Threshold costs 0b (0%)

Counts

130 → 1

Compiler

Compiled 10614 to 6418 computations (39.5% saved)

simplify2.0ms (0.1%)

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	12	16
1	17	16
2	22	16
3	26	16
4	29	16
5	30	16
6	29	16

end149.0ms (3.5%)

Compiler: Compiled 139 to 95 computations (31.7% saved)

Details

analyze386.0ms (9%)

sample1.2s (27.1%)

simplify70.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series80.0ms (1.9%)

rewrite64.0ms (1.5%)

simplify82.0ms (1.9%)

prune103.0ms (2.4%)

localize8.0ms (0.2%)

series87.0ms (2%)

rewrite69.0ms (1.6%)

simplify93.0ms (2.2%)

prune114.0ms (2.7%)

localize16.0ms (0.4%)

series93.0ms (2.2%)

rewrite120.0ms (2.8%)

simplify70.0ms (1.6%)

prune395.0ms (9.3%)

localize8.0ms (0.2%)

series106.0ms (2.5%)

rewrite92.0ms (2.2%)

simplify128.0ms (3%)

prune294.0ms (6.9%)

regimes473.0ms (11.1%)

simplify2.0ms (0.1%)

end149.0ms (3.5%)

Profiling