Details

analyze33.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample124.0ms (3.2%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	7×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify116.0ms (3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	13.9b	(/.f64 b (*.f64 a a))

series43.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 b (*.f64 a a))
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 44

Calls

2 calls:

3.0ms	(/.f64 b (*.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

simplify87.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

553×	`div-sub_binary64`
385×	`associate-/l*_binary64`
361×	`associate-/l/_binary64`
322×	`*-commutative_binary64`
270×	`fma-def_binary64`

Counts

92 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1190
1	131	1118
2	258	1118
3	623	1118
4	1939	1118
5	2527	1118
6	4267	1118
7	5200	1118

prune40.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Error

0.0b

Counts

54 → 3

Alt Table

Status	Error	Program
	14.3b	(.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
	14.3b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 946 to 469 computations (50.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.3b	(/.f64 (/.f64 b a) a)

series42.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (/.f64 b a) a)
13.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

2 → 93

Calls

2 calls:

4.0ms	(/.f64 (/.f64 b a) a)
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

simplify140.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

360×	`distribute-rgt-in_binary64`
345×	`fma-neg_binary64`
327×	`associate-/l/_binary64`
305×	`distribute-lft-in_binary64`
298×	`fma-def_binary64`

Counts

141 → 146

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	174	2231
1	333	2103
2	605	2031
3	1372	2007
4	1707	2002
5	2563	1952
6	4418	1922
7	4987	1922
8	4849	1922

prune108.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	145	4	149

Error

Counts

149 → 4

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	14.3b	(.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 2779 to 1247 computations (55.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	0.3b	(/.f64 (/.f64 b a) a)

series34.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
14.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`exp-prod_binary64`
14×	`sqrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`log-pow_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 44

Calls

2 calls:

3.0ms	(exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
3.0ms	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

simplify149.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

554×	`unswap-sqr_binary64`
524×	`associate-/r/_binary64`
500×	`fma-def_binary64`
366×	`exp-sum_binary64`
353×	`log-prod_binary64`

Counts

92 → 76

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	71	1651
1	81	1539
2	108	1539
3	151	1539
4	265	1539
5	602	1539
6	1750	1539
7	2926	1533
8	4392	1533
9	4784	1533
10	4986	1533
11	4916	1533

prune232.0ms (6.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	222	4	226

Error

Counts

226 → 4

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
▶	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	14.3b	(.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 4684 to 2388 computations (49% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	0.3b	(/.f64 (/.f64 b a) a)

series1.1s (29.9%)

Counts

2 → 48

Calls

2 calls:

1.1s	(log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
14.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

simplify153.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1128×	`fma-def_binary64`
971×	`div-sub_binary64`
494×	`associate-/r/_binary64`
458×	`unswap-sqr_binary64`
376×	`fma-neg_binary64`

Counts

70 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	1234
1	44	1165
2	59	1165
3	90	1165
4	171	1165
5	429	1165
6	1381	1165
7	2197	1165
8	2517	1165
9	2951	1165
10	3798	1165
11	4153	1165
12	4834	1165
13	5944	1165

prune216.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (exp.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	14.3b	(.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (.f64 a a)) -1)))) (sqrt.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 3746 to 1902 computations (49.2% saved)

regimes131.0ms (3.4%)

Accuracy

Total 0.0b remaining (76.9%)

Threshold costs 0.0b (76.9%)

Counts

20 → 1

Compiler

Compiled 2520 to 1654 computations (34.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	11	19

end0.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample970.0ms (25.3%)

Algorithm

1×

intervals

Results

375.0ms	8000×	body	128	valid
233.0ms	8000×	pre	128	true
8.0ms	366×	pre	128	false

Compiler

Compiled 107 to 70 computations (34.6% saved)

Details

analyze33.0ms (0.9%)

sample124.0ms (3.2%)

simplify116.0ms (3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series43.0ms (1.1%)

rewrite7.0ms (0.2%)

simplify87.0ms (2.3%)

prune40.0ms (1.1%)

localize7.0ms (0.2%)

series42.0ms (1.1%)

rewrite13.0ms (0.3%)

simplify140.0ms (3.7%)

prune108.0ms (2.8%)

localize10.0ms (0.3%)

series34.0ms (0.9%)

rewrite8.0ms (0.2%)

simplify149.0ms (3.9%)

prune232.0ms (6.1%)

localize10.0ms (0.3%)

series1.1s (29.9%)

rewrite2.0ms (0%)

simplify153.0ms (4%)

prune216.0ms (5.6%)

regimes131.0ms (3.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample970.0ms (25.3%)

Profiling