Details

analyze83.0ms (1.3%)

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)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	15×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify46.0ms (0.7%)

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%)

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

16.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.8b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize6.0ms (0.1%)

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)))
✓	16.6b	(/.f64 b (*.f64 a a))

series42.0ms (0.7%)

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)))

rewrite8.0ms (0.1%)

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

simplify98.0ms (1.6%)

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

prune46.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	1	54

Error

0.0b

Counts

54 → 1

Alt Table

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

Compiler

Compiled 868 to 419 computations (51.7% saved)

localize6.0ms (0.1%)

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)

series41.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(/.f64 (/.f64 b a) a)
12.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite15.0ms (0.2%)

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:

7.0ms	(/.f64 (/.f64 b a) a)
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

simplify145.0ms (2.3%)

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

prune136.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	2	147

Error

Counts

147 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))) -1)))
	0.0b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Status

Error

Program

▶

0.0b

(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))) -1)))

0.0b

(cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 2785 to 1233 computations (55.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))
✓	0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a)))
✓	0.7b	(cbrt.f64 (/.f64 b a))

series1.7s (27.8%)

Counts

4 → 88

Calls

4 calls:

680.0ms	(*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a)))
584.0ms	(/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))
414.0ms	(cbrt.f64 (/.f64 b a))
70.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a)))

rewrite113.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

404×	`times-frac_binary64`
307×	`add-sqr-sqrt_binary64`
258×	`cbrt-prod_binary64`
217×	`*-un-lft-identity_binary64`
217×	`add-cube-cbrt_binary64`

Counts

4 → 394

Calls

4 calls:

36.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a)))
11.0ms	(*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a)))
6.0ms	(/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))
2.0ms	(cbrt.f64 (/.f64 b a))

simplify381.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-/r*_binary64`
346×	`associate-l_binary64`
331×	`associate-*r/_binary64`
287×	`associate-r_binary64`
284×	`associate-*l/_binary64`

Counts

482 → 538

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	449	12596
1	1007	11740
2	3411	11098
3	4615	10876
4	4977	10876
5	4979	10876

prune573.0ms (9.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	614	0	614
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	614	2	616

Error

Counts

616 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))) -1)))
▶	0.0b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Status

Error

Program

✓

0.0b

(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))) -1)))

▶

0.0b

(cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 21399 to 5835 computations (72.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series71.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

53.0ms

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

13.0ms

(cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

5.0ms

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

rewrite62.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`add-sqr-sqrt_binary64`
105×	`rem-sqrt-square_binary64`
64×	`sqrt-prod_binary64`
63×	`mul-fabs_binary64`
59×	`fabs-mul_binary64`

Counts

3 → 182

Calls

3 calls:

12.0ms

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

10.0ms

(cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

8.0ms

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

simplify181.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

623×	`distribute-rgt-in_binary64`
622×	`times-frac_binary64`
609×	`distribute-lft-in_binary64`
509×	`exp-prod_binary64`
452×	`associate-l_binary64`

Counts

254 → 215

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	5198
1	208	4049
2	366	3706
3	990	3463
4	3356	3326
5	4380	3326
6	5144	3326

prune548.0ms (8.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	551	0	551
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	551	2	553

Error

Counts

553 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

(sqrt.f64 (fabs.f64 (fma.f64 b (*.f64 (/.f64 (*.f64 (cbrt.f64 (/.f64 b a)) (cbrt.f64 (/.f64 b a))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (/.f64 b a)) (sqrt.f64 a))) -1)))

✓

0.0b

(cbrt.f64 (*.f64 (*.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))) (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 21480 to 9668 computations (55% saved)

regimes972.0ms (15.4%)

Accuracy

Total 0.0b remaining (38.7%)

Threshold costs 0.0b (38.7%)

Counts

169 → 1

Compiler

Compiled 24959 to 16212 computations (35% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	20	35
2	18	35

end1.0ms (0%)

Compiler: Compiled 24 to 14 computations (41.7% saved)

sample914.0ms (14.5%)

Algorithm

1×

intervals

Results

365.0ms	8000×	body	128	valid
192.0ms	8000×	pre	128	true
10.0ms	387×	pre	128	false

Compiler

Compiled 114 to 63 computations (44.7% saved)

Details

analyze83.0ms (1.3%)

sample30.0ms (0.5%)

simplify46.0ms (0.7%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series42.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify98.0ms (1.6%)

prune46.0ms (0.7%)

localize6.0ms (0.1%)

series41.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify145.0ms (2.3%)

prune136.0ms (2.2%)

localize12.0ms (0.2%)

series1.7s (27.8%)

rewrite113.0ms (1.8%)

simplify381.0ms (6.1%)

prune573.0ms (9.1%)

localize11.0ms (0.2%)

series71.0ms (1.1%)

rewrite62.0ms (1%)

simplify181.0ms (2.9%)

prune548.0ms (8.7%)

regimes972.0ms (15.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample914.0ms (14.5%)

Profiling