Details

analyze96.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 20 to 11 computations (45% saved)

sample28.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 37 to 21 computations (43.2% saved)

simplify56.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
494×	`associate-r_binary64`
376×	`fabs-div_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	25	17
2	68	17
3	187	17
4	441	17
5	1424	17
6	4841	17
7	5086	17

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.3b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
27.8b	(/.f64 (.f64 b b) (.f64 a a))

rewrite159.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
12×	`sqrt-prod_binary64`

Counts

3 → 68

Calls

3 calls:

5.0ms	(/.f64 (.f64 b b) (.f64 a a))
5.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
4.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))

Compiler

Compiled 1315 to 535 computations (59.3% saved)

series60.0ms (2.5%)

Error

0.5b

Counts

3 → 24

Calls

3 calls:

24.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
19.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
15.0ms	(/.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 549 to 467 computations (14.9% saved)

simplify114.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

808×	`times-frac_binary64`
589×	`unswap-sqr_binary64`
451×	`associate-l_binary64`
417×	`associate-/l*_binary64`
372×	`associate-r_binary64`

Counts

92 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	1672
1	263	1459
2	731	1401
3	3988	1355
4	4977	1355
5	4937	1355

prune18.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Error

Counts

62 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))
▶	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))

Compiler

Compiled 427 to 227 computations (46.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))
0.5b	(pow.f64 (/.f64 b a) 6)
25.0b	(cbrt.f64 (pow.f64 (/.f64 b a) 6))

rewrite136.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

65×	`add-sqr-sqrt_binary64`
50×	`cbrt-prod_binary64`
47×	`unpow-prod-down_binary64`
45×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))
9.0ms	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))
3.0ms	(pow.f64 (/.f64 b a) 6)
3.0ms	(cbrt.f64 (pow.f64 (/.f64 b a) 6))

Compiler

Compiled 2452 to 1670 computations (31.9% saved)

series77.0ms (3.2%)

Error

Counts

4 → 30

Calls

4 calls:

23.0ms	(-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))
20.0ms	(pow.f64 (/.f64 b a) 6)
16.0ms	(cbrt.f64 (pow.f64 (/.f64 b a) 6))
15.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))

Compiler

Compiled 729 to 621 computations (14.8% saved)

simplify133.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

419×	`associate-l_binary64`
412×	`associate-r_binary64`
391×	`log-prod_binary64`
317×	`exp-prod_binary64`
182×	`associate-*l/_binary64`

Counts

157 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	3015
1	459	2530
2	965	2458
3	3459	2431
4	4925	2431

prune34.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	109	2	111

Error

Counts

111 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))

Compiler

Compiled 783 to 544 computations (30.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))
0.0b	(-.f64 1 (fabs.f64 (/.f64 b a)))
0.0b	(*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))

rewrite188.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

80×	`add-sqr-sqrt_binary64`
54×	`cancel-sign-sub-inv_binary64`
48×	`fabs-mul_binary64`
46×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`

Counts

3 → 138

Calls

3 calls:

20.0ms	(*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))
8.0ms	(-.f64 1 (fabs.f64 (/.f64 b a)))
2.0ms	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))

Compiler

Compiled 3844 to 1745 computations (54.6% saved)

series40.0ms (1.7%)

Error

Counts

3 → 18

Calls

3 calls:

14.0ms	(*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))
14.0ms	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))
9.0ms	(-.f64 1 (fabs.f64 (/.f64 b a)))

Compiler

Compiled 629 to 407 computations (35.3% saved)

simplify154.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

604×	`associate-*l/_binary64`
502×	`neg-mul-1_binary64`
258×	`distribute-rgt-neg-out_binary64`
250×	`distribute-lft-neg-out_binary64`
247×	`associate-l_binary64`

Counts

156 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	4223
1	665	4056
2	2194	3381
3	4401	3264
4	5027	3264

prune60.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

146 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 1 (fabs.f64 (/.f64 b a))) (-.f64 1 (fabs.f64 (/.f64 b a))))))
	0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (cbrt.f64 (pow.f64 (/.f64 b a) 6)))))

Compiler

Compiled 1872 to 944 computations (49.6% saved)

regimes130.0ms (5.3%)

Accuracy

Total 0.0b remaining (6.3%)

Threshold costs 0.0b (6.3%)

Compiler

Compiled 2059 to 1412 computations (31.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	19	20
2	25	20
3	28	20
4	29	20
5	27	20

end1.0ms (0%)

Compiler: Compiled 14 to 12 computations (14.3% saved)

sample927.0ms (38%)

Algorithm

1×

intervals

Results

378.0ms	8000×	body	128	valid
175.0ms	8000×	pre	128	true
3.0ms	161×	pre	128	false

Compiler

Compiled 65 to 46 computations (29.2% saved)

Details

analyze96.0ms (3.9%)

sample28.0ms (1.2%)

simplify56.0ms (2.3%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite159.0ms (6.5%)

series60.0ms (2.5%)

simplify114.0ms (4.7%)

prune18.0ms (0.7%)

localize8.0ms (0.3%)

rewrite136.0ms (5.6%)

series77.0ms (3.2%)

simplify133.0ms (5.4%)

prune34.0ms (1.4%)

localize8.0ms (0.3%)

rewrite188.0ms (7.7%)

series40.0ms (1.7%)

simplify154.0ms (6.3%)

prune60.0ms (2.5%)

regimes130.0ms (5.3%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample927.0ms (38%)

Profiling