Details

analyze831.0ms (11.1%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample108.0ms (1.4%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	93×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	19

prune4.0ms (0%)

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

12.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.6b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	30.4b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	1.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	13.5b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series63.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

29.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
27.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64`
49×	`prod-diff_binary64`

Counts

3 → 137

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
4.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
3.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify368.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
355×	`distribute-rgt-in_binary64`
349×	`distribute-lft-in_binary64`
265×	`fma-neg_binary64`
183×	`exp-prod_binary64`

Counts

233 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4494
1	395	4071
2	1546	3650
3	4392	3650
4	4970	3650

prune182.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	5	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	193	5	198

Error

Counts

198 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	12.8b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 x x))) y)) y))
	12.6b	(.f64 -1/2 (-.f64 (/.f64 (fma.f64 z z (neg.f64 (.f64 x x))) y) y))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))

Compiler

Compiled 5267 to 1304 computations (75.2% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) y)
✓	0.1b	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

series29.0ms (0.4%)

Counts

2 → 64

Calls

2 calls:

20.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))
9.0ms	(/.f64 (-.f64 z x) y)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z x) y)
0.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
583×	`fma-def_binary64`
471×	`fma-neg_binary64`
222×	`div-sub_binary64`
217×	`associate-/l/_binary64`

Counts

114 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1574
1	230	1428
2	519	1428
3	1571	1426
4	4322	1426
5	4995	1426

prune65.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	79	5	84

Error

Counts

84 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	12.8b	(.f64 -1/2 (-.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 x x))) y)) y))
	12.6b	(.f64 -1/2 (-.f64 (/.f64 (fma.f64 z z (neg.f64 (.f64 x x))) y) y))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))

Compiler

Compiled 1746 to 682 computations (60.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
✓	0.0b	(/.f64 y (-.f64 z x))
✓	0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series71.0ms (1%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
23.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
22.0ms	(/.f64 y (-.f64 z x))

rewrite143.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

753×	`times-frac_binary64`
750×	`*-un-lft-identity_binary64`
545×	`add-sqr-sqrt_binary64`
402×	`add-cube-cbrt_binary64`
267×	`prod-diff_binary64`

Counts

3 → 543

Calls

3 calls:

31.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
9.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
4.0ms	(/.f64 y (-.f64 z x))

simplify472.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

361×	`fma-neg_binary64`
213×	`associate-*l/_binary64`
202×	`associate-/l*_binary64`
199×	`associate-/r/_binary64`
183×	`*-commutative_binary64`

Counts

639 → 561

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	17494
1	881	16388
2	3922	15169
3	4593	15169
4	4939	15169

prune385.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	562	4	566

Error

Counts

566 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y))
	12.6b	(.f64 -1/2 (-.f64 (/.f64 (fma.f64 z z (neg.f64 (.f64 x x))) y) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))) y))

Compiler

Compiled 18044 to 3985 computations (77.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y)
	0.0b	(/.f64 y (-.f64 z x))
✓	0.2b	(/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))
✓	0.9b	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))

series109.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

56.0ms	(/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))
28.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y)
25.0ms	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))

rewrite590.0ms (7.9%)

Algorithm

1×	rewrite-expression-head

Rules

3825×	`times-frac_binary64`
2865×	`*-un-lft-identity_binary64`
2166×	`add-sqr-sqrt_binary64`
1729×	`add-cube-cbrt_binary64`
825×	`prod-diff_binary64`

Counts

3 → 1643

Calls

3 calls:

94.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y)
23.0ms	(/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))
18.0ms	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))

simplify1.2s (16.1%)

Algorithm

1×	egg-herbie

Rules

358×	`associate-/r/_binary64`
303×	`associate-/l*_binary64`
294×	`associate-/l/_binary64`
289×	`fma-neg_binary64`
261×	`times-frac_binary64`

Counts

1751 → 1405

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	58456
1	1153	51671
2	4724	51671
3	4974	51671

prune999.0ms (13.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1459	1	1460
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	1460	4	1464

Error

Counts

1464 → 4

Alt Table

Status	Error	Program
	12.6b	(.f64 -1/2 (-.f64 (/.f64 (.f64 (+.f64 z x) (-.f64 z x)) y) y))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 y (-.f64 z x)))) y))

Compiler

Compiled 56562 to 16956 computations (70% saved)

regimes533.0ms (7.1%)

Accuracy

Total 0.1b remaining (54.9%)

Threshold costs 0.1b (54.9%)

Counts

82 → 1

Compiler

Compiled 10643 to 6424 computations (39.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	22	19
2	27	19
3	30	19
4	31	19
5	30	19

end1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample1.0s (14.1%)

Algorithm

1×

intervals

Results

485.0ms	8000×	body	128	valid
158.0ms	2868×	body	128	invalid

Compiler

Compiled 117 to 72 computations (38.5% saved)

Details

analyze831.0ms (11.1%)

sample108.0ms (1.4%)

simplify73.0ms (1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series63.0ms (0.8%)

rewrite28.0ms (0.4%)

simplify368.0ms (4.9%)

prune182.0ms (2.4%)

localize11.0ms (0.1%)

series29.0ms (0.4%)

rewrite9.0ms (0.1%)

simplify115.0ms (1.5%)

prune65.0ms (0.9%)

localize8.0ms (0.1%)

series71.0ms (1%)

rewrite143.0ms (1.9%)

simplify472.0ms (6.3%)

prune385.0ms (5.1%)

localize9.0ms (0.1%)

series109.0ms (1.5%)

rewrite590.0ms (7.9%)

simplify1.2s (16.1%)

prune999.0ms (13.4%)

regimes533.0ms (7.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.0s (14.1%)

Profiling