Details

analyze876.0ms (10.6%)

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)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
4.0ms	87×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

simplify74.0ms (0.9%)

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

16.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	28.8b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (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))
✓	16.5b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series89.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

49.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
33.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite31.0ms (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)
5.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
3.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify140.0ms (1.7%)

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

prune127.0ms (1.5%)

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

0.0b

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)))
	16.2b	(.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))
	16.2b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
	0.6b	(.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 5233 to 1302 computations (75.1% saved)

localize9.0ms (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))

series33.0ms (0.4%)

Counts

2 → 64

Calls

2 calls:

24.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))
9.0ms	(/.f64 (-.f64 z x) y)

rewrite7.0ms (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:

5.0ms	(/.f64 (-.f64 z x) y)
0.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

simplify84.0ms (1%)

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

prune63.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Error

Counts

84 → 6

Alt Table

Status	Error	Program
	16.2b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
	0.7b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 y))) (neg.f64 y)))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	16.2b	(.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))
	0.6b	(.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 1784 to 716 computations (59.9% 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)))

series74.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
27.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
19.0ms	(/.f64 y (-.f64 z x))

rewrite156.0ms (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:

35.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
12.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
4.0ms	(/.f64 y (-.f64 z x))

simplify449.0ms (5.5%)

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

prune367.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	562	5	567

Error

Counts

567 → 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)))
	16.2b	(.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))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y))
	0.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 (cbrt.f64 y) (-.f64 z x)))) y))

Compiler

Compiled 18074 to 4001 computations (77.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
✓	0.0b	(/.f64 (+.f64 z x) y)
✓	0.0b	(/.f64 1 (-.f64 z x))
✓	0.3b	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))

series74.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

30.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
24.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
10.0ms	(/.f64 (+.f64 z x) y)
10.0ms	(/.f64 1 (-.f64 z x))

rewrite739.0ms (9%)

Algorithm

1×	rewrite-expression-head

Rules

4207×	`times-frac_binary64`
3088×	`*-un-lft-identity_binary64`
2465×	`add-sqr-sqrt_binary64`
1946×	`add-cube-cbrt_binary64`
1023×	`prod-diff_binary64`

Counts

4 → 1865

Calls

4 calls:

112.0ms	(-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y)
20.0ms	(/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x)))
4.0ms	(/.f64 1 (-.f64 z x))
4.0ms	(/.f64 (+.f64 z x) y)

simplify2.0s (24%)

Algorithm

1×	egg-herbie

Rules

405×	`associate-*l/_binary64`
400×	`associate-/l/_binary64`
303×	`fma-udef_binary64`
300×	`associate-r_binary64`
291×	`associate-*r/_binary64`

Counts

1985 → 1577

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	724	70248
1	1364	58321
2	4901	58318
3	5064	58318

prune1.2s (14.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1577	0	1577
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1577	5	1582

Error

Counts

1582 → 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)))
	16.2b	(.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))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (/.f64 (+.f64 z x) y) (/.f64 1 (-.f64 z x))) y))
	0.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 x z)) (cbrt.f64 (+.f64 x z))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (+.f64 x z)) (/.f64 (cbrt.f64 y) (-.f64 z x)))) y))

Compiler

Compiled 63280 to 20390 computations (67.8% saved)

regimes576.0ms (7%)

Accuracy

Total 0.1b remaining (55.6%)

Threshold costs 0.1b (55.6%)

Counts

85 → 1

Compiler

Compiled 12076 to 7058 computations (41.6% saved)

simplify5.0ms (0.1%)

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 (12.2%)

Algorithm

1×

intervals

Results

413.0ms	8000×	body	128	valid
152.0ms	2897×	body	128	invalid

Compiler

Compiled 140 to 85 computations (39.3% saved)

Details

analyze876.0ms (10.6%)

sample28.0ms (0.3%)

simplify74.0ms (0.9%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series89.0ms (1.1%)

rewrite31.0ms (0.4%)

simplify140.0ms (1.7%)

prune127.0ms (1.5%)

localize9.0ms (0.1%)

series33.0ms (0.4%)

rewrite7.0ms (0.1%)

simplify84.0ms (1%)

prune63.0ms (0.8%)

localize8.0ms (0.1%)

series74.0ms (0.9%)

rewrite156.0ms (1.9%)

simplify449.0ms (5.5%)

prune367.0ms (4.5%)

localize9.0ms (0.1%)

series74.0ms (0.9%)

rewrite739.0ms (9%)

simplify2.0s (24%)

prune1.2s (14.8%)

regimes576.0ms (7%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (12.2%)

Profiling