Details

analyze1.6s (16.7%)

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)

sample59.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
9.0ms	95×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

simplify91.0ms (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

prune6.0ms (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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 63 to 36 computations (42.9% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.9b	(-.f64 (.f64 z z) (.f64 x x))
✓	10.8b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series136.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

62.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
61.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
13.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite53.0ms (0.6%)

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:

15.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
8.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
5.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify230.0ms (2.4%)

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

prune282.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	193	4	197

Error

0.0b

Counts

197 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	40.3b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) (sqrt.f64 y)) (sqrt.f64 y)) y))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	11.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 5171 to 1262 computations (75.6% saved)

localize15.0ms (0.2%)

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)))

series326.0ms (3.4%)

Counts

3 → 96

Calls

3 calls:

215.0ms	(/.f64 y (-.f64 z x))
63.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
47.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

rewrite344.0ms (3.6%)

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:

77.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
19.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
8.0ms	(/.f64 y (-.f64 z x))

simplify842.0ms (8.8%)

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

prune698.0ms (7.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	560	5	565

Error

Counts

565 → 5

Alt Table

Status	Error	Program
	0.2b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 y (/.f64 1 (-.f64 z x)))) y))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) 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))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	11.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 18072 to 3999 computations (77.9% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series151.0ms (1.6%)

Counts

3 → 100

Calls

3 calls:

69.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
59.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
22.0ms	(/.f64 (-.f64 z x) y)

rewrite72.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

25.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
19.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
10.0ms	(/.f64 (-.f64 z x) y)

simplify206.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-/l*_binary64`
645×	`fma-def_binary64`
220×	`fma-neg_binary64`
213×	`associate-/l/_binary64`
160×	`associate-l_binary64`

Counts

205 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	2969
1	460	2808
2	2080	2785
3	4757	2785
4	4973	2785

prune258.0ms (2.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
▶	0.2b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 y (/.f64 1 (-.f64 z x)))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) 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))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	11.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 3532 to 1087 computations (69.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z x))
✓	0.0b	(-.f64 (/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x)))) y)
✓	0.2b	(/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x))))
✓	0.3b	(*.f64 y (/.f64 1 (-.f64 z x)))

series163.0ms (1.7%)

Counts

4 → 132

Calls

4 calls:

58.0ms	(-.f64 (/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x)))) y)
48.0ms	(/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x))))
38.0ms	(*.f64 y (/.f64 1 (-.f64 z x)))
18.0ms	(/.f64 1 (-.f64 z x))

rewrite103.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 180

Calls

4 calls:

27.0ms	(-.f64 (/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x)))) y)
23.0ms	(/.f64 (+.f64 z x) (*.f64 y (/.f64 1 (-.f64 z x))))
18.0ms	(*.f64 y (/.f64 1 (-.f64 z x)))
8.0ms	(/.f64 1 (-.f64 z x))

simplify264.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-def_binary64`
587×	`distribute-rgt-in_binary64`
189×	`associate-l_binary64`
166×	`associate-/l*_binary64`
165×	`cancel-sign-sub-inv_binary64`

Counts

312 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	4999
1	590	4615
2	2494	4361
3	5556	4361

prune453.0ms (4.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	269	5	274

Error

Counts

274 → 5

Alt Table

Status	Error	Program
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 y (/.f64 1 (-.f64 z x)))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) 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))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	11.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 6412 to 2709 computations (57.8% saved)

regimes1.3s (13.2%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Counts

90 → 1

Compiler

Compiled 13753 to 7631 computations (44.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	17	19
2	25	19
3	29	19
4	31	19
5	31	19

end1.0ms (0%)

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

sample1.9s (19.7%)

Algorithm

1×

intervals

Results

826.0ms	8000×	body	128	valid
271.0ms	2754×	body	128	invalid

Compiler

Compiled 138 to 83 computations (39.9% saved)

Details

analyze1.6s (16.7%)

sample59.0ms (0.6%)

simplify91.0ms (1%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

series136.0ms (1.4%)

rewrite53.0ms (0.6%)

simplify230.0ms (2.4%)

prune282.0ms (3%)

localize15.0ms (0.2%)

series326.0ms (3.4%)

rewrite344.0ms (3.6%)

simplify842.0ms (8.8%)

prune698.0ms (7.3%)

localize17.0ms (0.2%)

series151.0ms (1.6%)

rewrite72.0ms (0.8%)

simplify206.0ms (2.2%)

prune258.0ms (2.7%)

localize19.0ms (0.2%)

series163.0ms (1.7%)

rewrite103.0ms (1.1%)

simplify264.0ms (2.8%)

prune453.0ms (4.7%)

regimes1.3s (13.2%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (19.7%)

Profiling