Details

analyze906.0ms (10%)

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)

sample1.5s (16.1%)

Results

1.0s	8256×	body	128	valid
363.0ms	3022×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify76.0ms (0.8%)

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

14.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.1b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	29.0b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize9.0ms (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)
✓	0.9b	(-.f64 (.f64 z z) (.f64 x x))
✓	14.1b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series61.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

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

rewrite29.0ms (0.3%)

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))

simplify152.0ms (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

prune159.0ms (1.8%)

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
	14.1b	(.f64 -1/2 (+.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) (neg.f64 y)))
▶	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	14.2b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	12.3b	(*.f64 -1/2 (neg.f64 (fma.f64 x (/.f64 x y) y)))

Compiler

Compiled 5209 to 1290 computations (75.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series64.0ms (0.7%)

Counts

3 → 100

Calls

3 calls:

28.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
24.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
12.0ms	(/.f64 (-.f64 z x) y)

rewrite29.0ms (0.3%)

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:

9.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
7.0ms	(-.f64 (*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)
6.0ms	(/.f64 (-.f64 z x) y)

simplify104.0ms (1.1%)

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

prune110.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	163	6	169

Error

Counts

169 → 6

Alt Table

Status	Error	Program
	12.3b	(*.f64 -1/2 (neg.f64 (fma.f64 x (/.f64 x y) y)))
	0.6b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (/.f64 (-.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y))) y))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	33.9b	(.f64 -1/2 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 x z) (+.f64 x z)) (+.f64 x z)) (.f64 (.f64 (/.f64 (-.f64 z x) y) (/.f64 (-.f64 z x) y)) (/.f64 (-.f64 z x) y)))) y))
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	14.2b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))

Compiler

Compiled 3608 to 1127 computations (68.8% 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))
✓	0.3b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series72.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

28.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
25.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
19.0ms	(/.f64 y (-.f64 z x))

rewrite149.0ms (1.7%)

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:

34.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
11.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
4.0ms	(/.f64 y (-.f64 z x))

simplify433.0ms (4.8%)

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

prune354.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	560	1	561
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	561	6	567

Error

Counts

567 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
▶	0.2b	(*.f64 -1/2 (-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	33.9b	(.f64 -1/2 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 x z) (+.f64 x z)) (+.f64 x z)) (.f64 (.f64 (/.f64 (-.f64 z x) y) (/.f64 (-.f64 z x) y)) (/.f64 (-.f64 z x) y)))) y))
	14.2b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	12.3b	(*.f64 -1/2 (neg.f64 (fma.f64 x (/.f64 x y) y)))

Compiler

Compiled 18106 to 4017 computations (77.8% saved)

localize17.0ms (0.2%)

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))
✓	0.8b	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))

series109.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

53.0ms	(/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))
30.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y)
26.0ms	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))

rewrite840.0ms (9.3%)

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:

93.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y)
18.0ms	(/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x)))
11.0ms	(/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))

simplify1.3s (14.7%)

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

prune1.3s (14.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1460	0	1460
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1460	6	1466

Error

Counts

1466 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
✓	0.2b	(*.f64 -1/2 (-.f64 (/.f64 1 (/.f64 (/.f64 y (-.f64 z x)) (+.f64 z x))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	33.9b	(.f64 -1/2 (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 x z) (+.f64 x z)) (+.f64 x z)) (.f64 (.f64 (/.f64 (-.f64 z x) y) (/.f64 (-.f64 z x) y)) (/.f64 (-.f64 z x) y)))) y))
	14.2b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	12.3b	(*.f64 -1/2 (neg.f64 (fma.f64 x (/.f64 x y) y)))

Compiler

Compiled 56600 to 16976 computations (70% saved)

regimes1.2s (13.1%)

Accuracy

Total 0.1b remaining (64.2%)

Threshold costs 0.1b (64.2%)

Counts

159 → 1

Compiler

Compiled 24256 to 15004 computations (38.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	18	19
2	26	19
3	30	19
4	32	19
5	32	19

end96.0ms (1.1%)

Compiler: Compiled 149 to 87 computations (41.6% saved)

Details

analyze906.0ms (10%)

sample1.5s (16.1%)

simplify76.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series61.0ms (0.7%)

rewrite29.0ms (0.3%)

simplify152.0ms (1.7%)

prune159.0ms (1.8%)

localize8.0ms (0.1%)

series64.0ms (0.7%)

rewrite29.0ms (0.3%)

simplify104.0ms (1.1%)

prune110.0ms (1.2%)

localize8.0ms (0.1%)

series72.0ms (0.8%)

rewrite149.0ms (1.7%)

simplify433.0ms (4.8%)

prune354.0ms (3.9%)

localize17.0ms (0.2%)

series109.0ms (1.2%)

rewrite840.0ms (9.3%)

simplify1.3s (14.7%)

prune1.3s (14.1%)

regimes1.2s (13.1%)

simplify3.0ms (0%)

end96.0ms (1.1%)

Profiling