Details

analyze902.0ms (15.4%)

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)

sample1.4s (24.5%)

Results

971.0ms	8256×	body	128	valid
367.0ms	3057×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify71.0ms (1.2%)

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 (0.1%)

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

12.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	32.1b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
▶	12.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

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)
✓	0.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	12.3b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series60.0ms (1%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
26.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite29.0ms (0.5%)

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:

10.0ms	(-.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))

simplify134.0ms (2.3%)

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

prune153.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	189	7	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	7	198

Error

0.0b

Counts

198 → 7

Alt Table

Status	Error	Program
	12.5b	(.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))
	32.6b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (pow.f64 z 4) (pow.f64 x 4)) (fma.f64 x x (.f64 z z))) y) y))
	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	6.5b	(.f64 -1/2 (-.f64 (/.f64 (.f64 z z) y) (fma.f64 x (/.f64 x y) y)))
	33.8b	(.f64 -1/2 (.f64 (sqrt.f64 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y)) (sqrt.f64 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.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)))
	12.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) (cbrt.f64 y))) y))

Compiler

Compiled 5379 to 1362 computations (74.7% saved)

localize9.0ms (0.2%)

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 (0.5%)

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:

4.0ms	(/.f64 (-.f64 z x) y)
0.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

simplify80.0ms (1.4%)

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

prune69.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Error

0.0b

Counts

86 → 7

Alt Table

Status	Error	Program
	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z 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)))
	12.5b	(.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))
▶	0.1b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	32.6b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (pow.f64 z 4) (pow.f64 x 4)) (fma.f64 x x (.f64 z z))) y) y))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	12.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) (cbrt.f64 y))) y))

Compiler

Compiled 1876 to 760 computations (59.5% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 (+.f64 z x) 1) (*.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y))
✓	0.2b	(*.f64 (-.f64 z x) (/.f64 1 y))

series29.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 54

Calls

2 calls:

8.0ms	(*.f64 (-.f64 z x) (/.f64 1 y))
0.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (*.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

449×	`fma-neg_binary64`
302×	`distribute-rgt-neg-out_binary64`
297×	`distribute-lft-neg-out_binary64`
282×	`exp-prod_binary64`
268×	`associate-l_binary64`

Counts

126 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1584
1	247	1404
2	712	1404
3	2316	1402
4	4432	1402
5	4992	1402

prune100.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	103	7	110

Error

0.0b

Counts

110 → 7

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z 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)))
	12.5b	(.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))
✓	0.1b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	32.6b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (pow.f64 z 4) (pow.f64 x 4)) (fma.f64 x x (.f64 z z))) y) y))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	12.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) (cbrt.f64 y))) y))

Compiler

Compiled 2496 to 1153 computations (53.8% 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)))

series80.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

43.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
22.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
15.0ms	(/.f64 y (-.f64 z x))

rewrite143.0ms (2.4%)

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:

33.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
8.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
3.0ms	(/.f64 y (-.f64 z x))

simplify688.0ms (11.8%)

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

prune486.0ms (8.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	2	2	4
Picked	0	1	1
Done	1	1	2
Total	562	6	568

Error

Counts

568 → 6

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z 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) (/.f64 1 y)) (neg.f64 y)))
	32.6b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (-.f64 (pow.f64 z 4) (pow.f64 x 4)) (fma.f64 x x (.f64 z z))) y) y))
	0.6b	(.f64 -1/2 (-.f64 (/.f64 (/.f64 (+.f64 x z) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) (-.f64 z x))) y))
	30.6b	(*.f64 -1/2 (-.f64 (/.f64 (/.f64 (+.f64 x z) (sqrt.f64 y)) (/.f64 (sqrt.f64 y) (-.f64 z x))) y))

Compiler

Compiled 18042 to 3985 computations (77.9% saved)

regimes1.1s (19.3%)

Accuracy

Total 0.1b remaining (70.9%)

Threshold costs 0.1b (70.9%)

Counts

163 → 1

Compiler

Compiled 24204 to 13995 computations (42.2% saved)

simplify2.0ms (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	11	19
1	19	19
2	24	19
3	27	19
4	28	19
5	28	19

end99.0ms (1.7%)

Compiler: Compiled 170 to 102 computations (40% saved)

Details

analyze902.0ms (15.4%)

sample1.4s (24.5%)

simplify71.0ms (1.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series60.0ms (1%)

rewrite29.0ms (0.5%)

simplify134.0ms (2.3%)

prune153.0ms (2.6%)

localize9.0ms (0.2%)

series29.0ms (0.5%)

rewrite9.0ms (0.1%)

simplify80.0ms (1.4%)

prune69.0ms (1.2%)

localize12.0ms (0.2%)

series29.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify79.0ms (1.4%)

prune100.0ms (1.7%)

localize8.0ms (0.1%)

series80.0ms (1.4%)

rewrite143.0ms (2.4%)

simplify688.0ms (11.8%)

prune486.0ms (8.3%)

regimes1.1s (19.3%)

simplify2.0ms (0%)

end99.0ms (1.7%)

Profiling