Details

analyze858.0ms (17%)

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 (27.2%)

Results

945.0ms	8256×	body	128	valid
342.0ms	2997×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify79.0ms (1.6%)

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

14.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.7b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	29.5b	(/.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 (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	14.8b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series56.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

25.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
24.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite28.0ms (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:

10.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
4.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
2.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify130.0ms (2.6%)

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

prune126.0ms (2.5%)

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)))
	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	14.7b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	0.6b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (-.f64 z x) (cbrt.f64 y)) (neg.f64 y)))
	32.2b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))

Compiler

Compiled 5241 to 1306 computations (75.1% 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 (0.6%)

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)

rewrite8.0ms (0.2%)

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))

simplify85.0ms (1.7%)

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

prune56.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	79	5	84

Error

0.0b

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)))
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	14.7b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	32.2b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (/.f64 (-.f64 z x) (sqrt.f64 y)) (sqrt.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)))

Compiler

Compiled 1718 to 690 computations (59.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series61.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

25.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
22.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
14.0ms	(/.f64 y (-.f64 z x))

rewrite144.0ms (2.9%)

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:

32.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
8.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
7.0ms	(/.f64 y (-.f64 z x))

simplify422.0ms (8.4%)

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

prune391.0ms (7.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	559	2	561
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	560	6	566

Error

Counts

566 → 6

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 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	14.7b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	32.4b	(*.f64 -1/2 (fma.f64 (/.f64 1 (sqrt.f64 (/.f64 y (-.f64 z x)))) (/.f64 (+.f64 z x) (sqrt.f64 (/.f64 y (-.f64 z x)))) (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)))
	0.2b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 y (/.f64 1 (-.f64 z x)))) y))

Compiler

Compiled 18102 to 4029 computations (77.7% saved)

localize10.0ms (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))
✓	0.3b	(*.f64 (-.f64 z x) (/.f64 1 y))

series29.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(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))

rewrite10.0ms (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:

7.0ms	(*.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))

simplify81.0ms (1.6%)

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

prune121.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	103	6	109

Error

Counts

109 → 6

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 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
	14.7b	(.f64 -1/2 (fma.f64 (-.f64 (.f64 z z) (*.f64 x x)) (/.f64 1 y) (neg.f64 y)))
	32.4b	(*.f64 -1/2 (fma.f64 (/.f64 1 (sqrt.f64 (/.f64 y (-.f64 z x)))) (/.f64 (+.f64 z x) (sqrt.f64 (/.f64 y (-.f64 z x)))) (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)))
	0.2b	(.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (.f64 y (/.f64 1 (-.f64 z x)))) y))

Compiler

Compiled 2304 to 1059 computations (54% saved)

regimes822.0ms (16.3%)

Accuracy

Total 0.1b remaining (84.2%)

Threshold costs 0.1b (84.2%)

Counts

91 → 1

Compiler

Compiled 11961 to 7340 computations (38.6% 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

end98.0ms (1.9%)

Compiler: Compiled 148 to 94 computations (36.5% saved)

Details

analyze858.0ms (17%)

sample1.4s (27.2%)

simplify79.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series56.0ms (1.1%)

rewrite28.0ms (0.6%)

simplify130.0ms (2.6%)

prune126.0ms (2.5%)

localize9.0ms (0.2%)

series29.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify85.0ms (1.7%)

prune56.0ms (1.1%)

localize8.0ms (0.2%)

series61.0ms (1.2%)

rewrite144.0ms (2.9%)

simplify422.0ms (8.4%)

prune391.0ms (7.7%)

localize10.0ms (0.2%)

series29.0ms (0.6%)

rewrite10.0ms (0.2%)

simplify81.0ms (1.6%)

prune121.0ms (2.4%)

regimes822.0ms (16.3%)

simplify2.0ms (0%)

end98.0ms (1.9%)

Profiling