Details

analyze1.3s (25%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (23.9%)

Results

1.1s	8252×	body	128	valid
112.0ms	729×	body	128	invalid
1.0ms	2×	body	2048	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify121.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series59.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
19.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify142.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune118.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
▶	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 3418 to 1143 computations (66.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series91.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
28.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
21.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
8.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify177.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune267.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	337	5	342

Error

Counts

342 → 5

Alt Table

Status	Error	Program
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
▶	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 8695 to 2781 computations (68% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series69.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

40.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
21.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

12.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify132.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
675×	`times-frac_binary64`
380×	`fma-neg_binary64`
354×	`sub-neg_binary64`
192×	`+-commutative_binary64`

Counts

225 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4903
1	792	4646
2	2764	4604
3	4923	4603
4	5113	4603

prune188.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	227	5	232

Error

Counts

232 → 5

Alt Table

Status	Error	Program
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
▶	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 5330 to 1960 computations (63.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	4.3b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	9.0b	(/.f64 (*.f64 y t) (-.f64 a t))

series101.0ms (1.9%)

Counts

3 → 81

Calls

3 calls:

49.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
28.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
23.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
35×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 137

Calls

3 calls:

15.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
5.0ms	(/.f64 (*.f64 y t) (-.f64 a t))

simplify150.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

325×	`sub-neg_binary64`
223×	`associate-/l*_binary64`
207×	`fma-neg_binary64`
194×	`times-frac_binary64`
168×	`associate-l_binary64`

Counts

218 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	406	9032
1	1097	6626
2	4117	6581
3	5067	6581

prune152.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	242	5	247

Error

Counts

247 → 5

Alt Table

Status	Error	Program
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
✓	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 8374 to 1614 computations (80.7% saved)

regimes728.0ms (13.6%)

Accuracy

Total 1.4b remaining (98%)

Threshold costs 0b (0%)

Counts

84 → 1

Compiler

Compiled 11944 to 7240 computations (39.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	22	16
3	24	16
4	25	16
5	25	16

end72.0ms (1.4%)

Compiler: Compiled 141 to 76 computations (46.1% saved)

Details

analyze1.3s (25%)

sample1.3s (23.9%)

simplify121.0ms (2.3%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series59.0ms (1.1%)

rewrite12.0ms (0.2%)

simplify142.0ms (2.7%)

prune118.0ms (2.2%)

localize12.0ms (0.2%)

series91.0ms (1.7%)

rewrite41.0ms (0.8%)

simplify177.0ms (3.3%)

prune267.0ms (5%)

localize8.0ms (0.2%)

series69.0ms (1.3%)

rewrite22.0ms (0.4%)

simplify132.0ms (2.5%)

prune188.0ms (3.5%)

localize10.0ms (0.2%)

series101.0ms (1.9%)

rewrite38.0ms (0.7%)

simplify150.0ms (2.8%)

prune152.0ms (2.9%)

regimes728.0ms (13.6%)

simplify3.0ms (0.1%)

end72.0ms (1.4%)

Profiling