Details

analyze1.3s (24.6%)

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)

sample1.2s (23.1%)

Results

1.1s	8255×	body	128	valid
99.0ms	710×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify119.0ms (2.2%)

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

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

1.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 49 computations (44.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series73.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

51.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
22.0ms	(/.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)

simplify122.0ms (2.3%)

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

prune119.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Status	Error	Program
	2.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	32.5b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
▶	1.8b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)
	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	41.3b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x) 3))

Compiler

Compiled 3446 to 1173 computations (66% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a t))
✓	0.0b	(/.f64 t (-.f64 a t))
✓	1.7b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

series82.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

52.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)
19.0ms	(/.f64 z (-.f64 a t))
10.0ms	(/.f64 t (-.f64 a t))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

3 → 88

Calls

3 calls:

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

simplify118.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
762×	`times-frac_binary64`
515×	`cancel-sign-sub-inv_binary64`
228×	`fma-neg_binary64`
206×	`sub-neg_binary64`

Counts

196 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	4312
1	678	4193
2	2169	3874
3	4936	3874
4	5034	3874

prune118.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Error

0.0b

Counts

168 → 6

Alt Table

Status	Error	Program
	2.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	32.5b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
✓	1.8b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)
▶	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	41.3b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x) 3))

Compiler

Compiled 4043 to 1194 computations (70.5% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.0b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series89.0ms (1.7%)

Counts

2 → 108

Calls

2 calls:

50.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
37.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

12.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
3.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

499×	`distribute-rgt-in_binary64`
394×	`sub-neg_binary64`
222×	`associate--l+_binary64`
199×	`fma-neg_binary64`
167×	`associate-/l*_binary64`

Counts

176 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4479
1	798	4041
2	3157	3638
3	5307	3638

prune169.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	250	5	255

Error

Counts

255 → 5

Alt Table

Status	Error	Program
	30.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))))
▶	2.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	32.5b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
	10.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 6249 to 1914 computations (69.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	10.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series104.0ms (2%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
37.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
18.0ms	(/.f64 y (-.f64 a t))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

12.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
5.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms	(/.f64 y (-.f64 a t))

simplify209.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune176.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	309	4	313

Error

Counts

313 → 4

Alt Table

Status	Error	Program
	30.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))))
	2.8b	(fma.f64 (-.f64 z t) (/.f64 y (-.f64 a t)) x)
	10.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	1.8b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 7957 to 2024 computations (74.6% saved)

regimes965.0ms (18.1%)

Accuracy

Total 0.9b remaining (98.3%)

Threshold costs 0.9b (98.3%)

Counts

84 → 3

Compiler

Compiled 12021 to 7231 computations (39.8% saved)

bsearch20.0ms (0.4%)

Steps

Iters	Range		Point
3	2.8223299479526395e-123	4.405377189292774e-122	3.208986056831293e-122
4	-1.3027587407642273e+65	-8.065825821754518e+64	-8.181875273801221e+64

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`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	27	65
1	36	65
2	45	65
3	49	65
4	51	65
5	50	65

end70.0ms (1.3%)

Compiler: Compiled 169 to 89 computations (47.3% saved)

Details

analyze1.3s (24.6%)

sample1.2s (23.1%)

simplify119.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series73.0ms (1.4%)

rewrite12.0ms (0.2%)

simplify122.0ms (2.3%)

prune119.0ms (2.2%)

localize8.0ms (0.2%)

series82.0ms (1.5%)

rewrite13.0ms (0.3%)

simplify118.0ms (2.2%)

prune118.0ms (2.2%)

localize15.0ms (0.3%)

series89.0ms (1.7%)

rewrite22.0ms (0.4%)

simplify97.0ms (1.8%)

prune169.0ms (3.2%)

localize8.0ms (0.2%)

series104.0ms (2%)

rewrite36.0ms (0.7%)

simplify209.0ms (3.9%)

prune176.0ms (3.3%)

regimes965.0ms (18.1%)

bsearch20.0ms (0.4%)

simplify5.0ms (0.1%)

end70.0ms (1.3%)

Profiling