Details

analyze1.3s (22.8%)

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
12.5%	87.3%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
23.4%	76.4%	0.2%	11
31.6%	68.2%	0.2%	12
34.5%	64.9%	0.6%	13
40.3%	59.2%	0.6%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.8s (31.2%)

Results

1.2s	8256×	body	128	valid
463.0ms	3122×	body	128	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.7b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (/.f64 t y))
✓	0.4b	(/.f64 -1/3 z)
✓	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

series29.0ms (0.5%)

Counts

3 → 54

Calls

3 calls:

23.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
4.0ms	(-.f64 y (/.f64 t y))
1.0ms	(/.f64 -1/3 z)

rewrite89.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
231×	`fma-def_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
185×	`egg-rr`

Counts

3 → 185

Calls

3 calls:

84.0ms	(-.f64 y (/.f64 t y))
84.0ms	(/.f64 -1/3 z)
84.0ms	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	223	25
2	2955	25
3	4917	25
0	0	0
1	0	0

simplify136.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1875×	`fma-neg_binary64`
858×	`distribute-rgt-in_binary64`
782×	`fma-def_binary64`
630×	`div-sub_binary64`
438×	`cancel-sign-sub-inv_binary64`

Counts

239 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	796
1	63	664
2	112	658
3	211	592
4	355	592
5	554	592
6	975	592
7	1507	592
8	2381	592
9	2470	592
10	2908	592
11	3179	592
12	3354	592
13	3356	592
14	5426	592

prune265.0ms (4.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	194	7	201
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	195	8	203

Error

0.0b

Counts

203 → 8

Alt Table

Status	Error	Program
	31.2b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)
	3.0b	(fma.f64 (pow.f64 (/.f64 z -1/3) -1) (-.f64 y (/.f64 t y)) x)
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	34.2b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
	2.7b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
▶	2.6b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
	2.7b	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)
	30.9b	(/.f64 (-.f64 (.f64 (.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))) (.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))) (.f64 x x)) (-.f64 (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))) x))

Compiler

Compiled 5324 to 1902 computations (64.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
✓	0.3b	(*.f64 1/3 (/.f64 y z))
✓	0.3b	(.f64 1/3 (/.f64 t (.f64 y z)))
✓	4.9b	(/.f64 t (*.f64 y z))

series65.0ms (1.1%)

Counts

4 → 15

Calls

4 calls:

26.0ms	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
18.0ms	(.f64 1/3 (/.f64 t (.f64 y z)))
15.0ms	(/.f64 t (*.f64 y z))
6.0ms	(*.f64 1/3 (/.f64 y z))

rewrite85.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

284×	`expm1-udef_binary64`
284×	`log1p-udef_binary64`
157×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Counts

4 → 141

Calls

4 calls:

82.0ms	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 1/3 (/.f64 y z)))
82.0ms	(*.f64 1/3 (/.f64 y z))
82.0ms	(.f64 1/3 (/.f64 t (.f64 y z)))
82.0ms	(/.f64 t (*.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	304	44
2	4370	44
3	5178	44
0	0	0
1	0	0

simplify144.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1234×	`fma-def_binary64`
995×	`fma-neg_binary64`
645×	`distribute-rgt-in_binary64`
610×	`unsub-neg_binary64`
579×	`distribute-lft-in_binary64`

Counts

156 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	115
1	53	115
2	95	109
3	175	109
4	297	109
5	454	109
6	744	109
7	1137	109
8	2010	109
9	2303	109
10	2331	109
11	2811	109
12	2886	109
13	2976	109
14	3900	109
15	4876	109
16	5265	109

prune138.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	153	7	160

Error

0.0b

Counts

160 → 7

Alt Table

Status	Error	Program
	31.2b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)
	3.0b	(fma.f64 (pow.f64 (/.f64 z -1/3) -1) (-.f64 y (/.f64 t y)) x)
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	34.2b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
▶	2.7b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
	2.7b	(fma.f64 (*.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)) x)
	2.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (/.f64 1 (/.f64 z (*.f64 y 1/3))))

Compiler

Compiled 3394 to 1637 computations (51.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 t y) y)
✓	0.2b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
✓	2.4b	(/.f64 (-.f64 (/.f64 t y) y) z)

series43.0ms (0.8%)

Counts

3 → 82

Calls

3 calls:

24.0ms	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
14.0ms	(/.f64 (-.f64 (/.f64 t y) y) z)
4.0ms	(-.f64 (/.f64 t y) y)

rewrite181.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

872×	`prod-diff_binary64`
343×	`egg-rr`
213×	`log1p-udef_binary64`
117×	`add-sqr-sqrt_binary64`
111×	`log1p-expm1-u_binary64`

Counts

3 → 343

Calls

3 calls:

171.0ms	(-.f64 (/.f64 t y) y)
171.0ms	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
171.0ms	(/.f64 (-.f64 (/.f64 t y) y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	224	31
2	3112	31
3	5184	31
0	0	0
1	0	0

simplify147.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1733×	`fma-neg_binary64`
929×	`div-sub_binary64`
662×	`fma-def_binary64`
583×	`times-frac_binary64`
386×	`neg-mul-1_binary64`

Counts

425 → 366

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	1121
1	76	989
2	140	961
3	278	851
4	484	851
5	937	851
6	1934	851
7	2873	851
8	2934	851
9	3186	851
10	3138	851
11	3365	851
12	4940	851

prune278.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	365	1	366
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	366	7	373

Error

Counts

373 → 7

Alt Table

Status	Error	Program
	31.2b	(/.f64 (-.f64 (.f64 1/3 (/.f64 t y)) (.f64 1/3 y)) z)
	3.0b	(fma.f64 (pow.f64 (/.f64 z -1/3) -1) (-.f64 y (/.f64 t y)) x)
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	34.2b	(fma.f64 (pow.f64 (sqrt.f64 (/.f64 -1/3 z)) 2) (-.f64 y (/.f64 t y)) x)
✓	2.7b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
	2.7b	(fma.f64 1/3 (+.f64 (fma.f64 (/.f64 t 1) (/.f64 (/.f64 1 y) z) (neg.f64 (.f64 (/.f64 1 z) y))) (fma.f64 (neg.f64 (/.f64 1 z)) y (.f64 (/.f64 1 z) y))) x)
▶	2.7b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (/.f64 1 (/.f64 z (*.f64 y 1/3))))

Compiler

Compiled 12376 to 3350 computations (72.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 1/3 (/.f64 t (.f64 y z)))
✓	0.4b	(/.f64 1 (/.f64 z (*.f64 y 1/3)))
✓	0.4b	(*.f64 y 1/3)
	4.9b	(/.f64 t (*.f64 y z))

series10.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(/.f64 1 (/.f64 z (*.f64 y 1/3)))
1.0ms	(*.f64 y 1/3)

rewrite47.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

785×	`log1p-expm1-u_binary64`
785×	`expm1-log1p-u_binary64`
142×	`log1p-udef_binary64`
82×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Counts

2 → 62

Calls

2 calls:

46.0ms	(/.f64 1 (/.f64 z (*.f64 y 1/3)))
46.0ms	(*.f64 y 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	168	11
2	2050	11
3	5105	11
0	0	0
1	0	0

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-/r/_binary64`

Counts

98 → 63

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	216
1	10	216
2	14	216
3	16	216
4	17	216
5	17	216

prune120.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	130	6	136

Error

Counts

136 → 6

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 1/3 (/.f64 (-.f64 (/.f64 t y) y) z) x)
	2.8b	(-.f64 (+.f64 (/.f64 (.f64 1/3 (/.f64 t y)) z) x) (/.f64 1 (/.f64 z (.f64 y 1/3))))
	2.6b	(-.f64 (+.f64 (.f64 1/3 (/.f64 t (.f64 y z))) x) (*.f64 (/.f64 1 z) (pow.f64 (/.f64 3 y) -1)))
	3.0b	(fma.f64 (pow.f64 (/.f64 z -1/3) -1) (-.f64 y (/.f64 t y)) x)
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.7b	(fma.f64 1/3 (+.f64 (fma.f64 (/.f64 t 1) (/.f64 (/.f64 1 y) z) (neg.f64 (.f64 (/.f64 1 z) y))) (fma.f64 (neg.f64 (/.f64 1 z)) y (.f64 (/.f64 1 z) y))) x)

Compiler

Compiled 2778 to 1580 computations (43.1% saved)

regimes611.0ms (10.7%)

Accuracy

Total 1.6b remaining (98.1%)

Threshold costs 0b (0%)

Counts

107 → 1

Compiler

Compiled 11428 to 7881 computations (31% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	22	25
2	28	25
3	30	25
4	31	25
5	29	25

end101.0ms (1.8%)

Compiler: Compiled 169 to 119 computations (29.6% saved)

Details

analyze1.3s (22.8%)

sample1.8s (31.2%)

simplify93.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series29.0ms (0.5%)

rewrite89.0ms (1.6%)

simplify136.0ms (2.4%)

prune265.0ms (4.6%)

localize9.0ms (0.2%)

series65.0ms (1.1%)

rewrite85.0ms (1.5%)

simplify144.0ms (2.5%)

prune138.0ms (2.4%)

localize7.0ms (0.1%)

series43.0ms (0.8%)

rewrite181.0ms (3.2%)

simplify147.0ms (2.6%)

prune278.0ms (4.9%)

localize10.0ms (0.2%)

series10.0ms (0.2%)

rewrite47.0ms (0.8%)

simplify16.0ms (0.3%)

prune120.0ms (2.1%)

regimes611.0ms (10.7%)

simplify3.0ms (0%)

end101.0ms (1.8%)

Profiling