Details

analyze1.2s (19.9%)

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
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	24×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify170.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1133×	`div-sub_binary64`
860×	`sub-neg_binary64`
750×	`associate-/r/_binary64`
699×	`cancel-sign-sub-inv_binary64`
610×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	86	16
4	166	16
5	293	16
6	570	16
7	1559	16
8	2366	16
9	2268	16
10	2532	16
11	2753	16
12	2839	16
13	3034	16
14	4109	16
15	4495	16
16	4543	16
17	4973	16

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

12.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.2b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 t (*.f64 a z))
11.8b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 941 to 165 computations (82.5% saved)

series113.0ms (1.9%)

Error

5.1b

Counts

2 → 52

Calls

2 calls:

83.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
19.0ms	(-.f64 t (*.f64 a z))

Compiler

Compiled 2266 to 1390 computations (38.7% saved)

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

954×	`times-frac_binary64`
636×	`associate-/l*_binary64`
332×	`cancel-sign-sub-inv_binary64`
178×	`distribute-rgt-in_binary64`
165×	`distribute-lft-in_binary64`

Counts

96 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2212
1	403	2131
2	1450	2035
3	5098	2035

prune44.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Error

5.1b

Counts

83 → 9

Alt Table

Status	Error	Program
	12.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 z a)))))
	41.2b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	12.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	33.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
▶	12.2b	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
	40.3b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (.f64 z z))))) (/.f64 x (.f64 z a)))
	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	12.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	31.0b	(/.f64 x (-.f64 t (*.f64 z a)))

Compiler

Compiled 1453 to 429 computations (70.5% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 t (neg.f64 (*.f64 z a)))
11.8b	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

21×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
3.0ms	(+.f64 t (neg.f64 (*.f64 z a)))

Compiler

Compiled 1045 to 173 computations (83.4% saved)

series130.0ms (2.2%)

Error

5.1b

Counts

2 → 52

Calls

2 calls:

99.0ms	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
19.0ms	(+.f64 t (neg.f64 (*.f64 z a)))

Compiler

Compiled 2266 to 1390 computations (38.7% saved)

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary64`
346×	`distribute-rgt-in_binary64`
345×	`div-sub_binary64`
296×	`distribute-lft-in_binary64`
254×	`cancel-sign-sub-inv_binary64`

Counts

103 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	2331
1	425	2227
2	1595	2127
3	4654	2127
4	5174	2127

prune31.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	87	9	96

Error

5.1b

Counts

96 → 9

Alt Table

Status	Error	Program
	12.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 z a)))))
	41.2b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	12.9b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	33.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
✓	12.2b	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
	40.3b	(-.f64 (+.f64 (/.f64 y a) (.f64 (/.f64 t (.f64 a a)) (-.f64 (/.f64 y z) (/.f64 x (.f64 z z))))) (/.f64 x (.f64 z a)))
▶	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	12.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	31.0b	(/.f64 x (-.f64 t (*.f64 z a)))

Compiler

Compiled 1443 to 417 computations (71.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.2b	(/.f64 1 (-.f64 t (*.f64 z a)))
11.7b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

rewrite86.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 87

Calls

3 calls:

8.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
3.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
2.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 1898 to 576 computations (69.7% saved)

series152.0ms (2.5%)

Error

5.1b

Counts

3 → 76

Calls

3 calls:

81.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
39.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
18.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 3255 to 2089 computations (35.8% saved)

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/l*_binary64`
370×	`cancel-sign-sub-inv_binary64`
277×	`distribute-rgt-in_binary64`
254×	`distribute-lft-in_binary64`
183×	`associate-/r/_binary64`

Counts

163 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	3554
1	492	3288
2	1839	3163
3	5132	3163

prune41.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	123	8	131

Error

1.9b

Counts

131 → 8

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (-.f64 t (.f64 z a))) (+.f64 x (.f64 y z)))
	12.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 z a)))))
	41.2b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	27.8b	(/.f64 (neg.f64 y) (-.f64 (/.f64 t z) a))
	33.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
✓	12.2b	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
	38.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 t (*.f64 z a)) 3))))
▶	12.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))

Compiler

Compiled 1547 to 489 computations (68.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
11.8b	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))

rewrite103.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

90×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
55×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

3 → 128

Calls

3 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
6.0ms	(-.f64 t (*.f64 z a))
5.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))

Compiler

Compiled 3377 to 812 computations (76% saved)

series219.0ms (3.7%)

Error

1.9b

Counts

3 → 84

Calls

3 calls:

88.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
83.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))
30.0ms	(-.f64 t (*.f64 z a))

Compiler

Compiled 4113 to 2567 computations (37.6% saved)

simplify212.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

550×	`cancel-sign-sub-inv_binary64`
287×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`
252×	`div-sub_binary64`
189×	`distribute-rgt-neg-in_binary64`

Counts

212 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	5679
1	656	5356
2	2352	5146
3	4534	5146
4	4984	5146
5	4965	5146

prune71.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	180	8	188

Error

1.9b

Counts

188 → 8

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (-.f64 t (.f64 z a))) (+.f64 x (.f64 y z)))
	41.2b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	27.8b	(/.f64 (neg.f64 y) (-.f64 (/.f64 t z) a))
	33.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 z a)))))
	12.2b	(/.f64 (-.f64 x (.f64 y z)) (+.f64 t (neg.f64 (.f64 z a))))
	12.3b	(/.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 x (.f64 y z))))
	38.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 t (*.f64 z a)) 3))))
	12.2b	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))

Compiler

Compiled 2389 to 561 computations (76.5% saved)

regimes2.1s (34.9%)

Accuracy

Total 0.7b remaining (34.9%)

Threshold costs 0.7b (34.9%)

Compiler

Compiled 19466 to 11316 computations (41.9% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`sub-neg_binary64`
11×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	151
1	58	151
2	77	151
3	90	151
4	96	151
5	96	151

end1.0ms (0%)

Compiler: Compiled 106 to 30 computations (71.7% saved)

sample892.0ms (14.9%)

Algorithm

1×

intervals

Results

376.0ms	8000×	body	128	valid
32.0ms	713×	body	128	invalid

Compiler

Compiled 299 to 145 computations (51.5% saved)

Details

analyze1.2s (19.9%)

sample24.0ms (0.4%)

simplify170.0ms (2.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite53.0ms (0.9%)

series113.0ms (1.9%)

simplify67.0ms (1.1%)

prune44.0ms (0.7%)

localize10.0ms (0.2%)

rewrite41.0ms (0.7%)

series130.0ms (2.2%)

simplify104.0ms (1.7%)

prune31.0ms (0.5%)

localize8.0ms (0.1%)

rewrite86.0ms (1.4%)

series152.0ms (2.5%)

simplify104.0ms (1.7%)

prune41.0ms (0.7%)

localize9.0ms (0.1%)

rewrite103.0ms (1.7%)

series219.0ms (3.7%)

simplify212.0ms (3.6%)

prune71.0ms (1.2%)

regimes2.1s (34.9%)

bsearch6.0ms (0.1%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample892.0ms (14.9%)

Profiling