Details

analyze386.0ms (13.7%)

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
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
37.4%	62.4%	0.1%	8
46.8%	46.8%	6.4%	9
54.6%	39%	6.4%	10
62.8%	30.8%	6.4%	11
66.9%	23.6%	9.5%	12
71.7%	18.8%	9.5%	13
75.3%	15.2%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample31.0ms (1.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 24 to 18 computations (25% saved)

simplify22.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`
23×	`distribute-lft-neg-in_binary64`
21×	`distribute-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	25	10
3	31	10
4	56	10
5	93	10
6	150	10
7	248	10
8	253	10
9	260	10
10	254	10
11	209	10

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 20 to 14 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 x 3) y) z)
0.3b	(.f64 (.f64 x 3) y)

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 32

Calls

2 calls:

4.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
4.0ms	(.f64 (.f64 x 3) y)

Compiler

Compiled 421 to 267 computations (36.6% saved)

series34.0ms (1.2%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

22.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
9.0ms	(.f64 (.f64 x 3) y)

Compiler

Compiled 382 to 271 computations (29.1% saved)

simplify72.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

614×	`distribute-rgt-neg-in_binary64`
563×	`associate-r_binary64`
377×	`neg-mul-1_binary64`
256×	`unsub-neg_binary64`
228×	`times-frac_binary64`

Counts

56 → 29

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	554
1	176	533
2	489	530
3	1324	530
4	2514	530
5	4459	530
6	4953	530

prune17.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	24	5	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	6	30

Error

0.0b

Counts

30 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
▶	0.1b	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
	25.5b	(-.f64 (.f64 (sqrt.f64 (.f64 3 (.f64 y x))) (sqrt.f64 (.f64 3 (*.f64 y x)))) z)
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (.f64 y x))) (cbrt.f64 (.f64 3 (.f64 y x)))) (cbrt.f64 (.f64 3 (.f64 y x)))) z)
	17.7b	(-.f64 (.f64 (.f64 (*.f64 3 x) (sqrt.f64 y)) (sqrt.f64 y)) z)
	35.4b	(/.f64 (-.f64 (.f64 y (.f64 (.f64 y x) (.f64 x 9))) (.f64 z z)) (+.f64 (.f64 3 (*.f64 y x)) z))

Compiler

Compiled 436 to 258 computations (40.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
0.2b	(.f64 3 (.f64 y x))

rewrite35.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`add-sqr-sqrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 35

Calls

2 calls:

4.0ms	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
4.0ms	(.f64 3 (.f64 y x))

Compiler

Compiled 538 to 334 computations (37.9% saved)

series34.0ms (1.2%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

22.0ms	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
10.0ms	(.f64 3 (.f64 y x))

Compiler

Compiled 415 to 300 computations (27.7% saved)

simplify90.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

538×	`associate-l_binary64`
425×	`distribute-rgt-in_binary64`
417×	`associate-r_binary64`
389×	`distribute-lft-in_binary64`
354×	`times-frac_binary64`

Counts

59 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	612
1	171	591
2	461	591
3	1692	591
4	3925	591
5	4529	591
6	5005	591

prune14.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	25	6	31

Error

0.0b

Counts

31 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.1b	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
	0.3b	(-.f64 (pow.f64 (.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3))) 1) z)
▶	0.2b	(-.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 y x) (cbrt.f64 3))) 1) z)
	17.7b	(-.f64 (.f64 (.f64 (*.f64 3 x) (sqrt.f64 y)) (sqrt.f64 y)) z)
	35.4b	(/.f64 (-.f64 (.f64 y (.f64 (.f64 y x) (.f64 x 9))) (.f64 z z)) (+.f64 (.f64 3 (*.f64 y x)) z))

Compiler

Compiled 382 to 247 computations (35.3% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b

(-.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3))) 1) z)

0.2b

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3)))

0.3b

(*.f64 (*.f64 y x) (cbrt.f64 3))

rewrite81.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`add-exp-log_binary64`
29×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 66

Calls

3 calls:

10.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3)))

5.0ms

(-.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3))) 1) z)

5.0ms

(*.f64 (*.f64 y x) (cbrt.f64 3))

Compiler

Compiled 1469 to 1096 computations (25.4% saved)

series109.0ms (3.9%)

Error

0.0b

Counts

3 → 30

Calls

3 calls:

56.0ms

(-.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3))) 1) z)

26.0ms

(*.f64 (*.f64 (cbrt.f64 3) (cbrt.f64 3)) (*.f64 (*.f64 y x) (cbrt.f64 3)))

18.0ms

(*.f64 (*.f64 y x) (cbrt.f64 3))

Compiler

Compiled 819 to 656 computations (19.9% saved)

simplify102.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

539×	`times-frac_binary64`
384×	`*-commutative_binary64`
297×	`sqr-pow_binary64`
259×	`distribute-rgt-in_binary64`
233×	`distribute-lft-in_binary64`

Counts

96 → 78

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	126	1531
1	266	967
2	876	967
3	1598	967
4	3385	967
5	4635	967
6	5394	967

prune30.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	78	6	84

Error

0.0b

Counts

84 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.1b	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
	17.7b	(-.f64 (.f64 (.f64 (*.f64 3 x) (sqrt.f64 y)) (sqrt.f64 y)) z)
	16.6b	(-.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (cbrt.f64 (.f64 3 (pow.f64 (.f64 y x) 3)))) 1) z)
▶	0.3b	(-.f64 (pow.f64 (.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3))) 1) z)
✓	0.2b	(-.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 y x) (cbrt.f64 3))) 1) z)

Compiler

Compiled 613 to 457 computations (25.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (pow.f64 (.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3))) 1) z)
0.3b	(.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3)))
0.3b	(.f64 (.f64 y x) (sqrt.f64 3))

rewrite79.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 62

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3)))
5.0ms	(.f64 (.f64 y x) (sqrt.f64 3))
5.0ms	(-.f64 (pow.f64 (.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3))) 1) z)

Compiler

Compiled 1185 to 853 computations (28% saved)

series81.0ms (2.9%)

Error

0.0b

Counts

3 → 30

Calls

3 calls:

40.0ms	(-.f64 (pow.f64 (.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3))) 1) z)
20.0ms	(.f64 (sqrt.f64 3) (.f64 (*.f64 y x) (sqrt.f64 3)))
16.0ms	(.f64 (.f64 y x) (sqrt.f64 3))

Compiler

Compiled 734 to 582 computations (20.7% saved)

simplify93.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

438×	`times-frac_binary64`
384×	`*-commutative_binary64`
236×	`sqr-pow_binary64`
232×	`distribute-rgt-in_binary64`
206×	`distribute-lft-in_binary64`

Counts

92 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1242
1	254	949
2	795	949
3	1378	941
4	2955	941
5	4320	941
6	4936	941

prune34.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	0	2
Picked	1	0	1
Done	1	2	3
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)
	0.1b	(-.f64 (pow.f64 (.f64 3 (.f64 y x)) 1) z)
	0.3b	(-.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (.f64 y (*.f64 (sqrt.f64 3) x)) (sqrt.f64 (cbrt.f64 3)))) 1) z)
	0.2b	(-.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (.f64 y (*.f64 (sqrt.f64 3) x)) (cbrt.f64 (sqrt.f64 3)))) 1) z)

Compiler

Compiled 596 to 443 computations (25.7% saved)

regimes396.0ms (14%)

Accuracy

Total 0.1b remaining (93.4%)

Threshold costs 0.1b (93.4%)

Compiler

Compiled 6569 to 5019 computations (23.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	16	10
2	20	10
3	22	10
4	23	10
5	22	10

end8.0ms (0.3%)

Compiler: Compiled 30 to 21 computations (30% saved)

sample1.0s (35.8%)

Algorithm

1×

intervals

Results

248.0ms	8000×	body	128	valid
10.0ms	294×	body	128	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	25	10
3	31	10
4	56	10
5	93	10
6	150	10
7	248	10
8	253	10
9	260	10
10	254	10
11	209	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	25	10
3	31	10
4	56	10
5	93	10
6	150	10
7	248	10
8	253	10
9	260	10
10	254	10
11	209	10

Details

analyze386.0ms (13.7%)

sample31.0ms (1.1%)

simplify22.0ms (0.8%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite32.0ms (1.1%)

series34.0ms (1.2%)

simplify72.0ms (2.5%)

prune17.0ms (0.6%)

localize6.0ms (0.2%)

rewrite35.0ms (1.2%)

series34.0ms (1.2%)

simplify90.0ms (3.2%)

prune14.0ms (0.5%)

localize10.0ms (0.4%)

rewrite81.0ms (2.9%)

series109.0ms (3.9%)

simplify102.0ms (3.6%)

prune30.0ms (1.1%)

localize8.0ms (0.3%)

rewrite79.0ms (2.8%)

series81.0ms (2.9%)

simplify93.0ms (3.3%)

prune34.0ms (1.2%)

regimes396.0ms (14%)

simplify3.0ms (0.1%)

end8.0ms (0.3%)

sample1.0s (35.8%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	25	10
3	31	10
4	56	10
5	93	10
6	150	10
7	248	10
8	253	10
9	260	10
10	254	10
11	209	10