Details

analyze214.0ms (4.9%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
373×	`neg-sub0_binary64`
373×	`neg-mul-1_binary64`
340×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2510	46
6	4609	46
7	5033	46

prune4.0ms (0.1%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 99 to 63 computations (36.4% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite176.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

4 → 80

Calls

4 calls:

12.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3111 to 1674 computations (46.2% saved)

series216.0ms (4.9%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

80.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
49.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
28.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
13.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 3088 to 2287 computations (25.9% saved)

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-in_binary64`
794×	`distribute-lft-in_binary64`
274×	`cancel-sign-sub-inv_binary64`
246×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

134 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3017
1	533	2697
2	1756	2612
3	5455	2612

prune106.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Error

Counts

107 → 2

Alt Table

Status	Error	Program
	11.4b	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) 1)
▶	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)

Status

Error

Program

11.4b

(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) 1)

▶

0.0b

(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (*.f64 (*.f64 b b) (-.f64 4 (*.f64 a 12)))) 1)

Compiler

Compiled 2284 to 1266 computations (44.6% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 b b))
0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
0.6b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
1.1b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

rewrite162.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`cbrt-unprod_binary64`

Counts

4 → 80

Calls

4 calls:

13.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
11.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
6.0ms	(.f64 2 (.f64 b b))

Compiler

Compiled 3374 to 2150 computations (36.3% saved)

series179.0ms (4.1%)

Error

Counts

4 → 39

Calls

4 calls:

64.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))
46.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 1 a))))
28.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
11.0ms	(.f64 2 (.f64 b b))

Compiler

Compiled 2766 to 2120 computations (23.4% saved)

simplify106.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

490×	`unswap-sqr_binary64`
334×	`associate-l_binary64`
292×	`associate-r_binary64`
245×	`exp-prod_binary64`
193×	`sub-neg_binary64`

Counts

119 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2477
1	500	2231
2	1848	2198
3	3864	2198
4	5528	2198

prune95.0ms (2.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 (pow.f64 a 3) (+.f64 4 a))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)

Status

Error

Program

▶

0.8b

(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (*.f64 (pow.f64 a 3) (+.f64 4 a))) (*.f64 (*.f64 b b) (-.f64 4 (*.f64 a 12)))) 1)

✓

0.0b

(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (*.f64 (*.f64 b b) (-.f64 4 (*.f64 a 12)))) 1)

Compiler

Compiled 2303 to 1515 computations (34.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 4 (*.f64 a 12))
0.0b	(+.f64 (+.f64 (pow.f64 b 4) (.f64 (pow.f64 a 3) (+.f64 4 a))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
0.1b	(*.f64 (pow.f64 a 3) (+.f64 4 a))
1.1b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

rewrite177.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 (pow.f64 a 3) (+.f64 4 a))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
9.0ms	(*.f64 (pow.f64 a 3) (+.f64 4 a))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
3.0ms	(-.f64 4 (*.f64 a 12))

Compiler

Compiled 3059 to 2193 computations (28.3% saved)

series138.0ms (3.2%)

Error

Counts

4 → 40

Calls

4 calls:

59.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 (pow.f64 a 3) (+.f64 4 a))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
24.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
16.0ms	(*.f64 (pow.f64 a 3) (+.f64 4 a))
9.0ms	(-.f64 4 (*.f64 a 12))

Compiler

Compiled 1697 to 1335 computations (21.3% saved)

simplify158.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

402×	`cancel-sign-sub-inv_binary64`
351×	`exp-prod_binary64`
340×	`associate-l_binary64`
308×	`associate-r_binary64`
245×	`unswap-sqr_binary64`

Counts

134 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2840
1	613	2690
2	2738	2642
3	4534	2642
4	4988	2642
5	4986	2642

prune112.0ms (2.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	104	2	106

Error

Counts

106 → 2

Alt Table

Status	Error	Program
	0.8b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 (pow.f64 a 3) (+.f64 4 a))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)

Status

Error

Program

0.8b

(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (*.f64 (pow.f64 a 3) (+.f64 4 a))) (*.f64 (*.f64 b b) (-.f64 4 (*.f64 a 12)))) 1)

0.0b

(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) (*.f64 4 (+.f64 1 a)))) (pow.f64 a 4))) (*.f64 (*.f64 b b) (-.f64 4 (*.f64 a 12)))) 1)

Compiler

Compiled 2116 to 1509 computations (28.7% saved)

regimes1.5s (33.3%)

Accuracy

Total 0.0b remaining (18.1%)

Threshold costs 0.0b (18.1%)

Compiler

Compiled 27141 to 18613 computations (31.4% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	58
1	48	58
2	55	58
3	59	58
4	62	58
5	63	58
6	60	58

end1.0ms (0%)

Compiler: Compiled 41 to 31 computations (24.4% saved)

sample834.0ms (19.1%)

Algorithm

1×

intervals

Results

495.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 139 to 100 computations (28.1% saved)

Details

analyze214.0ms (4.9%)

sample27.0ms (0.6%)

simplify64.0ms (1.5%)

prune4.0ms (0.1%)

localize17.0ms (0.4%)

rewrite176.0ms (4%)

series216.0ms (4.9%)

simplify91.0ms (2.1%)

prune106.0ms (2.4%)

localize20.0ms (0.5%)

rewrite162.0ms (3.7%)

series179.0ms (4.1%)

simplify106.0ms (2.4%)

prune95.0ms (2.2%)

localize13.0ms (0.3%)

rewrite177.0ms (4.1%)

series138.0ms (3.2%)

simplify158.0ms (3.6%)

prune112.0ms (2.6%)

regimes1.5s (33.3%)

simplify8.0ms (0.2%)

end1.0ms (0%)

sample834.0ms (19.1%)

Profiling