Details

analyze210.0ms (4.4%)

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)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

localize16.0ms (0.3%)

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	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite182.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.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)

series242.0ms (5.1%)

Error

Counts

4 → 53

Calls

4 calls:

94.0ms	(+.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))))))
57.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
28.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
15.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 3053 to 2263 computations (25.9% saved)

simplify87.0ms (1.8%)

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

133 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3004
1	533	2684
2	1756	2599
3	5456	2599

prune97.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

0.0b

Counts

106 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

✓

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 2268 to 1266 computations (44.2% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
0.3b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
2.8b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))

rewrite219.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-log-exp_binary64`
14×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64` `associate-*r/_binary64`
7×	`sum-log_binary64`
6×	`pow-prod-down_binary64` `prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `-un-lft-identity_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-r*_binary64`

Counts

4 → 83

Calls

4 calls:

21.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
13.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
12.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
8.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 4438 to 2844 computations (35.9% saved)

series288.0ms (6.1%)

Error

Counts

4 → 54

Calls

4 calls:

94.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12))))
70.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1)))) (pow.f64 a 4))
49.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (*.f64 4 (+.f64 a 1))))
31.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 3409 to 2663 computations (21.9% saved)

simplify192.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

501×	`cancel-sign-sub-inv_binary64`
396×	`associate-l_binary64`
356×	`associate-r_binary64`
252×	`distribute-rgt-neg-in_binary64`
226×	`distribute-rgt-in_binary64`

Counts

137 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4780
1	772	4465
2	3139	4447
3	4977	4447
4	4995	4447
5	4931	4447

prune134.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
✓	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)
▶	28.7b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 4)))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)

Compiler

Compiled 3377 to 2222 computations (34.2% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))
0.6b	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))))
5.5b	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8))
41.4b	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4))))) (pow.f64 a 4)))

rewrite413.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64` `associate-*r/_binary64`

Counts

4 → 118

Calls

4 calls:

41.0ms	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4))))) (pow.f64 a 4)))
26.0ms	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8))
24.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))))
12.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 10313 to 7009 computations (32% saved)

series450.0ms (9.5%)

Error

Counts

4 → 45

Calls

4 calls:

226.0ms	(/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (*.f64 a 4))))) (pow.f64 a 4)))
62.0ms	(-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8))
61.0ms	(.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4)))))
39.0ms	(.f64 (.f64 b b) (-.f64 4 (*.f64 a 12)))

Compiler

Compiled 6471 to 4952 computations (23.5% saved)

simplify245.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

440×	`associate-l_binary64`
430×	`associate-r_binary64`
278×	`exp-prod_binary64`
266×	`distribute-rgt-in_binary64`
263×	`distribute-lft-in_binary64`

Counts

163 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	8526
1	1060	7855
2	4436	7729
3	4869	7729
4	5179	7729

prune155.0ms (3.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
	0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (+.f64 (.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) (.f64 4 (+.f64 a 1)))) (pow.f64 a 4))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)
	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)
	28.7b	(-.f64 (+.f64 (+.f64 (pow.f64 b 4) (/.f64 (-.f64 (.f64 (pow.f64 a 4) (.f64 (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))) (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 8)) (-.f64 (.f64 a (.f64 a (+.f64 (.f64 2 (.f64 b b)) (+.f64 4 (.f64 a 4))))) (pow.f64 a 4)))) (.f64 (.f64 b b) (-.f64 4 (.f64 a 12)))) 1)

Compiler

Compiled 5142 to 3513 computations (31.7% saved)

regimes752.0ms (15.9%)

Accuracy

Total 0.0b remaining (64.1%)

Threshold costs 0.0b (64.1%)

Compiler

Compiled 16556 to 11504 computations (30.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`1-exp_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	61
1	48	61
2	58	61
3	62	61
4	64	61
5	61	61

end2.0ms (0%)

Compiler: Compiled 43 to 34 computations (20.9% saved)

sample894.0ms (18.9%)

Algorithm

1×

intervals

Results

501.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 218 to 153 computations (29.8% saved)

Details

analyze210.0ms (4.4%)

sample28.0ms (0.6%)

simplify60.0ms (1.3%)

prune4.0ms (0.1%)

localize16.0ms (0.3%)

rewrite182.0ms (3.8%)

series242.0ms (5.1%)

simplify87.0ms (1.8%)

prune97.0ms (2%)

localize22.0ms (0.5%)

rewrite219.0ms (4.6%)

series288.0ms (6.1%)

simplify192.0ms (4.1%)

prune134.0ms (2.8%)

localize29.0ms (0.6%)

rewrite413.0ms (8.7%)

series450.0ms (9.5%)

simplify245.0ms (5.2%)

prune155.0ms (3.3%)

regimes752.0ms (15.9%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample894.0ms (18.9%)

Profiling