Details

analyze46.0ms

Algorithm

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample35.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	4979	53
1	4979	53

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 55.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
34.3b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
47.2b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac_binary64`
66×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `frac-times_binary64`
34×	`associate-*r/_binary64`
30×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-*l/_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`pow1_binary64`
14×	`difference-of-sqr-1_binary64` `associate-/l*_binary64`
9×	`associate-/l/_binary64` `div-inv_binary64`
7×	`associate-/r*_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
3×	`swap-sqr_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 228

Calls

4 calls:

14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
44.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
26.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series763.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
31.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
643.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
74.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify94.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4989	12174
1	4989	12174

prune358.0ms

Filtered

152 candidates to 240 candidates (-57.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	5	241

Merged error: 33.4b

Counts

241 → 5

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b

(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

33.7b

(/.f64 (*.f64 (*.f64 i i) 1/4) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`pow1_binary64`
8×	`add-cube-cbrt_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `times-frac_binary64` `flip-+_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `frac-times_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `associate-/r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64` `-commutative_binary64`

Counts

2 → 66

Calls

2 calls:

14.0ms

(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

22.0ms

(/.f64 (*.f64 (*.f64 i i) 1/4) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

series77.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms

(*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

61.0ms

(/.f64 (*.f64 (*.f64 i i) 1/4) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))

simplify31.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4981	1242
1	4981	1242

prune93.0ms

Filtered

48 candidates to 72 candidates (-50.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 33.3b

Counts

77 → 7

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b

(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

29.8b

(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`associate-/r*_binary64` `times-frac_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-cube-cbrt_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r/_binary64` `difference-of-squares_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

2 → 61

Calls

2 calls:

25.0ms

(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

11.0ms

(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

series63.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms

(/.f64 (*.f64 (/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

17.0ms

(/.f64 (*.f64 i i) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

simplify28.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5069	1360

prune93.0ms

Filtered

42 candidates to 67 candidates (-59.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	65	9	74

Merged error: 7.3b

Counts

74 → 9

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b

(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

0.1b

(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

0.1b

(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
24×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
11×	`associate-/r*_binary64`
7×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`associate-/r/_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64` `associate-/l*_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

3 → 106

Calls

3 calls:

10.0ms

(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

23.0ms

(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

14.0ms

(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))

series83.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms

(/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))

49.0ms

(/.f64 (*.f64 (*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))) 1/4) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 1))

17.0ms

(*.f64 i (/.f64 i (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))

simplify50.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4953	2032
1	4953	2032

prune116.0ms

Filtered

75 candidates to 115 candidates (-53.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 7.3b

Counts

124 → 13

regimes281.0ms

Accuracy

26.5% (4.1b remaining)

Error of 11.4b against oracle of 7.3b and baseline of 12.9b

bsearch12.0ms

Steps

Iters	Range		Point
4	2.316113881829469e+49	4.324400894895351e+49	4.260945402677668e+49

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	86
1	50	86

end0.0ms

sample997.0ms

Algorithm

intervals

Results

641.0ms	8000×	body	80	valid
175.0ms	8000×	pre	80	true

Details

analyze46.0ms

sample35.0ms

simplify19.0ms

prune9.0ms

localize15.0ms

rewrite109.0ms

series763.0ms

simplify94.0ms

prune358.0ms

localize11.0ms

rewrite38.0ms

series77.0ms

simplify31.0ms

prune93.0ms

localize14.0ms

rewrite39.0ms

series63.0ms

simplify28.0ms

prune93.0ms

localize16.0ms

rewrite50.0ms

series83.0ms

simplify50.0ms

prune116.0ms

regimes281.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample997.0ms

Profiling