Details

analyze516.0ms

Algorithm

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 28.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.3b	(+.f64 (.f64 a c) (.f64 b d))
28.0b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (.f64 a c) (.f64 b d))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(+.f64 (.f64 a c) (.f64 b d))
33.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify45.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5169	820

prune88.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 27.7b

Counts

49 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b	(+.f64 (.f64 a c) (.f64 b d))
18.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
32.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
32.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+.f64 (.f64 a c) (.f64 b d))
10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+.f64 (.f64 a c) (.f64 b d))
38.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify62.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5503	1525

prune110.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	93	12	105

Merged error: 25.4b

Counts

105 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
1.3b	(+.f64 (.f64 a c) (.f64 b d))
27.7b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
11×	`associate-/r/_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 126

Calls

3 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
10.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))

series63.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
11.0ms	(+.f64 (.f64 a c) (.f64 b d))
20.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5027	3070

prune122.0ms

Filtered

93 candidates to 135 candidates (-45.2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	135	12	147

Merged error: 25.4b

Counts

147 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

19.4b	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
19.4b	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
32.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
32.5b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
35.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify55.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5589	740

prune64.0ms

Filtered

62 candidates to 68 candidates (-9.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	6	8
Picked	0	1	1
Done	0	3	3
Total	68	12	80

Merged error: 25.4b

Counts

80 → 12

regimes467.0ms

Accuracy

-25.4% (3.7b remaining)

Error of 26.9b against oracle of 23.1b and baseline of 26.1b

bsearch11.0ms

Steps

Iters	Range		Point
5	1.1516004749705331e+22	3.4049745653750204e+22	3.3582445621159293e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	39
1	21	39

end0.0ms

sample580.0ms

Algorithm

intervals

Results

349.0ms	8000×	body	80	valid
23.0ms	482×	body	80	invalid

Details

analyze516.0ms

sample22.0ms

simplify5.0ms

prune4.0ms

localize10.0ms

rewrite15.0ms

series44.0ms

simplify45.0ms

prune88.0ms

localize12.0ms

rewrite25.0ms

series64.0ms

simplify62.0ms

prune110.0ms

localize11.0ms

rewrite30.0ms

series63.0ms

simplify63.0ms

prune122.0ms

localize17.0ms

rewrite18.0ms

series85.0ms

simplify55.0ms

prune64.0ms

regimes467.0ms

bsearch11.0ms

simplify2.0ms

end0.0ms

sample580.0ms

Profiling