Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample54.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
9.0ms	108×	body	80	nan
3.0ms	37×	body	80	invalid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5038	27

prune2.0ms

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: 17.3b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
11.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`associate-l_binary64`
10×	`unswap-sqr_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 116

Calls

4 calls:

8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series589.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
26.0ms	(/.f64 (.f64 M D) (.f64 2 d))
169.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
98.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify63.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5851	2845

prune135.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	7	129

Merged error: 10.6b

Counts

129 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.6b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
26×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64` `add-cube-cbrt_binary64` `pow-exp_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64` `times-frac_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-l_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
107.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
26.0ms	(/.f64 (.f64 M D) (.f64 2 d))
347.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))

simplify58.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5064	2183

prune93.0ms

Filtered

67 candidates to 111 candidates (-65.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	110	8	118

Merged error: 10.4b

Counts

118 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

5.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
6.5b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-prod_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
8.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
29.0ms	(/.f64 (.f64 M D) (.f64 2 d))
340.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
42.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))

simplify85.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5229	1781

prune83.0ms

Filtered

61 candidates to 101 candidates (-65.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 10.4b

Counts

109 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

4.5b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
4.6b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
5.7b	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64` `prod-exp_binary64`
25×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`associate-r_binary64`
16×	`associate-l_binary64`
10×	`pow-exp_binary64`
7×	`pow1_binary64` `unswap-sqr_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 123

Calls

4 calls:

7.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
6.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

series607.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
102.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
366.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
25.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

simplify84.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5043	2553

prune110.0ms

Filtered

90 candidates to 135 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	6	6
Picked	0	1	1
Done	1	0	1
Total	134	9	143

Merged error: 9.5b

Counts

143 → 9

regimes576.0ms

Accuracy

26.4% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 8.9b

bsearch1.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	167	110
1	167	110

end0.0ms

sample1.5s

Algorithm

intervals

Results

663.0ms	8000×	body	80	valid
268.0ms	3119×	body	80	nan
119.0ms	1306×	body	80	invalid

Details

analyze2.4s

sample54.0ms

simplify64.0ms

prune2.0ms

localize14.0ms

rewrite34.0ms

series589.0ms

simplify63.0ms

prune135.0ms

localize14.0ms

rewrite33.0ms

series595.0ms

simplify58.0ms

prune93.0ms

localize14.0ms

rewrite32.0ms

series434.0ms

simplify85.0ms

prune83.0ms

localize14.0ms

rewrite35.0ms

series607.0ms

simplify84.0ms

prune110.0ms

regimes576.0ms

bsearch1.0ms

simplify6.0ms

end0.0ms

sample1.5s

Profiling