Details

analyze2.2s

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

sample58.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
8.0ms	95×	body	80	nan
3.0ms	34×	body	80	invalid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5464	18

prune5.0ms

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: 12.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
9.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite37.0ms

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:

10.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(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))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series233.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
71.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
36.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify60.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4983	1890
1	4983	1890

prune176.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 6.7b

Counts

129 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
6.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
40×	`div-exp_binary64`
30×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`
23×	`associate-r_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`cbrt-unprod_binary64` `times-frac_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
7×	`pow1_binary64`
6×	`cbrt-undiv_binary64` `unpow-prod-down_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64`
3×	`div-inv_binary64` `sqrt-prod_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `un-div-inv_binary64` `flip--_binary64`

Counts

4 → 130

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

series219.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
44.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
40.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

simplify48.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5192	1853

prune139.0ms

Filtered

72 candidates to 142 candidates (-97.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Merged error: 6.3b

Counts

150 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))
5.7b	(*.f64 (/.f64 M 2) (/.f64 D d))
6.4b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
40×	`div-exp_binary64`
32×	`associate-r_binary64`
31×	`times-frac_binary64`
30×	`add-cbrt-cube_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow-exp_binary64`
17×	`associate-l_binary64`
11×	`cbrt-unprod_binary64`
9×	`pow1_binary64`
8×	`1-exp_binary64` `rec-exp_binary64`
7×	`unswap-sqr_binary64`
6×	`cbrt-undiv_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64`
3×	`div-inv_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`pow-prod-down_binary64` `unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `un-div-inv_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 154

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))
11.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
8.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))
46.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))
8.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
38.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

simplify64.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4980	2090
1	4980	2090

prune375.0ms

Filtered

96 candidates to 166 candidates (-72.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	166	8	174

Merged error: 6.3b

Counts

174 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
10.4b	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`cbrt-unprod_binary64` `prod-exp_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `times-frac_binary64`
7×	`pow1_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`sqrt-prod_binary64`
2×	`associate-/r_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
12.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 h l) (/.f64 (.f64 M D) (.f64 2 d))))))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))
21.0ms	(.f64 (/.f64 h l) (/.f64 (.f64 M D) (*.f64 2 d)))

simplify35.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5056	1435

prune94.0ms

Filtered

73 candidates to 121 candidates (-65.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	8	129

Merged error: 6.3b

Counts

129 → 8

regimes1.5s

Accuracy

57% (1.5b remaining)

Error of 9.2b against oracle of 7.7b and baseline of 11.1b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	197	57
1	197	57

end0.0ms

sample1.4s

Algorithm

intervals

Results

616.0ms	8000×	body	80	valid
253.0ms	3134×	body	80	nan
109.0ms	1331×	body	80	invalid

Details

analyze2.2s

sample58.0ms

simplify29.0ms

prune5.0ms

localize13.0ms

rewrite37.0ms

series233.0ms

simplify60.0ms

prune176.0ms

localize14.0ms

rewrite37.0ms

series219.0ms

simplify48.0ms

prune139.0ms

localize15.0ms

rewrite43.0ms

series217.0ms

simplify64.0ms

prune375.0ms

localize13.0ms

rewrite36.0ms

series108.0ms

simplify35.0ms

prune94.0ms

regimes1.5s

bsearch1.0ms

simplify4.0ms

end0.0ms

sample1.4s

Profiling