Details

analyze2.3s

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

sample53.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
8.0ms	102×	body	80	nan
3.0ms	36×	body	80	invalid

simplify65.0ms

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: 15.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

3.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
12.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite36.0ms

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)))))
7.0ms	(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))

series581.0ms

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)))))
168.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
22.0ms	(/.f64 (.f64 M D) (.f64 2 d))
96.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify65.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5851	2845

prune144.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 9.6b

Counts

129 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

3.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
5.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-exp-log_binary64`
88×	`prod-exp_binary64`
52×	`div-exp_binary64`
28×	`add-cbrt-cube_binary64`
25×	`pow-exp_binary64`
24×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64`
13×	`associate-l_binary64`
11×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unswap-sqr_binary64`
8×	`cbrt-undiv_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`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 → 132

Calls

4 calls:

11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
17.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
173.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
24.0ms	(/.f64 (.f64 M D) (.f64 2 d))
217.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

simplify104.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4971	3642
1	4971	3642

prune124.0ms

Filtered

77 candidates to 144 candidates (-87.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Merged error: 9.2b

Counts

153 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.6b	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-exp-log_binary64`
118×	`add-cbrt-cube_binary64`
73×	`cbrt-unprod_binary64` `prod-exp_binary64`
48×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
5×	`associate-r_binary64` `associate-l_binary64` `times-frac_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 → 131

Calls

4 calls:

14.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
20.0ms	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

397.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
23.0ms	(/.f64 (.f64 M D) (.f64 2 d))
25.0ms	(/.f64 (.f64 M D) (.f64 2 d))
201.0ms	(.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

simplify111.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5072	3223

prune102.0ms

Filtered

64 candidates to 143 candidates (-123.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	143	8	151

Merged error: 9.2b

Counts

151 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
10.0b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

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` `associate-r*_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
7×	`pow1_binary64`
5×	`associate-l_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 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
14.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

series287.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
24.0ms	(/.f64 (.f64 M D) (.f64 2 d))
25.0ms	(/.f64 (.f64 M D) (.f64 2 d))
65.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

simplify84.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5084	2149

prune86.0ms

Filtered

70 candidates to 121 candidates (-72.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	121	8	129

Merged error: 9.2b

Counts

129 → 8

regimes267.0ms

Accuracy

0% (2.2b remaining)

Error of 9.3b against oracle of 7.1b and baseline of 9.3b

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	122	60
1	122	60

end0.0ms

sample1.5s

Algorithm

intervals

Results

634.0ms	8000×	body	80	valid
255.0ms	3088×	body	80	nan
119.0ms	1349×	body	80	invalid

Details

analyze2.3s

sample53.0ms

simplify65.0ms

prune2.0ms

localize15.0ms

rewrite36.0ms

series581.0ms

simplify65.0ms

prune144.0ms

localize26.0ms

rewrite47.0ms

series717.0ms

simplify104.0ms

prune124.0ms

localize23.0ms

rewrite54.0ms

series647.0ms

simplify111.0ms

prune102.0ms

localize14.0ms

rewrite36.0ms

series287.0ms

simplify84.0ms

prune86.0ms

regimes267.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample1.5s

Profiling