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

sample54.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
8.0ms	95×	body	80	nan
3.0ms	34×	body	80	invalid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	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 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
9.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
35×	`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`
14×	`times-frac_binary64`
12×	`associate-l_binary64`
10×	`pow-exp_binary64`
8×	`unswap-sqr_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×	`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 → 113

Calls

4 calls:

7.0ms	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
10.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

series636.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
180.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
222.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

simplify66.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	1927
1	4977	1927

prune178.0ms

Filtered

84 candidates to 125 candidates (-48.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 6.7b

Counts

126 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
6.4b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

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`
22×	`associate-r_binary64`
21×	`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`
3×	`unswap-sqr_binary64` `div-inv_binary64` `sqrt-prod_binary64`
2×	`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 → 128

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
11.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
7.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

series684.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
189.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
331.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5085	1894

prune143.0ms

Filtered

76 candidates to 140 candidates (-84.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 6.3b

Counts

148 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
3.8b	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
5.7b	(*.f64 (/.f64 M 2.0) (/.f64 D d))
6.4b	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log_binary64`
91×	`prod-exp_binary64`
44×	`add-sqr-sqrt_binary64`
40×	`div-exp_binary64`
31×	`associate-r_binary64` `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`
6×	`cbrt-undiv_binary64` `unswap-sqr_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` `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 → 152

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
11.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
11.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))
6.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

series680.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
191.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
7.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))
327.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	2107
1	4979	2107

prune172.0ms

Filtered

100 candidates to 164 candidates (-64.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Merged error: 6.3b

Counts

172 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
4.7b	(/.f64 (.f64 M D) (.f64 2.0 d))
10.4b	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
11.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2)) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))))))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
402.0ms	(.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4986	1788
1	4986	1788

prune132.0ms

Filtered

79 candidates to 122 candidates (-54.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Merged error: 6.3b

Counts

130 → 8

regimes1.5s

Accuracy

57% (1.5b remaining)

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

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	169	68
1	169	68

end0.0ms

sample1.4s

Algorithm

intervals

Results

615.0ms	8000×	body	80	valid
246.0ms	3134×	body	80	nan
107.0ms	1331×	body	80	invalid

Details

analyze2.2s

sample54.0ms

simplify56.0ms

prune5.0ms

localize13.0ms

rewrite34.0ms

series636.0ms

simplify66.0ms

prune178.0ms

localize17.0ms

rewrite37.0ms

series684.0ms

simplify39.0ms

prune143.0ms

localize18.0ms

rewrite40.0ms

series680.0ms

simplify64.0ms

prune172.0ms

localize15.0ms

rewrite35.0ms

series599.0ms

simplify59.0ms

prune132.0ms

regimes1.5s

bsearch1.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling