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

sample53.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
6.0ms	81×	body	80	nan
4.0ms	46×	body	80	invalid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

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: 17.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
5.4b	(/.f64 (.f64 M D) (.f64 2.0 d))
5.6b	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
11.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

rewrite33.0ms

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:

8.0ms	(.f64 w0 (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))
4.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

series637.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(.f64 w0 (sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0) (/.f64 h l)))))
13.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
189.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))))
226.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0) (/.f64 h l))

simplify67.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	1927
1	4977	1927

prune192.0ms

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: 10.1b

Counts

126 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.6b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
5.4b	(/.f64 (.f64 M D) (.f64 2.0 d))
5.6b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
6.5b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

rewrite40.0ms

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:

12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
7.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

series668.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(.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))
136.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) 2.0)) (/.f64 1 l))))
330.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5085	1894

prune147.0ms

Filtered

76 candidates to 140 candidates (-84.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	142	6	148

Merged error: 9.4b

Counts

148 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (.f64 M D) (.f64 2.0 d))
5.4b	(/.f64 (.f64 M D) (.f64 2.0 d))
5.5b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))
5.6b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2))) (/.f64 1 l))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))
10.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2))) (/.f64 1 l))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
7.0ms	(/.f64 (.f64 M D) (.f64 2.0 d))
332.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2)))
136.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2.0 d)) (/.f64 2.0 2))) (pow.f64 (/.f64 (.f64 M D) (*.f64 2.0 d)) (/.f64 2.0 2))) (/.f64 1 l))))

simplify64.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4981	1292
1	4981	1292

prune136.0ms

Filtered

66 candidates to 100 candidates (-51.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Merged error: 9.4b

Counts

106 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b	(*.f64 (/.f64 M 2.0) (/.f64 D d))
4.6b	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
5.6b	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
6.5b	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

rewrite39.0ms

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:

10.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))
11.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
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))))
6.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

series666.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (/.f64 M 2.0) (/.f64 D d))
191.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))
132.0ms	(sqrt.f64 (-.f64 1.0 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0)) (/.f64 1 l))))
335.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2.0) (/.f64 D d)) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4979	2107
1	4979	2107

prune146.0ms

Filtered

101 candidates to 164 candidates (-62.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	164	6	170

Merged error: 8.9b

Counts

170 → 6

regimes1.3s

Accuracy

0% (1.7b remaining)

Error of 9.1b against oracle of 7.5b and baseline of 9.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	34
1	110	34

end0.0ms

sample1.4s

Algorithm

intervals

Results

615.0ms	8000×	body	80	valid
243.0ms	3001×	body	80	nan
113.0ms	1342×	body	80	invalid

Details

analyze2.2s

sample53.0ms

simplify53.0ms

prune5.0ms

localize14.0ms

rewrite33.0ms

series637.0ms

simplify67.0ms

prune192.0ms

localize16.0ms

rewrite40.0ms

series668.0ms

simplify37.0ms

prune147.0ms

localize18.0ms

rewrite34.0ms

series484.0ms

simplify64.0ms

prune136.0ms

localize17.0ms

rewrite39.0ms

series666.0ms

simplify65.0ms

prune146.0ms

regimes1.3s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling