Details

sample44.0ms

Algorithm

intervals

Results

16.0ms	287×	body	80	valid
8.0ms	102×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	182	9
3	456	9
4	1557	9
5	5001	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 12.8b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
11.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 121

Calls

4 calls:

6.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

394.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
356.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
692.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	630	1135
1	2779	1057
2	5002	1054

prune414.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 6.1b

Counts

134 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

2.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))
10.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts

4 → 12

Calls

4 calls:

359.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
27.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(/ (* M D) (* 2.0 d))
677.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify68.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	595	1196
1	2618	1077
2	5001	1076

prune419.0ms

Filtered

130 candidates to 86 candidates (66.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Merged error: 5.4b

Counts

138 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

5.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))
6.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
35×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
14×	`add-sqr-sqrt`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

series1.6s

Counts

4 → 12

Calls

4 calls:

700.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(/ (* M D) (* 2.0 d))
868.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	512	859
1	2386	728
2	5001	728

prune396.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	119	8	127

Merged error: 5.4b

Counts

127 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
22.8b	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
22.8b	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
22.8b	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
21×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac` `div-exp`
11×	`prod-exp`
9×	`add-cbrt-cube`
5×	`pow-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/r*`
2×	`cbrt-undiv`
1×	`pow-to-exp` `frac-2neg` `clear-num` `cbrt-unprod` `associate-/l*`

Counts

4 → 83

Calls

4 calls:

8.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
5.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
5.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

series2.2s

Counts

4 → 12

Calls

4 calls:

696.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
499.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
495.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))
507.0ms	(cbrt (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	405	1075
1	1431	978
2	5001	972

prune464.0ms

Filtered

95 candidates to 78 candidates (82.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	95	8	103

Merged error: 5.4b

Counts

103 → 8

regimes814.0ms

Accuracy

-16.6% (1.6b remaining)

Error of 9.2b against oracle of 7.5b and baseline of 8.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	27
1	46	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

550.0ms	9309×	body	80	valid
186.0ms	3109×	body	80	nan