Details

sample49.0ms

Algorithm

intervals

Results

18.0ms	303×	body	80	valid
8.0ms	123×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0b	(/ (* M D) (* 2.0 d))
7.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

453×	`add-sqr-sqrt`
342×	`times-frac`
307×	`associate-l`
186×	`associate-r`
178×	`unpow-prod-down` `*-un-lft-identity`
169×	`add-cube-cbrt`
118×	`unswap-sqr`
67×	`add-exp-log`
52×	`*-commutative`
41×	`sqrt-prod`
30×	`difference-of-squares`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp`
16×	`associate-/l*`
15×	`associate-/r*`
11×	`associate-*r/`
10×	`pow-exp`
9×	`pow1`
7×	`cbrt-unprod` `sqr-pow`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `div-inv`
2×	`pow-to-exp` `flip3--` `frac-2neg` `pow-prod-down` `un-div-inv` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 482

Calls

4 calls:

100.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
129.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms	(/ (* M D) (* 2.0 d))
61.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

431.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
389.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms	(/ (* M D) (* 2.0 d))
741.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify96.0ms

Algorithm

egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2155	4067
1	5001	4010

prune1.6s

Filtered

494 candidates to 375 candidates (24.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	487	7	494
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	488	7	495

Merged error: 9.4b

Counts

495 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.0b	(/ (* M D) (* 2.0 d))
6.0b	(/ (* M D) (* 2.0 d))
8.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite730.0ms

Algorithm

rewrite-expression-head

Rules

1113×	`add-sqr-sqrt`
621×	`times-frac`
417×	`unswap-sqr`
381×	`associate-l`
303×	`unpow-prod-down`
249×	`*-un-lft-identity`
244×	`add-cube-cbrt`
241×	`associate-r`
111×	`sqrt-prod`
106×	`difference-of-squares`
77×	`add-exp-log` `*-commutative`
33×	`add-cbrt-cube`
32×	`sqr-pow`
30×	`prod-exp`
28×	`associate-/l*`
27×	`associate-/r*`
23×	`div-exp`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-*r/`
7×	`pow1`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg`
2×	`pow-to-exp` `sqrt-div` `un-div-inv` `distribute-lft-out--`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`

Counts

4 → 718

Calls

4 calls:

580.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
13.0ms	(/ (* M D) (* 2.0 d))
13.0ms	(/ (* M D) (* 2.0 d))
64.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts

4 → 12

Calls

4 calls:

402.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
31.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(/ (* M D) (* 2.0 d))
767.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify169.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	3083	9482
1	5002	9395

prune2.9s

Filtered

730 candidates to 563 candidates (22.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	727	3	730
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	731	6	737

Merged error: 8.5b

Counts

737 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
5.7b	(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
6.0b	(/ (* M D) (* 2.0 d))
6.0b	(/ (* M D) (* 2.0 d))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1501×	`times-frac`
1422×	`add-sqr-sqrt`
1052×	`associate-r`
692×	`unpow-prod-down`
637×	`*-un-lft-identity`
633×	`add-cube-cbrt`
457×	`associate-l`
368×	`unswap-sqr`
191×	`associate-/l*`
152×	`*-commutative`
69×	`sqrt-prod`
64×	`difference-of-squares`
58×	`add-exp-log`
33×	`add-cbrt-cube`
27×	`associate-/r*`
24×	`sqr-pow`
20×	`div-exp`
19×	`prod-exp`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
7×	`div-inv`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`sqrt-div` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 1152

Calls

4 calls:

1.2s	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
86.0ms	(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
17.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(/ (* M D) (* 2.0 d))

series1.2s

Counts

4 → 12

Calls

4 calls:

446.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
708.0ms	(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
35.0ms	(/ (* M D) (* 2.0 d))
45.0ms	(/ (* M D) (* 2.0 d))

simplify211.0ms

Algorithm

egg-herbie

Counts

1164 → 1164

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	15397

prune4.5s

Filtered

1164 candidates to 866 candidates (25.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1161	3	1164
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	1164	6	1170

Merged error: 8.5b

Counts

1170 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (pow (/ (* M D) d) (/ 2.0 2)) l)
6.0b	(/ (* M D) (* 2.0 d))
6.0b	(/ (* M D) d)
6.0b	(* (* h (pow (/ 1 2.0) (/ 2.0 2))) (/ (pow (/ (* M D) d) (/ 2.0 2)) l))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

797×	`times-frac`
654×	`add-sqr-sqrt`
400×	`*-un-lft-identity`
392×	`add-cube-cbrt`
372×	`unpow-prod-down`
315×	`associate-r`
202×	`add-exp-log`
195×	`associate-l`
131×	`unswap-sqr`
113×	`associate-/l*`
91×	`prod-exp`
74×	`div-exp`
56×	`*-commutative`
50×	`associate-*r/`
48×	`pow-exp`
35×	`add-cbrt-cube`
22×	`sqr-pow`
21×	`associate-/r*`
14×	`pow-to-exp`
13×	`div-inv`
11×	`cbrt-unprod`
9×	`pow1` `cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`clear-num`
4×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`un-div-inv`

Counts

4 → 764

Calls

4 calls:

24.0ms	(/ (pow (/ (* M D) d) (/ 2.0 2)) l)
13.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(/ (* M D) d)
105.0ms	(* (* h (pow (/ 1 2.0) (/ 2.0 2))) (/ (pow (/ (* M D) d) (/ 2.0 2)) l))

series1.3s

Counts

4 → 12

Calls

4 calls:

491.0ms	(/ (pow (/ (* M D) d) (/ 2.0 2)) l)
35.0ms	(/ (* M D) (* 2.0 d))
22.0ms	(/ (* M D) d)
779.0ms	(* (* h (pow (/ 1 2.0) (/ 2.0 2))) (/ (pow (/ (* M D) d) (/ 2.0 2)) l))

simplify164.0ms

Algorithm

egg-herbie

Counts

776 → 776

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3107	8262
1	5001	8127

prune3.4s

Filtered

776 candidates to 574 candidates (26.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	775	1	776
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	777	5	782

Merged error: 8.5b

Counts

782 → 5

regimes778.0ms

Accuracy

0% (1.0b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 8.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

608.0ms	9317×	body	80	valid
196.0ms	3066×	body	80	nan