Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	302×	body	80	valid
7.0ms	98×	body	80	nan

simplify52.0ms

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: 13.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b	(/ (* M D) (* 2.0 d))
12.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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:

397.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
358.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms	(/ (* M D) (* 2.0 d))
673.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (60.0ms)

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

prune384.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 7.5b

Counts

134 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.6b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(/ (* M D) (* 2.0 d))
7.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 104

Calls

4 calls:

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

series1.9s

Counts

4 → 12

Calls

4 calls:

356.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
671.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
27.0ms	(/ (* M D) (* 2.0 d))
892.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify65.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	576	880
1	2585	798
2	5001	796

prune303.0ms

Filtered

116 candidates to 78 candidates (67.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	117	5	122

Merged error: 6.5b

Counts

122 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.9b	(/ (* M D) (* 2.0 d))
4.9b	(/ (* M D) (* 2.0 d))
7.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
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×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 158

Calls

4 calls:

14.0ms	(/ (* (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))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.4s

Counts

4 → 12

Calls

4 calls:

677.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
32.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
699.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify88.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	882	1759
1	3170	1336
2	5001	1332

prune348.0ms

Filtered

170 candidates to 80 candidates (47.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	168	7	175

Merged error: 6.3b

Counts

175 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* 2.0 d))
4.9b	(/ (* M D) (* 2.0 d))
5.6b	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
7.2b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

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-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/r*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 108

Calls

4 calls:

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

series1.3s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
581.0ms	(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
705.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify59.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	510	871
1	2271	740
2	5001	740

prune324.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	120	7	127

Merged error: 6.3b

Counts

127 → 7

regimes555.0ms

Accuracy

0% (1.3b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	16
1	24	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

684.0ms	9329×	body	80	valid
243.0ms	3171×	body	80	nan