Details

sample44.0ms

Algorithm

intervals

Results

18.0ms	299×	body	80	valid
6.0ms	97×	body	80	nan

simplify56.0ms

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

prune4.0ms

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: 15.6b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.3b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.5b	(/ (* M D) (* 2.0 d))
11.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite31.0ms

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))))
7.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
377.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
53.0ms	(/ (* M D) (* 2.0 d))
745.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (61.0ms)

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

prune396.0ms

Filtered

133 candidates to 89 candidates (66.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	10	134

Merged error: 8.1b

Counts

134 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.9b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.5b	(/ (* M D) (* 2.0 d))
7.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
11.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 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:

400.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
698.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
33.0ms	(/ (* M D) (* 2.0 d))
732.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify89.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	768	1192
1	3493	1070
2	5003	1057

prune349.0ms

Filtered

148 candidates to 82 candidates (55.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	149	9	158

Merged error: 7.9b

Counts

158 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
4.9b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.5b	(/ (* M D) (* 2.0 d))
6.5b	(/ (* M D) (* 2.0 d))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

1381×	`add-exp-log`
896×	`prod-exp`
362×	`div-exp`
300×	`pow-exp`
60×	`pow-to-exp`
57×	`rec-exp` `1-exp`
49×	`add-cbrt-cube`
20×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cbrt-undiv` `times-frac`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `pow-prod-down` `un-div-inv` `-commutative` `flip--`

Counts

4 → 324

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)) (/ 1 l))))
19.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series1.3s

Counts

4 → 12

Calls

4 calls:

363.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
869.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
37.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))

simplify127.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1537	4621
1	4209	3218
2	5002	3206

prune336.0ms

Filtered

336 candidates to 74 candidates (22.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	335	10	345

Merged error: 7.5b

Counts

345 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.6b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.5b	(/ (* M D) (* 2.0 d))
6.5b	(/ (* M D) (* 2.0 d))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-exp-log`
84×	`prod-exp`
40×	`div-exp` `add-cbrt-cube`
20×	`pow-exp`
14×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac`
10×	`cbrt-undiv`
8×	`rec-exp` `1-exp`
7×	`pow1`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `pow-prod-down` `un-div-inv` `-commutative` `flip--`

Counts

4 → 126

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) (/ 1 l)))))
15.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series1.1s

Counts

4 → 12

Calls

4 calls:

365.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
699.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
27.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(/ (* M D) (* 2.0 d))

simplify78.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	685	1303
1	3025	1139
2	5003	1121

prune300.0ms

Filtered

138 candidates to 72 candidates (52.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	137	11	148

Merged error: 7.5b

Counts

148 → 11

regimes1.0s

Accuracy

0% (1.4b remaining)

Error of 8.3b against oracle of 6.8b and baseline of 8.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

564.0ms	9372×	body	80	valid
195.0ms	3125×	body	80	nan