Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	291×	body	80	valid
4.0ms	79×	body	80	nan

simplify60.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b	(/ (* M D) (* 2.0 d))
10.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite40.0ms

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:

9.0ms	(* 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))))
4.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

411.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
357.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms	(/ (* M D) (* 2.0 d))
679.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (65.0ms)

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

prune434.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize15.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
3.6b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.9b	(/ (* M D) (* 2.0 d))
6.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite45.0ms

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))))
18.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

380.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
695.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
34.0ms	(/ (* M D) (* 2.0 d))
720.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify92.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (79.0ms)

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

prune424.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize18.0ms

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)) (/ 1 l))
4.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(/ (* M D) (* 2.0 d))
5.9b	(/ (* M D) (* 2.0 d))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

1402×	`add-exp-log`
907×	`prod-exp`
366×	`div-exp`
305×	`pow-exp`
61×	`pow-to-exp`
57×	`rec-exp` `1-exp`
51×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`pow1` `unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 340

Calls

4 calls:

54.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))

series1.5s

Counts

4 → 12

Calls

4 calls:

703.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
730.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
29.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(/ (* M D) (* 2.0 d))

simplify125.0ms

Algorithm

egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1604	4551
1	4628	3125
2	5001	3125

prune480.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(/ (* M D) (* 2.0 d))
6.0b	(* (* M D) (/ 1 (* 2.0 d)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

3771×	`add-exp-log`
2746×	`prod-exp`
825×	`pow-exp`
818×	`div-exp`
269×	`rec-exp` `1-exp`
101×	`pow-to-exp`
60×	`add-cbrt-cube`
28×	`cbrt-unprod`
23×	`associate-r`
21×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
11×	`pow1` `cbrt-undiv` `associate-l`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
2×	`associate-*r/` `un-div-inv` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 679

Calls

4 calls:

61.0ms	(* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(* (* M D) (/ 1 (* 2.0 d)))

series1.5s

Counts

4 → 12

Calls

4 calls:

710.0ms	(* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
737.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
37.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(* (* M D) (/ 1 (* 2.0 d)))

simplify124.0ms

Algorithm

egg-herbie

Counts

691 → 691

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	3382	10136
1	5002	7037

prune574.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

regimes766.0ms

Accuracy

0% (1.5b remaining)

Error of 8.9b against oracle of 7.4b and baseline of 8.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

508.0ms	9453×	body	80	valid
161.0ms	3018×	body	80	nan