Details

sample53.0ms

Algorithm

intervals

Results

25.0ms	296×	body	80	valid
7.0ms	84×	body	80	nan

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b	(/ (* M D) (* 2.0 d))
11.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite37.0ms

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×	`sqrt-div` `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 → 113

Calls

4 calls:

8.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

413.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
368.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms	(/ (* M D) (* 2.0 d))
688.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune398.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.3b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.3b	(/ (* M D) (* 2.0 d))
5.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite42.0ms

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×	`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 → 128

Calls

4 calls:

2.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
16.0ms	(* (* (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:

369.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
692.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
33.0ms	(/ (* M D) (* 2.0 d))
717.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify89.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	752	1136
1	3460	1014
2	5002	1001

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

4.3b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
5.3b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* M D) (* 2.0 d))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite106.0ms

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×	`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 → 332

Calls

4 calls:

47.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.7s

Counts

4 → 12

Calls

4 calls:

899.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
28.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))
729.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify125.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1558	4491
1	4576	3065
2	5002	3053

prune419.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize18.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ (* M D) (* 2.0 d))
5.3b	(/ (* M D) (* 2.0 d))
5.7b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-exp-log`
95×	`prod-exp`
44×	`div-exp`
42×	`add-cbrt-cube`
25×	`pow-exp`
19×	`add-sqr-sqrt`
16×	`associate-r`
15×	`cbrt-unprod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`cbrt-undiv` `associate-l`
8×	`rec-exp` `1-exp`
6×	`pow1` `unpow-prod-down`
5×	`pow-to-exp`
4×	`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 → 134

Calls

4 calls:

4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.5s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(/ (* M D) (* 2.0 d))
686.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
705.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify82.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	701	1167
1	3212	993
2	5001	980

prune397.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

regimes686.0ms

Accuracy

0% (1.4b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 8.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	34
1	34	34

end0.0ms

sample1.5s

Algorithm

intervals

Results

796.0ms	9291×	body	80	valid
281.0ms	3081×	body	80	nan