Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	301×	body	80	valid
4.0ms	85×	body	80	nan

simplify54.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
3.1b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.8b	(/ (* M D) (* 2.0 d))
10.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite74.0ms

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:

7.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
17.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
12.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

529.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
393.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
30.0ms	(/ (* M D) (* 2.0 d))
644.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify77.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (60.0ms)

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

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize19.0ms

Local error

Found 4 expressions with local error:

3.1b	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
5.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.9b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
7.8b	(/ (* M D) (* 2.0 d))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
92×	`prod-exp`
40×	`div-exp`
32×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
25×	`pow-exp`
22×	`associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
12×	`cbrt-unprod`
11×	`times-frac`
8×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `-commutative` `div-inv`
2×	`sqrt-div` `pow-prod-down` `sqr-pow`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l`

Counts

4 → 145

Calls

4 calls:

17.0ms	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
25.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
38.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
12.0ms	(/ (* M D) (* 2.0 d))

series1.7s

Counts

4 → 12

Calls

4 calls:

394.0ms	(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
678.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
641.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
28.0ms	(/ (* M D) (* 2.0 d))

simplify89.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	807	1302
1	3683	1167
2	5001	1154

prune414.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
7.8b	(/ (* M D) (* 2.0 d))
7.8b	(/ (* M D) (* 2.0 d))

rewrite205.0ms

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:

25.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
115.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
12.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(/ (* M D) (* 2.0 d))

series1.4s

Counts

4 → 12

Calls

4 calls:

687.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
653.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
25.0ms	(/ (* M D) (* 2.0 d))
25.0ms	(/ (* M D) (* 2.0 d))

simplify129.0ms

Algorithm

egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1604	4551
1	4639	3125
2	5002	3125

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
5.9b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))
7.7b	(/ (* 2.0 d) (* M D))
7.8b	(/ (* M D) (* 2.0 d))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

3650×	`add-exp-log`
2250×	`prod-exp`
1218×	`div-exp`
844×	`pow-exp`
279×	`rec-exp` `1-exp`
105×	`pow-to-exp`
51×	`add-cbrt-cube`
32×	`add-sqr-sqrt`
31×	`times-frac`
25×	`associate-l`
23×	`unpow-prod-down` `*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`cbrt-unprod`
16×	`associate-r`
11×	`cbrt-undiv`
7×	`div-inv`
6×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv`

Counts

4 → 676

Calls

4 calls:

42.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
169.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))
12.0ms	(/ (* 2.0 d) (* M D))
12.0ms	(/ (* M D) (* 2.0 d))

series1.4s

Counts

4 → 12

Calls

4 calls:

682.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
670.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))
25.0ms	(/ (* 2.0 d) (* M D))
35.0ms	(/ (* M D) (* 2.0 d))

simplify136.0ms

Algorithm

egg-herbie

Counts

688 → 688

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	3420	10131
1	5002	9886

prune608.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

regimes584.0ms

Accuracy

0% (1.7b remaining)

Error of 9.2b against oracle of 7.5b and baseline of 9.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

469.0ms	9262×	body	80	valid
167.0ms	3051×	body	80	nan