Details

sample45.0ms

Algorithm

intervals

Results

16.0ms	282×	body	80	valid
5.0ms	100×	body	80	nan

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b	(/ (* M D) (* 2.0 d))
13.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite71.0ms

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:

17.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.0ms	(/ (* M D) (* 2.0 d))
30.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

454.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
394.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms	(/ (* M D) (* 2.0 d))
712.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

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

prune384.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.2b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.3b	(/ (* M D) (* 2.0 d))
8.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite85.0ms

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:

37.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
14.0ms	(/ (* M D) (* 2.0 d))
23.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.9s

Counts

4 → 12

Calls

4 calls:

728.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
403.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
29.0ms	(/ (* M D) (* 2.0 d))
748.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify85.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (74.0ms)

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

prune381.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.4b

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))
5.1b	(/ (* 2.0 d) (* M D))
5.2b	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))))
8.2b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

435×	`add-exp-log`
230×	`prod-exp`
152×	`div-exp`
80×	`pow-exp`
44×	`rec-exp` `1-exp`
34×	`add-sqr-sqrt`
30×	`times-frac` `add-cbrt-cube`
25×	`associate-l`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt` `unpow-prod-down`
16×	`associate-r`
11×	`cbrt-unprod`
7×	`pow1`
6×	`cbrt-undiv` `div-inv`
5×	`pow-to-exp` `unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod`
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` `associate-/r/` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 200

Calls

4 calls:

56.0ms	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))
12.0ms	(/ (* 2.0 d) (* M D))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))))
44.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

series1.8s

Counts

4 → 12

Calls

4 calls:

726.0ms	(* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))
29.0ms	(/ (* 2.0 d) (* M D))
324.0ms	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) (/ 1 l))))
752.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

simplify105.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1133	1861
1	4277	1720
2	5002	1700

prune456.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.4b

localize19.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* 2.0 d) (* M D))
5.1b	(/ (* 2.0 d) (* M D))
5.2b	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
5.8b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
38×	`prod-exp`
30×	`div-exp` `add-cbrt-cube`
27×	`add-sqr-sqrt`
24×	`associate-l`
23×	`unpow-prod-down`
22×	`times-frac`
17×	`*-un-lft-identity`
16×	`add-cube-cbrt` `pow-exp`
9×	`cbrt-unprod`
8×	`cbrt-undiv`
6×	`div-inv`
5×	`pow1` `rec-exp` `1-exp` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `*-commutative` `flip--`

Counts

4 → 116

Calls

4 calls:

12.0ms	(/ (* 2.0 d) (* M D))
12.0ms	(/ (* 2.0 d) (* M D))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
43.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* 2.0 d) (* M D))
29.0ms	(/ (* 2.0 d) (* M D))
334.0ms	(sqrt (- 1.0 (* (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
770.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

simplify68.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	662	1203
1	2640	1092
2	5001	1075

prune423.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.4b

regimes730.0ms

Accuracy

0% (2.0b remaining)

Error of 9.5b against oracle of 7.5b and baseline of 9.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	20
1	36	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

462.0ms	9320×	body	80	valid
158.0ms	3037×	body	80	nan