Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	297×	body	80	valid
4.0ms	70×	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	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: 13.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
9.5b	(* (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×	`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:

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))))
8.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

412.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
366.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
668.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify70.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

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

prune401.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.5b	(/ (* M D) (* 2.0 d))

rewrite46.0ms

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:

21.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
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)
5.0ms	(/ (* M D) (* 2.0 d))

series1.8s

Counts

4 → 12

Calls

4 calls:

687.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
370.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
719.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
28.0ms	(/ (* M D) (* 2.0 d))

simplify85.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	752	1137
1	3460	1014
2	5002	1001

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))
5.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
30×	`add-cbrt-cube`
19×	`prod-exp`
14×	`add-sqr-sqrt`
12×	`div-exp`
9×	`associate-l` `cbrt-unprod`
8×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `pow-exp`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `sqrt-prod` `div-inv` `unswap-sqr`
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` `*-commutative` `flip--`

Counts

4 → 88

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))))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

373.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
28.0ms	(/ (* M D) (* 2.0 d))
28.0ms	(/ (* M D) (* 2.0 d))
724.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	442	888
1	1993	782
2	5001	781

prune363.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize21.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
5.1b	(/ (* 2.0 d) (* M D))
5.5b	(/ (* M D) (* 2.0 d))
5.6b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

rewrite48.0ms

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:

3.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
4.0ms	(/ (* 2.0 d) (* M D))
5.0ms	(/ (* M D) (* 2.0 d))
30.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

377.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) (/ 1 l))))
27.0ms	(/ (* 2.0 d) (* M D))
27.0ms	(/ (* M D) (* 2.0 d))
726.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

simplify88.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	739	1182
1	3340	1067
2	5003	1046

prune449.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

regimes808.0ms

Accuracy

0% (2.2b remaining)

Error of 9.0b against oracle of 6.9b and baseline of 9.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	18
1	33	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

488.0ms	9331×	body	80	valid
157.0ms	2962×	body	80	nan