Details

Time bar (total: 47.0s)

sample46.0ms

Algorithm
intervals
Results
17.0ms303×body80valid
7.0ms123×body80nan

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.8b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0b
(/ (* M D) (* 2.0 d))
7.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
453×add-sqr-sqrt
342×times-frac
307×associate-*l*
186×associate-*r*
178×unpow-prod-down *-un-lft-identity
169×add-cube-cbrt
118×unswap-sqr
67×add-exp-log
52×*-commutative
41×sqrt-prod
30×difference-of-squares
27×prod-exp
23×add-cbrt-cube
19×div-exp
16×associate-/l*
15×associate-/r*
11×associate-*r/
10×pow-exp
9×pow1
7×cbrt-unprod sqr-pow
5×cbrt-undiv
4×sqrt-div distribute-lft-out-- add-log-exp
3×clear-num div-inv
2×pow-to-exp flip3-- frac-2neg pow-prod-down un-div-inv flip--
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 474
Calls
4 calls:
100.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
92.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms
(/ (* M D) (* 2.0 d))
62.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
426.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
371.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
684.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify86.0ms

Algorithm
egg-herbie
Counts
486 → 486
Iterations

Useful iterations: 1 (42.0ms)

IterNodesCost
021344008
150023951

prune1.4s

Filtered
486 candidates to 368 candidates (24.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4797486
Fresh000
Picked101
Done000
Total4807487

Merged error: 9.4b

Counts
487 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(/ (* M D) (* 2.0 d))
8.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite644.0ms

Algorithm
rewrite-expression-head
Rules
1113×add-sqr-sqrt
621×times-frac
417×unswap-sqr
381×associate-*l*
303×unpow-prod-down
249×*-un-lft-identity
244×add-cube-cbrt
241×associate-*r*
111×sqrt-prod
106×difference-of-squares
77×add-exp-log *-commutative
33×add-cbrt-cube
32×sqr-pow
30×prod-exp
28×associate-/l*
27×associate-/r*
23×div-exp
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*r/
7×pow1
4×clear-num div-inv add-log-exp
3×frac-2neg
2×pow-to-exp sqrt-div un-div-inv distribute-lft-out--
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
Counts
4 → 710
Calls
4 calls:
484.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
13.0ms
(/ (* M D) (* 2.0 d))
18.0ms
(/ (* M D) (* 2.0 d))
67.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts
4 → 12
Calls
4 calls:
378.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
34.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
709.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify150.0ms

Algorithm
egg-herbie
Counts
722 → 722
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
030649417
150019330

prune2.8s

Filtered
722 candidates to 554 candidates (23.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New7184722
Fresh426
Picked101
Done000
Total7236729

Merged error: 8.5b

Counts
729 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
5.7b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(/ (* M D) (* 2.0 d))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
3776×times-frac
2816×add-sqr-sqrt
2621×associate-*l*
1763×unpow-prod-down
1548×*-un-lft-identity
1544×add-cube-cbrt
1058×associate-*r*
613×unswap-sqr
558×distribute-lft-neg-in distribute-rgt-neg-in
327×*-commutative
198×associate-/l*
186×neg-mul-1
69×sqrt-prod
64×difference-of-squares
58×add-exp-log
38×sqr-pow
34×associate-/r*
33×add-cbrt-cube
20×div-exp
19×prod-exp
14×div-inv
10×cbrt-undiv
9×cbrt-unprod
5×pow1 pow-exp
4×add-log-exp
3×frac-2neg clear-num
2×sqrt-div distribute-lft-out--
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 distribute-frac-neg distribute-rgt-neg-out flip--
Counts
4 → 2398
Calls
4 calls:
3.3s
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
110.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
16.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
382.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
705.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
29.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(/ (* M D) (* 2.0 d))

simplify439.0ms

Algorithm
egg-herbie
Counts
2410 → 2410
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0500140130

prune9.1s

Filtered
2410 candidates to 1639 candidates (32.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New240732410
Fresh235
Picked101
Done000
Total241062416

Merged error: 8.5b

Counts
2416 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l)
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(* (/ (- h) -1) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l))

rewrite949.0ms

Algorithm
rewrite-expression-head
Rules
4716×times-frac
4351×associate-/l*
4239×add-sqr-sqrt
3562×unpow-prod-down
2916×*-un-lft-identity
2915×add-cube-cbrt
2528×frac-times
2344×associate-*r*
1918×associate-*l*
652×unswap-sqr
629×*-commutative
555×associate-/r*
486×distribute-lft-neg-in distribute-rgt-neg-in
180×clear-num
179×frac-2neg
162×neg-mul-1
158×associate-*r/
117×add-exp-log
49×div-exp
42×add-cbrt-cube
36×prod-exp
29×div-inv
26×sqr-pow
16×associate-*l/
15×pow-exp
13×cbrt-undiv
12×cbrt-unprod
6×pow1
4×add-log-exp
3×pow-to-exp
2×un-div-inv
1×distribute-lft-neg-out distribute-frac-neg pow-prod-down
Counts
4 → 4245
Calls
4 calls:
52.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l)
12.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(/ (* M D) (* 2.0 d))
379.0ms
(* (/ (- h) -1) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l))

series1.3s

Counts
4 → 12
Calls
4 calls:
646.0ms
(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l)
29.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))
582.0ms
(* (/ (- h) -1) (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l))

simplify811.0ms

Algorithm
egg-herbie
Counts
4257 → 4257
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
0524265812

prune19.2s

Filtered
4257 candidates to 3327 candidates (21.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New425434257
Fresh325
Picked101
Done000
Total425854263

Merged error: 8.5b

Counts
4263 → 5

regimes792.0ms

Accuracy

0% (0.9b remaining)

Error of 8.8b against oracle of 7.9b and baseline of 8.8b

bsearch0.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03819
14219
25319
35819
45819

end0.0ms

sample1.3s

Algorithm
intervals
Results
599.0ms9317×body80valid
208.0ms3066×body80nan