Details

Time bar (total: 9.3s)

sample47.0ms

Algorithm
intervals
Results
18.0ms310×body80valid
6.0ms109×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(/ (* M D) (* 2.0 d))
6.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
404.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
31.0ms
(/ (* M D) (* 2.0 d))
358.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
660.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091075
12742997
25002994

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.9b

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.4b
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
4.9b
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
6.5b
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
210×add-exp-log
121×prod-exp
43×div-exp
33×add-cbrt-cube
31×associate-*r*
30×pow-exp
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity times-frac
19×cbrt-unprod
9×cbrt-prod
7×pow1 cbrt-undiv
6×pow-to-exp unpow-prod-down
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div associate-*l* *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* flip-- associate-/l*
Counts
4 → 142
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
11.0ms
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
2.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))

series1.4s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
597.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
443.0ms
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
284.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))

simplify125.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08771783
145031603
250021576

prune431.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize25.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* M D) (* 2.0 d))
4.0b
(/ (* M D) (* 2.0 d))
4.4b
(* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
6.5b
(sqrt (- 1.0 (* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
929×add-exp-log
618×prod-exp
201×div-exp
160×pow-exp
56×add-cbrt-cube
34×cbrt-unprod
32×pow-to-exp
24×add-sqr-sqrt
22×times-frac associate-*r*
18×add-cube-cbrt *-un-lft-identity
13×cbrt-undiv
10×pow1 cbrt-prod
4×add-log-exp
3×pow-prod-down sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* *-commutative flip--
Counts
4 → 234
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
3.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))))

series948.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
601.0ms
(* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))
291.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))) (/ (cbrt h) l))))

simplify143.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
012813578
145423088
250033022

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:

4.0b
(/ (* M D) (* 2.0 d))
4.0b
(/ (* M D) (* 2.0 d))
6.5b
(sqrt (- 1.0 (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))
6.9b
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
96×add-exp-log
46×prod-exp
36×add-cbrt-cube
24×div-exp
22×associate-*r*
20×times-frac
19×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
10×cbrt-undiv pow-exp
9×cbrt-prod
7×pow1
4×add-log-exp
3×sqrt-prod div-inv
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* pow-prod-down *-commutative flip--
Counts
4 → 110
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))
13.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

series1.1s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))
285.0ms
(sqrt (- 1.0 (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l)))))
796.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

simplify98.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
06991397
134291231
250011224

prune420.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.2b

regimes656.0ms

Accuracy

0% (1.1b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 7.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03322
13322

end0.0ms

sample1.2s

Algorithm
intervals
Results
562.0ms9377×body80valid
193.0ms3069×body80nan