Details

Time bar (total: 9.4s)

sample47.0ms

Algorithm
intervals
Results
16.0ms310×body80valid
6.0ms109×body80nan

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

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))

rewrite35.0ms

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:
11.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
399.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
364.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
680.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify77.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091076
12742997
25002994

prune386.0ms

Filtered
125 candidates to 81 candidates (64.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.9b

localize18.0ms

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))))

rewrite85.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
53.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
18.0ms
(* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0))
3.0ms
(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:
35.0ms
(/ (* M D) (* 2.0 d))
621.0ms
(* (* (* (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))
276.0ms
(sqrt (- 1.0 (* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))))

simplify116.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
08771782
145031603
250021576

prune427.0ms

Filtered
154 candidates to 78 candidates (50.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize24.0ms

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))))

rewrite133.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
95.0ms
(* (* (* (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))))

series938.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
595.0ms
(* (* (* (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))
283.0ms
(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))))

simplify134.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
012813578
145423088
250033022

prune449.0ms

Filtered
246 candidates to 76 candidates (30.9%)
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))

rewrite39.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* 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)))))
20.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

series1.3s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
474.0ms
(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)))))
772.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

simplify102.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
06991398
134291231
250011224

prune386.0ms

Filtered
122 candidates to 71 candidates (58.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.2b

regimes601.0ms

Accuracy

0% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 7.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02821
12821

end0.0ms

sample1.1s

Algorithm
intervals
Results
501.0ms9377×body80valid
171.0ms3069×body80nan