Details

Time bar (total: 9.5s)

sample45.0ms

Algorithm
intervals
Results
17.0ms310×body80valid
6.0ms109×body80nan

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

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))

rewrite37.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u 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 → 121
Calls
4 calls:
12.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms
(/ (* M D) (* 2.0 d))
3.0ms
(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:
403.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
359.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
675.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301135
127791057
250011054

prune427.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.9b

localize19.0ms

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))))

rewrite87.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 150
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(* (* (* (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:
27.0ms
(/ (* M D) (* 2.0 d))
592.0ms
(* (* (* (cbrt h) (cbrt h)) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (cbrt h) l))
448.0ms
(* (* (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))))

simplify124.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
08881860
145341666
250011635

prune504.0ms

Filtered
162 candidates to 93 candidates (57.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize20.0ms

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))))

rewrite154.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 242
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
117.0ms
(* (* (* (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))
4.0ms
(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))))

series947.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(/ (* M D) (* 2.0 d))
596.0ms
(* (* (* (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))))

simplify135.0ms

Algorithm
egg-herbie
Counts
254 → 254
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
012903674
145713053
250023048

prune536.0ms

Filtered
254 candidates to 93 candidates (36.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.4b

localize20.0ms

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))

rewrite40.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 118
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* M D) (* 2.0 d))
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)))))
20.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

series1.1s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
290.0ms
(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)))))
771.0ms
(* (* (cbrt h) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ (cbrt h) l))

simplify97.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07081477
134571311
250021304

prune444.0ms

Filtered
130 candidates to 79 candidates (60.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.2b

regimes626.0ms

Accuracy

2.1% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 7.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03126
13126

end0.0ms

sample1.2s

Algorithm
intervals
Results
535.0ms9377×body80valid
179.0ms3069×body80nan