Details

Time bar (total: 9.2s)

sample43.0ms

Algorithm
intervals
Results
18.0ms291×body80valid
5.0ms90×body80nan

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.4b
(* (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×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:
8.0ms
(* 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))))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
395.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
358.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
669.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06301136
127791057
250011054

prune432.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
684.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
27.0ms
(/ (* M D) (* 2.0 d))
356.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
705.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify64.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0576880
12585798
25001796

prune373.0ms

Filtered
116 candidates to 77 candidates (66.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))
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)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* 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-- distribute-lft-out-- difference-of-squares
Counts
4 → 98
Calls
4 calls:
13.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

series1.1s

Counts
4 → 12
Calls
4 calls:
707.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
386.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify51.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0457979
11916874
25001872

prune396.0ms

Filtered
110 candidates to 73 candidates (66.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) l)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
37×prod-exp
31×add-cbrt-cube
16×div-exp
12×add-sqr-sqrt
11×cbrt-unprod
10×pow-exp
9×*-un-lft-identity associate-*l*
8×cbrt-undiv
7×add-cube-cbrt
6×unpow-prod-down
5×pow1 sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r* *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
16.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) l)))

series1.1s

Counts
4 → 12
Calls
4 calls:
615.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
26.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
397.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) l)))

simplify55.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05151283
120321140
250011134

prune405.0ms

Filtered
116 candidates to 72 candidates (62.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

regimes469.0ms

Accuracy

0% (2.2b remaining)

Error of 9.6b against oracle of 7.5b and baseline of 9.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921

end0.0ms

sample1.1s

Algorithm
intervals
Results
482.0ms9256×body80valid
169.0ms3135×body80nan