Details

Time bar (total: 10.5s)

sample44.0ms

Algorithm
intervals
Results
17.0ms301×body80valid
6.0ms104×body80nan

simplify52.0ms

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: 11.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b
(/ (* M D) (* 2.0 d))
9.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite32.0ms

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:
6.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
408.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
357.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
31.0ms
(/ (* M D) (* 2.0 d))
678.0ms
(* (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
06301135
127791057
250021054

prune429.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

3.8b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.6b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.8b
(/ (* M D) (* 2.0 d))

rewrite31.0ms

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
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
8.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
369.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
703.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
727.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
32.0ms
(/ (* M D) (* 2.0 d))

simplify66.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0576881
12585798
25001796

prune380.0ms

Filtered
116 candidates to 79 candidates (68.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.6b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 158
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
18.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
736.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
711.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
28.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))

simplify83.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08821759
131701336
250021332

prune485.0ms

Filtered
170 candidates to 80 candidates (47.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))
5.7b
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 108
Calls
4 calls:
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

series1.4s

Counts
4 → 12
Calls
4 calls:
740.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
29.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
597.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

simplify63.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0510871
12272740
25001740

prune402.0ms

Filtered
120 candidates to 79 candidates (65.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.1b

regimes883.0ms

Accuracy

0% (1.3b remaining)

Error of 8.7b against oracle of 7.3b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02316
12316

end0.0ms

sample1.1s

Algorithm
intervals
Results
531.0ms9295×body80valid
184.0ms3096×body80nan