Details

Time bar (total: 10.7s)

sample46.0ms

Algorithm
intervals
Results
13.0ms282×body80valid
5.0ms100×body80nan

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize13.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b
(/ (* M D) (* 2.0 d))
13.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite73.0ms

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:
18.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
441.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
392.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
689.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301135
127791057
250021054

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.3b
(/ (* M D) (* 2.0 d))
8.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite73.0ms

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:
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
16.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
15.0ms
(/ (* M D) (* 2.0 d))
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
700.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
391.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
29.0ms
(/ (* M D) (* 2.0 d))
731.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify63.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0576880
12585798
25001796

prune373.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
5.1b
(/ (* 2.0 d) (* M D))
5.2b
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
8.2b
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
164×add-exp-log
67×div-exp
64×prod-exp
32×pow-exp
31×add-sqr-sqrt
24×times-frac associate-*l*
23×unpow-prod-down add-cbrt-cube
21×*-un-lft-identity
18×add-cube-cbrt
10×rec-exp 1-exp
6×cbrt-undiv cbrt-unprod div-inv
5×pow1 sqrt-prod unswap-sqr
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r*
2×pow-to-exp frac-2neg sqrt-div clear-num 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 → 143
Calls
4 calls:
22.0ms
(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
12.0ms
(/ (* 2.0 d) (* M D))
16.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
42.0ms
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
705.0ms
(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
29.0ms
(/ (* 2.0 d) (* M D))
325.0ms
(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
741.0ms
(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)

simplify78.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08181271
132661181
250011163

prune437.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.4b

localize28.0ms

Local error

Found 4 expressions with local error:

5.2b
(sqrt (- 1.0 (/ (* (pow (/ (sqrt 1) (* (cbrt (/ (* 2.0 d) (* M D))) (cbrt (/ (* 2.0 d) (* M D))))) 2.0) (* (pow (/ 1 (cbrt (/ (* 2.0 d) (* M D)))) 2.0) h)) l)))
15.0b
(cbrt (/ (* 2.0 d) (* M D)))
15.0b
(cbrt (/ (* 2.0 d) (* M D)))
15.0b
(cbrt (/ (* 2.0 d) (* M D)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt
5×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div times-frac pow1/3 div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 67
Calls
4 calls:
16.0ms
(sqrt (- 1.0 (/ (* (pow (/ (sqrt 1) (* (cbrt (/ (* 2.0 d) (* M D))) (cbrt (/ (* 2.0 d) (* M D))))) 2.0) (* (pow (/ 1 (cbrt (/ (* 2.0 d) (* M D)))) 2.0) h)) l)))
6.0ms
(cbrt (/ (* 2.0 d) (* M D)))
6.0ms
(cbrt (/ (* 2.0 d) (* M D)))
6.0ms
(cbrt (/ (* 2.0 d) (* M D)))

series1.1s

Counts
4 → 12
Calls
4 calls:
717.0ms
(sqrt (- 1.0 (/ (* (pow (/ (sqrt 1) (* (cbrt (/ (* 2.0 d) (* M D))) (cbrt (/ (* 2.0 d) (* M D))))) 2.0) (* (pow (/ 1 (cbrt (/ (* 2.0 d) (* M D)))) 2.0) h)) l)))
115.0ms
(cbrt (/ (* 2.0 d) (* M D)))
111.0ms
(cbrt (/ (* 2.0 d) (* M D)))
114.0ms
(cbrt (/ (* 2.0 d) (* M D)))

simplify71.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
02141031
1525973
22219967
35001965

prune410.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.4b

regimes795.0ms

Accuracy

46% (1.1b remaining)

Error of 8.9b against oracle of 7.8b and baseline of 9.9b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05442
15442

end0.0ms

sample1.2s

Algorithm
intervals
Results
451.0ms9320×body80valid
154.0ms3037×body80nan