Details

Time bar (total: 10.9s)

sample55.0ms

Algorithm
intervals
Results
23.0ms299×body80valid
11.0ms98×body80nan

simplify58.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.8b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b
(/ (* M D) (* 2.0 d))
5.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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)))))
6.0ms
(/ (* M D) (* 2.0 d))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
411.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms
(/ (* M D) (* 2.0 d))
372.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
678.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify81.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06301135
127791057
250011054

prune405.0ms

Filtered
133 candidates to 89 candidates (66.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1267133
Fresh000
Picked101
Done000
Total1277134

Merged error: 7.9b

Counts
134 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
5.1b
(/ (* (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)))
5.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite30.0ms

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
(/ (* M D) (* 2.0 d))
7.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.8s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
686.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
365.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
709.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify67.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0576880
12585798
25001796

prune326.0ms

Filtered
116 candidates to 77 candidates (66.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1142116
Fresh066
Picked101
Done000
Total1158123

Merged error: 7.5b

Counts
123 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
4.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.2b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
180×prod-exp
125×div-exp
80×pow-exp
27×add-cbrt-cube
18×add-sqr-sqrt
16×pow-to-exp
12×*-un-lft-identity
10×add-cube-cbrt
9×associate-*l*
8×cbrt-unprod
7×cbrt-undiv
6×unpow-prod-down
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×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 → 154
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
14.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
6.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

series1.8s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
715.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
698.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
363.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify90.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
09522025
133361640
250011632

prune368.0ms

Filtered
166 candidates to 79 candidates (47.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1642166
Fresh257
Picked101
Done000
Total1677174

Merged error: 7.3b

Counts
174 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
4.9b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.2b
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
6.6b
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×add-sqr-sqrt prod-exp
23×add-cbrt-cube
20×div-exp
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
8×times-frac sqrt-prod
7×unpow-prod-down
6×cbrt-undiv cbrt-unprod
5×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp difference-of-squares
3×associate-*r* div-inv unswap-sqr sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out--
Counts
4 → 107
Calls
4 calls:
6.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
37.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
7.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

series1.8s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
743.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
384.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))))
597.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

simplify88.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06911288
131211178
250021176

prune362.0ms

Filtered
119 candidates to 83 candidates (69.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1181119
Fresh066
Picked011
Done000
Total1188126

Merged error: 7.2b

Counts
126 → 8

regimes471.0ms

Accuracy

0% (1.2b remaining)

Error of 8.5b against oracle of 7.3b and baseline of 8.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02416
12416

end0.0ms

sample1.4s

Algorithm
intervals
Results
732.0ms9293×body80valid
238.0ms3084×body80nan