Details

Time bar (total: 9.2s)

sample43.0ms

Algorithm
intervals
Results
17.0ms295×body80valid
6.0ms110×body80nan

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize13.0ms

Local error

Found 4 expressions with local error:

3.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
12.1b
(* (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×sqrt-div 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 → 113
Calls
4 calls:
8.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts
4 → 12
Calls
4 calls:
383.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
346.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms
(/ (* M D) (* 2.0 d))
667.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091075
12742997
25003994

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize15.0ms

Local error

Found 4 expressions with local error:

3.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.9b
(/ (* M D) (* 2.0 d))
5.1b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
9.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
352.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
27.0ms
(/ (* M D) (* 2.0 d))
667.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
862.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify84.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07521136
134601014
250011001

prune383.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
5.1b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
1381×add-exp-log
896×prod-exp
362×div-exp
300×pow-exp
60×pow-to-exp
57×rec-exp 1-exp
49×add-cbrt-cube
20×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×cbrt-undiv times-frac
7×pow1
4×add-log-exp
3×sqrt-prod div-inv
2×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 un-div-inv *-commutative flip--
Counts
4 → 316
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
51.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series1.1s

Counts
4 → 12
Calls
4 calls:
347.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
30.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
663.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify116.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
014884540
141403138
250033126

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
156×add-exp-log
84×prod-exp
40×div-exp add-cbrt-cube
20×pow-exp
14×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×times-frac
10×cbrt-undiv
8×rec-exp 1-exp
7×pow1
4×pow-to-exp add-log-exp
3×sqrt-prod div-inv
2×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 un-div-inv *-commutative flip--
Counts
4 → 118
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

series1.1s

Counts
4 → 12
Calls
4 calls:
349.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
27.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
665.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

simplify77.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06711235
129941071
250031053

prune319.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

regimes444.0ms

Accuracy

0% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 8.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03017
13017

end0.0ms

sample1.1s

Algorithm
intervals
Results
485.0ms9368×body80valid
164.0ms3045×body80nan