Details

Time bar (total: 11.2s)

sample42.0ms

Algorithm
intervals
Results
14.0ms293×body80valid
5.0ms101×body80nan

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite69.0ms

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:
17.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
452.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms
(/ (* M D) (* 2.0 d))
377.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
880.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify78.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091075
12742997
25002994

prune357.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (* M D) (* 2.0 d))
4.2b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
9.1b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 110
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))
404.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
701.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify72.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05761132
125821013
250011012

prune402.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (* M D) (* 2.0 d))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
6.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite90.0ms

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:
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
42.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
402.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
724.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
746.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify97.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07701398
135121247
250011229

prune385.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize22.0ms

Local error

Found 4 expressions with local error:

5.3b
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
5.3b
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
6.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
22×add-sqr-sqrt prod-exp
18×associate-*l*
12×add-cube-cbrt unpow-prod-down *-un-lft-identity
10×pow-exp
8×div-exp add-cbrt-cube
6×cbrt-prod associate-*r* unswap-sqr
4×pow1 cbrt-div add-log-exp sqr-pow
2×pow-to-exp flip3-- times-frac pow1/3 *-commutative flip-- cbrt-unprod div-inv
Counts
4 → 88
Calls
4 calls:
3.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
3.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.0s

Counts
4 → 12
Calls
4 calls:
262.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
274.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
744.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
737.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03331350
111741242
250021236

prune486.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

regimes749.0ms

Accuracy

0% (1.2b remaining)

Error of 8.7b against oracle of 7.5b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03017
13017

end0.0ms

sample1.2s

Algorithm
intervals
Results
469.0ms9330×body80valid
156.0ms3041×body80nan