Details

Time bar (total: 11.3s)

sample77.0ms

Algorithm
intervals
Results
24.0ms293×body80valid
9.0ms101×body80nan

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize15.0ms

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))

rewrite84.0ms

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)))))
12.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
44.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
420.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms
(/ (* M D) (* 2.0 d))
394.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
669.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify68.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06301135
127791057
250011054

prune390.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.5b

localize15.0ms

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))

rewrite67.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 118
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))
376.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
704.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify68.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05951196
126181077
250011076

prune425.0ms

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)

rewrite94.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 136
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
40.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2.0 d))
392.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
713.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))
730.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify118.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
07861471
135451321
250011303

prune434.0ms

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)

rewrite60.0ms

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 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp sqr-pow
2×pow-to-exp flip3-- times-frac pow1/3 *-commutative flip-- cbrt-unprod div-inv
Counts
4 → 96
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)))))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series2.2s

Counts
4 → 12
Calls
4 calls:
454.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
267.0ms
(cbrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l)))))
737.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
740.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify50.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03451446
112011338
250021322

prune524.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

regimes729.0ms

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
465.0ms9330×body80valid
163.0ms3041×body80nan