Details

Time bar (total: 10.9s)

sample49.0ms

Algorithm
intervals
Results
14.0ms291×body80valid
9.0ms107×body80nan

simplify55.0ms

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: 14.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0b
(/ (* M D) (* 2.0 d))
10.5b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite72.0ms

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))
32.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
400.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
572.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
24.0ms
(/ (* M D) (* 2.0 d))
664.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301136
127791057
250021054

prune407.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize17.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
5.3b
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
5.6b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
6.0b
(/ (* M D) (* 2.0 d))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
210×add-exp-log
85×div-exp
79×prod-exp
57×times-frac
55×add-sqr-sqrt
33×add-cbrt-cube
30×pow-exp
25×add-cube-cbrt *-un-lft-identity
22×associate-*r*
18×unpow-prod-down
13×cbrt-undiv cbrt-prod associate-*l* cbrt-unprod
12×unswap-sqr
10×associate-/l*
7×pow1 div-inv
6×pow-to-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×frac-2neg sqrt-div clear-num associate-/r*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 184
Calls
4 calls:
21.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
61.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
7.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
15.0ms
(/ (* M D) (* 2.0 d))

series1.6s

Counts
4 → 12
Calls
4 calls:
456.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
687.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
397.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
29.0ms
(/ (* M D) (* 2.0 d))

simplify119.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010642410
149532226
250012226

prune678.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(/ (* M D) (* 2.0 d))
6.3b
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
112×times-frac
96×add-exp-log
58×associate-*l*
52×cbrt-prod
49×add-cube-cbrt *-un-lft-identity
38×div-exp
36×unpow-prod-down add-cbrt-cube
32×prod-exp
22×associate-*r*
21×unswap-sqr
12×cbrt-undiv cbrt-unprod sqr-pow
10×pow-exp div-inv
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×frac-times rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 198
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
12.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
68.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
405.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
32.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(/ (* M D) (* 2.0 d))
838.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

simplify118.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010972706
146702542
250012542

prune942.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.2b

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (* (cbrt l) (cbrt l))))))
6.0b
(/ (* M D) (* 2.0 d))
6.0b
(/ (* M D) (* 2.0 d))
6.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 96
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (* (cbrt l) (cbrt l))))))
14.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
24.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts
4 → 12
Calls
4 calls:
406.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (* (cbrt l) (cbrt l))))))
26.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))
704.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify72.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05391070
12624960
25002959

prune417.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.2b

regimes537.0ms

Accuracy

0% (1.2b remaining)

Error of 8.4b against oracle of 7.2b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02821
12821

end0.0ms

sample1.3s

Algorithm
intervals
Results
479.0ms9298×body80valid
164.0ms3068×body80nan