Details

Time bar (total: 11.1s)

sample49.0ms

Algorithm
intervals
Results
18.0ms291×body80valid
6.0ms107×body80nan

simplify54.0ms

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

localize15.0ms

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))

rewrite74.0ms

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:
18.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
414.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
377.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms
(/ (* M D) (* 2.0 d))
696.0ms
(* (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

prune408.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize25.0ms

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))

rewrite113.0ms

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×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 → 176
Calls
4 calls:
22.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
64.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
5.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))

series1.7s

Counts
4 → 12
Calls
4 calls:
478.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
726.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))
419.0ms
(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
30.0ms
(/ (* M D) (* 2.0 d))

simplify116.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
010432332
149132148
250012148

prune876.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize25.0ms

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)))

rewrite112.0ms

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×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 → 190
Calls
4 calls:
5.0ms
(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))
13.0ms
(/ (* M D) (* 2.0 d))
70.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
418.0ms
(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))))))
26.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))
856.0ms
(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

simplify117.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010832626
146392462
250012462

prune926.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.2b

localize23.0ms

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)

rewrite60.0ms

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×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 → 88
Calls
4 calls:
5.0ms
(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))))))
12.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts
4 → 12
Calls
4 calls:
421.0ms
(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))))))
27.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
745.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify73.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0525999
12596888
25002887

prune386.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.2b

regimes541.0ms

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
503.0ms9298×body80valid
168.0ms3068×body80nan