Details

Time bar (total: 10.0s)

sample39.0ms

Algorithm
intervals
Results
15.0ms291×body80valid
5.0ms90×body80nan

simplify53.0ms

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: 15.8b

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite36.0ms

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)))))
4.0ms
(/ (* M D) (* 2.0 d))
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
17.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
421.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms
(/ (* M D) (* 2.0 d))
374.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
704.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06091075
12742997
25002994

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series1.9s

Counts
4 → 12
Calls
4 calls:
709.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
28.0ms
(/ (* M D) (* 2.0 d))
380.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
735.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify69.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0560829
12559746
25002744

prune354.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×add-log-exp
3×times-frac associate-*r* 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-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* 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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
742.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
27.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
398.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0443917
11894812
25001810

prune530.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) l)))
21.0b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
21.0b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
21.0b
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity
5×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 44
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) l)))
3.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
3.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
3.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

series1.7s

Counts
4 → 12
Calls
4 calls:
419.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))) (cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)))) l)))
440.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
441.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))
437.0ms
(cbrt (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h))

simplify90.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01811148
15421072
226981066
350021066

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

regimes488.0ms

Accuracy

0% (2.2b remaining)

Error of 9.6b against oracle of 7.5b and baseline of 9.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02933
12933

end0.0ms

sample1.1s

Algorithm
intervals
Results
508.0ms9256×body80valid
172.0ms3135×body80nan