Details

Time bar (total: 10.9s)

sample41.0ms

Algorithm
intervals
Results
15.0ms297×body80valid
6.0ms107×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize15.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.3b
(/ (* M D) (* 2.0 d))
5.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
14.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite38.0ms

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))))
18.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
405.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
360.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
682.0ms
(* (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
06091076
12742997
25002994

prune380.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.1b

localize14.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b
(/ (* M D) (* 2.0 d))
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite33.0ms

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:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.0ms
(/ (* M D) (* 2.0 d))
6.0ms
(/ (* (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)))

series1.8s

Counts
4 → 12
Calls
4 calls:
723.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
28.0ms
(/ (* M D) (* 2.0 d))
697.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
363.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify62.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0560828
12559746
25001744

prune337.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.1b

localize20.0ms

Local error

Found 4 expressions with local error:

5.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b
(/ (* M D) (* 2.0 d))
5.6b
(/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h))
5.9b
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-sqr-sqrt add-cbrt-cube
20×div-exp
14×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
8×sqrt-prod
7×times-frac
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1
4×div-inv associate-/l* add-log-exp
3×associate-*r* difference-of-squares unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* distribute-lft-out-- sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 99
Calls
4 calls:
9.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h))
22.0ms
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
737.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
29.0ms
(/ (* M D) (* 2.0 d))
584.0ms
(/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h))
486.0ms
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ (* M D) (* 2.0 d)) 2.0) h)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0651958
13109862
25003857

prune347.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.1b

localize15.0ms

Local error

Found 4 expressions with local error:

4.7b
(/ M (/ (* 2.0 d) D))
5.1b
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
5.6b
(/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h))
5.9b
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
55×add-exp-log add-sqr-sqrt
43×*-un-lft-identity
39×add-cube-cbrt
30×associate-*l*
28×unpow-prod-down
22×div-exp
20×add-cbrt-cube
15×prod-exp
11×div-inv
8×pow-exp associate-/r* sqrt-prod
7×cbrt-undiv
6×associate-/l*
5×pow1
4×add-log-exp unswap-sqr
3×associate-*r* cbrt-unprod difference-of-squares
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r/ distribute-lft-out-- sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 146
Calls
4 calls:
4.0ms
(/ M (/ (* 2.0 d) D))
29.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
9.0ms
(/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h))
21.0ms
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ M (/ (* 2.0 d) D))
893.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
621.0ms
(/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h))
389.0ms
(sqrt (- 1.0 (/ 1 (/ l (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)))))

simplify89.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
08481268
137061178
250011173

prune563.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.9b

regimes455.0ms

Accuracy

24.5% (1.5b remaining)

Error of 8.9b against oracle of 7.4b and baseline of 9.3b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05645
15645

end0.0ms

sample1.1s

Algorithm
intervals
Results
478.0ms9318×body80valid
171.0ms3132×body80nan