Details

Time bar (total: 11.7s)

sample61.0ms

Algorithm
intervals
Results
31.0ms297×body80valid
9.0ms99×body80nan

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.2b
(/ (* M D) (* 2.0 d))
10.0b
(* (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×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:
10.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
418.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
376.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
708.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06301135
127791057
250021054

prune429.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.3b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.2b
(/ (* M D) (* 2.0 d))

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×expm1-log1p-u associate-/r* log1p-expm1-u 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 → 104
Calls
4 calls:
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
9.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
4.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
382.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
706.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
741.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
28.0ms
(/ (* M D) (* 2.0 d))

simplify68.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0576881
12585798
25001796

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize16.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.2b
(/ (* M D) (* 2.0 d))
6.2b
(/ (* M D) (* 2.0 d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 158
Calls
4 calls:
16.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
13.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
716.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
746.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
34.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify83.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08821759
131701336
250021332

prune437.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
4.3b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
4.4b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
7.0b
(* (/ M 2.0) (/ D d))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
41×add-sqr-sqrt
26×prod-exp
25×*-un-lft-identity times-frac
23×add-cube-cbrt add-cbrt-cube
20×div-exp
18×associate-*l*
16×associate-*r*
10×pow-exp
7×pow1
6×cbrt-undiv cbrt-unprod unswap-sqr
5×sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×pow-to-exp sqrt-div *-commutative sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 128
Calls
4 calls:
13.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
5.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
6.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
12.0ms
(* (/ M 2.0) (/ D d))

series2.0s

Counts
4 → 12
Calls
4 calls:
358.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
696.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
921.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
29.0ms
(* (/ M 2.0) (/ D d))

simplify80.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0717999
13046917
25001915

prune451.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

regimes710.0ms

Accuracy

46.2% (1.2b remaining)

Error of 8.4b against oracle of 7.2b and baseline of 9.5b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04639
14639

end0.0ms

sample1.7s

Algorithm
intervals
Results
923.0ms9322×body80valid
307.0ms3137×body80nan