Details

Time bar (total: 10.6s)

sample45.0ms

Algorithm
intervals
Results
15.0ms303×body80valid
5.0ms99×body80nan

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize17.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite71.0ms

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:
17.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms
(/ (* M D) (* 2.0 d))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
434.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
29.0ms
(/ (* M D) (* 2.0 d))
385.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
693.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify76.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301136
127791057
250011054
done50011054

prune398.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.9b

localize14.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
4.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.1b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite73.0ms

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:
12.0ms
(/ (* M D) (* 2.0 d))
22.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
19.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
746.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
724.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
389.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify63.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0576880
12585798
25001796
done5001796

prune351.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.9b

localize13.0ms

Local error

Found 4 expressions with local error:

4.7b
(* (/ M 2.0) (/ D d))
4.7b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
5.1b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
6.1b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

rewrite72.0ms

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:
21.0ms
(* (/ M 2.0) (/ D d))
13.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
17.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
16.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ M 2.0) (/ D d))
812.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
710.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
384.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

simplify87.0ms

Counts
140 → 140
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07171000
13046917
25002915
done5002915

prune426.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.9b

localize21.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
3.8b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
8.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 118
Calls
4 calls:
14.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* 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)))))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
390.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
706.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify67.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05951196
126181077
250011076
done50011076

prune419.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.9b

regimes415.0ms

Accuracy

70.3% (0.9b remaining)

Error of 8.8b against oracle of 7.9b and baseline of 10.9b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04229
14229
done4229

end0.0ms

sample1.3s

Algorithm
intervals
Results
488.0ms9406×body80valid
175.0ms3155×body80nan