Details

Time bar (total: 10.3s)

sample47.0ms

Algorithm
intervals
Results
17.0ms303×body80valid
5.0ms99×body80nan

simplify54.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019
done50019

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:

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))

rewrite72.0ms

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)))))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
432.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
31.0ms
(/ (* M D) (* 2.0 d))
381.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
672.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06091076
12742997
25002994
done5002994

prune355.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.9b

localize16.0ms

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) (/ 1 l))
6.1b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
12.0ms
(/ (* M D) (* 2.0 d))
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
41.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

series1.8s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
736.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
705.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
378.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))

simplify93.0ms

Counts
140 → 140
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07521136
134671014
250011001
done50011001

prune338.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 9.9b

localize15.0ms

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) (/ 1 l))
6.1b
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
44×add-sqr-sqrt
40×div-exp
31×times-frac
30×add-cbrt-cube
29×associate-*r*
28×add-cube-cbrt *-un-lft-identity
25×pow-exp
19×associate-*l*
11×cbrt-unprod
9×pow1
8×rec-exp 1-exp
6×cbrt-undiv unswap-sqr
5×pow-to-exp
4×add-log-exp
3×sqrt-prod *-commutative div-inv
2×sqrt-div associate-*r/ pow-prod-down sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*l/ un-div-inv flip--
Counts
4 → 152
Calls
4 calls:
22.0ms
(* (/ M 2.0) (/ D d))
13.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
33.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
5.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

series1.8s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ M 2.0) (/ D d))
736.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
695.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
390.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))

simplify92.0ms

Counts
164 → 164
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
08921255
139051133
250011120
done50011120

prune428.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 9.9b

localize16.0ms

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))

rewrite72.0ms

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×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 → 110
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
35.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))
393.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
705.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify69.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05761132
125821013
250011012
done50011012

prune375.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 9.9b

regimes423.0ms

Accuracy

70.3% (0.9b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 10.9b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04730
14730
done4730

end0.0ms

sample1.2s

Algorithm
intervals
Results
471.0ms9406×body80valid
162.0ms3155×body80nan