Details

Time bar (total: 54.2s)

sample94.0ms

Algorithm
intervals
Results
40.0ms308×body80valid
12.0ms97×body80nan

simplify9.4s

Counts
1 → 1
Iterations
IterNodes
done5049
64844
51480
4373
3161
279
136
017

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize68.0ms

Local error

Found 4 expressions with local error:

2.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0b
(/ (* M D) (* 2.0 d))
10.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite140.0ms

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:
35.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
16.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
24.0ms
(/ (* M D) (* 2.0 d))
57.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series3.5s

Counts
4 → 12
Calls
4 calls:
843.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
1.3s
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
65.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify3.2s

Counts
125 → 125
Iterations
IterNodes
done5305
22284
1598
0236

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.2b

localize107.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.0b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite185.0ms

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:
10.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
25.0ms
(/ (* M D) (* 2.0 d))
88.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
50.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series3.6s

Counts
4 → 12
Calls
4 calls:
760.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
54.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
1.4s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.5s

Counts
140 → 140
Iterations
IterNodes
done5316
22558
1692
0269

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize83.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M D) (* 2.0 d))
5.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

rewrite410.0ms

Algorithm
rewrite-expression-head
Rules
1402×add-exp-log
907×prod-exp
366×div-exp
305×pow-exp
61×pow-to-exp
57×rec-exp 1-exp
51×add-cbrt-cube
21×cbrt-unprod
19×add-sqr-sqrt
16×associate-*r*
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×cbrt-undiv
10×associate-*l*
6×pow1 unpow-prod-down
4×div-inv add-log-exp
3×unswap-sqr
2×frac-2neg clear-num associate-/r* *-commutative associate-/l* sqr-pow
1×associate-*r/ pow-prod-down un-div-inv
Counts
4 → 332
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
21.0ms
(/ (* M D) (* 2.0 d))
48.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
235.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

series3.1s

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(/ (* M D) (* 2.0 d))
1.5s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
1.4s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))

simplify6.7s

Counts
344 → 344
Iterations
IterNodes
done5001
23241
11208
0441

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize87.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M D) (* 2.0 d))
5.0b
(/ (* M D) (* 2.0 d))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
177×add-exp-log
95×prod-exp
44×div-exp
42×add-cbrt-cube
25×pow-exp
19×add-sqr-sqrt
16×associate-*r*
15×cbrt-unprod
14×add-cube-cbrt *-un-lft-identity
12×times-frac
10×cbrt-undiv associate-*l*
8×rec-exp 1-exp
6×pow1 unpow-prod-down
5×pow-to-exp
4×div-inv add-log-exp
3×unswap-sqr
2×frac-2neg clear-num associate-/r* *-commutative associate-/l* sqr-pow
1×associate-*r/ pow-prod-down un-div-inv
Counts
4 → 134
Calls
4 calls:
28.0ms
(/ (* M D) (* 2.0 d))
25.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
92.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

series2.9s

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (* M D) (* 2.0 d))
56.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
1.4s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (/ 1 l))

simplify3.3s

Counts
146 → 146
Iterations
IterNodes
done5000
22369
1662
0238

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

regimes4.0s

Accuracy

10.8% (1.4b remaining)

Error of 8.5b against oracle of 7.0b and baseline of 8.6b

bsearch3.0ms

simplify29.0ms

Iterations
IterNodes
done64
164
048

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.6s9324×body80valid
995.0ms3238×body80nan