Details

Time bar (total: 26.9s)

sample60.0ms

Algorithm
intervals
Results
21.0ms307×body80valid
7.0ms97×body80nan

simplify5.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318018
443218
5122118
6469218
done500018

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize37.0ms

Local error

Found 4 expressions with local error:

3.1b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b
(/ (* M D) (* 2.0 d))
13.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite84.0ms

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:
18.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
13.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.0s

Counts
4 → 12
Calls
4 calls:
549.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
553.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms
(/ (* M D) (* 2.0 d))
902.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts
133 → 133
Iterations

Useful iterations: 2 (469.0ms)

IterNodesCost
02442427
15982198
222962040
done50022040

prune511.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.3b

localize51.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2.0 d))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
609×add-exp-log
325×prod-exp
184×div-exp
75×pow-exp
54×add-cbrt-cube
45×associate-*r*
43×cbrt-unprod
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod
33×add-cube-cbrt *-un-lft-identity
22×cbrt-undiv
15×pow-to-exp
10×associate-*l*
7×pow1 unpow-prod-down
6×unswap-sqr
4×expm1-log1p-u associate-*r/ log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×sqrt-div *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* flip-- associate-/l*
Counts
4 → 250
Calls
4 calls:
153.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
23.0ms
(/ (* M D) (* 2.0 d))
80.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.4s

Counts
4 → 12
Calls
4 calls:
979.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
614.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
47.0ms
(/ (* M D) (* 2.0 d))
733.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify729.0ms

Counts
262 → 262
Iterations

Useful iterations: done (712.0ms)

IterNodesCost
04528045
111497127
done50015253

prune922.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.0b

localize69.0ms

Local error

Found 4 expressions with local error:

4.4b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2.0 d))
4.9b
(/ (* M D) (* 2.0 d))
6.1b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
189×add-exp-log
91×prod-exp
56×div-exp
38×add-cbrt-cube
25×pow-exp
17×cbrt-unprod
16×add-sqr-sqrt
12×cbrt-undiv
9×associate-*l*
8×add-cube-cbrt *-un-lft-identity
7×unpow-prod-down times-frac
6×unswap-sqr
5×pow1 pow-to-exp associate-*r*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×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 → 134
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
13.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))
59.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.4s

Counts
4 → 12
Calls
4 calls:
567.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
36.0ms
(/ (* M D) (* 2.0 d))
31.0ms
(/ (* M D) (* 2.0 d))
719.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify1.9s

Counts
146 → 146
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02563956
16713336
228862664
done50012514

prune657.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.0b

localize42.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.4b
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.6b
(/ M (/ (* 2.0 d) D))
6.8b
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
507×add-exp-log
240×prod-exp
183×div-exp
106×times-frac
75×add-sqr-sqrt
62×add-cube-cbrt *-un-lft-identity
60×pow-exp
51×add-cbrt-cube
45×associate-*r*
40×cbrt-unprod
36×cbrt-prod
31×associate-*l*
30×unpow-prod-down
23×cbrt-undiv
15×pow-to-exp
11×div-inv
8×unswap-sqr
7×pow1 associate-/r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×sqrt-prod associate-/l* sqr-pow
2×sqrt-div associate-/r/ *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num flip--
Counts
4 → 285
Calls
4 calls:
201.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
11.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
18.0ms
(/ M (/ (* 2.0 d) D))
111.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.2s

Counts
4 → 12
Calls
4 calls:
919.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
452.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
46.0ms
(/ M (/ (* 2.0 d) D))
763.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify811.0ms

Counts
297 → 297
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
05378465
113727614
done50015853

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.0b

regimes1.2s

Accuracy

64.4% (1.2b remaining)

Error of 8.9b against oracle of 7.7b and baseline of 11.1b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02852
13749
done3749

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.4s9264×body80valid
350.0ms3005×body80nan