Details

Time bar (total: 53.4s)

sample99.0ms

Algorithm
intervals
Results
37.0ms307×body80valid
12.0ms97×body80nan

simplify23.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
16518
231218
3352718
done500118

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize23.0ms

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))

rewrite128.0ms

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:
28.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
15.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
15.0ms
(/ (* M D) (* 2.0 d))
66.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
639.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
664.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
46.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify3.6s

Counts
133 → 133
Iterations

Useful iterations: done (3.5s)

IterNodesCost
02442427
137592198
done50012040

prune706.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.3b

localize38.0ms

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))))

rewrite339.0ms

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:
210.0ms
(* (* (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)))))
14.0ms
(/ (* M D) (* 2.0 d))
87.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.6s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
567.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
33.0ms
(/ (* M D) (* 2.0 d))
909.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify1.2s

Counts
262 → 262
Iterations

Useful iterations: done (1.2s)

IterNodesCost
04528045
done50017166

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize56.0ms

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))))

rewrite124.0ms

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))
14.0ms
(/ (* M D) (* 2.0 d))
82.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.6s

Counts
4 → 12
Calls
4 calls:
604.0ms
(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)))))
62.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(/ (* M D) (* 2.0 d))
860.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify4.7s

Counts
146 → 146
Iterations

Useful iterations: done (4.7s)

IterNodesCost
02563956
124253346
done50012651

prune784.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.0b

localize59.0ms

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))))

rewrite377.0ms

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:
217.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
7.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
11.0ms
(/ M (/ (* 2.0 d) D))
121.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
522.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
49.0ms
(/ M (/ (* 2.0 d) D))
807.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify996.0ms

Counts
297 → 297
Iterations

Useful iterations: done (976.0ms)

IterNodesCost
05378465
done50007657

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.0b

regimes1.2s

Accuracy

30.9% (1.4b remaining)

Error of 8.9b against oracle of 7.5b and baseline of 9.5b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02852
13749
done3749

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s9264×body80valid
414.0ms3005×body80nan