Details

Time bar (total: 25.6s)

sample72.0ms

Algorithm
intervals
Results
25.0ms303×body80valid
7.0ms88×body80nan

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318118
445718
5267818
done500118

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize35.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite163.0ms

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:
36.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
26.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
72.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
630.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
52.0ms
(/ (* M D) (* 2.0 d))
604.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
952.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.6s

Counts
133 → 133
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02442427
16442218
231122042
done50002040

prune615.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize43.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
6.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite387.0ms

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:
228.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
26.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
99.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
31.0ms
(/ (* M D) (* 2.0 d))
616.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
791.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify1.1s

Counts
262 → 262
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04528045
115117181
done50015297

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize57.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
4.4b
(/ (* M D) (* 2.0 d))
4.4b
(/ (* M D) (* 2.0 d))
6.1b
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip--
Counts
4 → 96
Calls
4 calls:
36.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
14.0ms
(/ (* M D) (* 2.0 d))
19.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
788.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
52.0ms
(/ (* M D) (* 2.0 d))
58.0ms
(/ (* M D) (* 2.0 d))
548.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

simplify1.3s

Counts
108 → 108
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01772603
14532408
220541934
done50011910

prune778.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize56.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
4.4b
(/ (* M D) (* 2.0 d))
4.4b
(* (* M D) (/ 1 (* 2.0 d)))
6.1b
(sqrt (- 1.0 (* (* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
125×add-exp-log
75×prod-exp
39×add-cbrt-cube
20×div-exp
16×cbrt-unprod
15×pow-exp
13×add-sqr-sqrt
10×pow1 associate-*r*
9×add-cube-cbrt *-un-lft-identity
8×cbrt-undiv rec-exp 1-exp
6×associate-*l*
4×expm1-log1p-u times-frac log1p-expm1-u add-log-exp
3×pow-prod-down sqrt-prod
2×sqrt-div *-commutative div-inv unswap-sqr sqr-pow
1×pow-to-exp unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 120
Calls
4 calls:
31.0ms
(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
13.0ms
(/ (* M D) (* 2.0 d))
50.0ms
(* (* M D) (/ 1 (* 2.0 d)))
13.0ms
(sqrt (- 1.0 (* (* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
655.0ms
(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))
33.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(* (* M D) (/ 1 (* 2.0 d)))
432.0ms
(sqrt (- 1.0 (* (* (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l)))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (fabs (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

simplify2.7s

Counts
132 → 132
Iterations

Useful iterations: done (2.7s)

IterNodesCost
02533138
17172829
240872392
done50002360

prune627.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

regimes1.4s

Accuracy

0% (1.0b remaining)

Error of 8.2b against oracle of 7.2b and baseline of 8.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02950
13950
done3950

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s9277×body80valid
369.0ms3012×body80nan