Details

Time bar (total: 28.8s)

sample89.0ms

Algorithm
intervals
Results
26.0ms306×body80valid
9.0ms102×body80nan

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318118
445718
5267818
done500118

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize36.0ms

Local error

Found 4 expressions with local error:

2.2b
(* 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))))
5.7b
(/ (* M D) (* 2.0 d))
9.9b
(* (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×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)))))
9.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
22.0ms
(/ (* M D) (* 2.0 d))
64.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
653.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
629.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
40.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.8s

Counts
133 → 133
Iterations

Useful iterations: 2 (486.0ms)

IterNodesCost
02442427
16442218
231322042
done50002042

prune775.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize26.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.5b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.7b
(/ (* M D) (* 2.0 d))
5.8b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite128.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 136
Calls
4 calls:
49.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
24.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
16.0ms
(/ (* M D) (* 2.0 d))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series3.2s

Counts
4 → 12
Calls
4 calls:
1.4s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
611.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
58.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.6s

Counts
148 → 148
Iterations

Useful iterations: 2 (769.0ms)

IterNodesCost
02772631
17872327
245371990
done50011990

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
4.5b
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
5.0b
(* (/ M 2.0) (/ D d))
5.8b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

rewrite181.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 160
Calls
4 calls:
68.0ms
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
14.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
48.0ms
(* (/ M 2.0) (/ D d))
38.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

series2.8s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))
552.0ms
(sqrt (- 1.0 (* (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) (/ 1 l))))
40.0ms
(* (/ M 2.0) (/ D d))
1.2s
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

simplify619.0ms

Counts
172 → 172
Iterations

Useful iterations: done (608.0ms)

IterNodesCost
03252857
19372543
done50002204

prune952.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize51.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
5.8b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.5b
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
6.5b
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
22×prod-exp
20×add-sqr-sqrt
14×*-un-lft-identity
10×cbrt-prod add-cube-cbrt associate-*l* pow-exp
8×div-exp add-cbrt-cube
6×associate-*r*
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp unswap-sqr sqr-pow
2×pow-to-exp unpow-prod-down flip3-- pow1/3 *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
14.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
18.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
22.0ms
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
13.0ms
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

series2.7s

Counts
4 → 12
Calls
4 calls:
987.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
990.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
342.0ms
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
391.0ms
(cbrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))

simplify827.0ms

Counts
102 → 102
Iterations

Useful iterations: done (822.0ms)

IterNodesCost
01391944
13201854
211161702
done50011692

prune627.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

regimes1.5s

Accuracy

74.6% (0.8b remaining)

Error of 8.5b against oracle of 7.6b and baseline of 10.9b

bsearch2.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
04085
15085
done5085

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s9353×body80valid
849.0ms3171×body80nan