Details

Time bar (total: 37.0s)

sample130.0ms

Algorithm
intervals
Results
53.0ms300×body80valid
15.0ms103×body80nan

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
318118
445718
5267818
done500118

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize46.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* M D) (* 2.0 d))
2.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.6b
(* (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:
26.0ms
(/ (* M D) (* 2.0 d))
38.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
75.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series3.0s

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (* M D) (* 2.0 d))
838.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
776.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
1.4s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.5s

Counts
133 → 133
Iterations

Useful iterations: 2 (652.0ms)

IterNodesCost
02442427
16442218
231142042
done50012042

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.0b

localize46.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* M D) (* 2.0 d))
2.9b
(* w0 (sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l))))
3.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
23×add-cbrt-cube
19×add-sqr-sqrt
16×div-exp prod-exp
14×*-un-lft-identity
11×sqrt-prod
10×add-cube-cbrt
8×associate-*r*
7×pow1
6×cbrt-undiv cbrt-unprod
5×pow-exp
4×expm1-log1p-u times-frac sqrt-div associate-/r* log1p-expm1-u add-log-exp
3×associate-*l*
2×flip3-- frac-2neg associate-*r/ clear-num flip-- div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 99
Calls
4 calls:
29.0ms
(/ (* M D) (* 2.0 d))
62.0ms
(* w0 (sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l))))
32.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
45.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series3.1s

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (* M D) (* 2.0 d))
873.0ms
(* w0 (sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l))))
1.4s
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
775.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify1.7s

Counts
111 → 111
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02142013
15351834
225431650
done50001646

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.0b

localize70.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
3.8b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.9b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
24×div-exp
22×prod-exp
16×add-sqr-sqrt
14×*-un-lft-identity add-cbrt-cube
10×add-cube-cbrt pow-exp sqrt-prod
6×pow1 times-frac associate-/r*
4×cbrt-undiv expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 clear-num flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
37.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
41.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
38.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
38.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

series4.7s

Counts
4 → 12
Calls
4 calls:
1.8s
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
1.4s
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
775.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
778.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))

simplify1.5s

Counts
108 → 108
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01482120
13531890
213611774
done50011754

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.0b

localize48.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* M D) (* 2.0 d))
2.9b
(* w0 (sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h)))))
4.9b
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))))
6.9b
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))

rewrite883.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
153×add-sqr-sqrt
110×*-un-lft-identity
106×add-cube-cbrt
74×unpow-prod-down
67×add-exp-log
33×div-exp
26×div-inv
23×sqrt-prod add-cbrt-cube
18×sqr-pow
14×associate-*r* associate-/r* difference-of-squares
13×prod-exp
10×pow-exp associate-/l*
7×pow1 cbrt-undiv
5×cbrt-unprod
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*l*
2×pow-to-exp flip3-- frac-2neg associate-*r/ clear-num flip-- distribute-lft-out-- unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/r/ *-commutative
Counts
4 → 250
Calls
4 calls:
26.0ms
(/ (* M D) (* 2.0 d))
437.0ms
(* w0 (sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h)))))
329.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))))
59.0ms
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))

series3.0s

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* M D) (* 2.0 d))
815.0ms
(* w0 (sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h)))))
715.0ms
(sqrt (- 1.0 (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))))
1.4s
(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (/ l h))

simplify1.0s

Counts
262 → 262
Iterations

Useful iterations: done (1.0s)

IterNodesCost
05186287
113255954
done50015742

prune2.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes1.5s

Accuracy

0% (1.7b remaining)

Error of 9.0b against oracle of 7.3b and baseline of 9.0b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02032
12532
done2532

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.9s9388×body80valid
530.0ms3026×body80nan