Details

Time bar (total: 13.1s)

sample48.0ms

Algorithm
intervals
Results
16.0ms295×body80valid
6.0ms110×body80nan

simplify697.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317718
443518
5135118
done500018

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.8b
(/ (* M D) (* 2.0 d))
10.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite35.0ms

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:
8.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
405.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
367.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms
(/ (* M D) (* 2.0 d))
694.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify702.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (202.0ms)

IterNodesCost
02442427
16292200
224992040
done50012040

prune442.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.4b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.8b
(/ (* M D) (* 2.0 d))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 104
Calls
4 calls:
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
713.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
737.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
364.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
33.0ms
(/ (* M D) (* 2.0 d))

simplify681.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
02321901
15811737
224661581
done50011581

prune403.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.2b

localize16.0ms

Local error

Found 4 expressions with local error:

3.9b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.4b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
6.8b
(/ (* M D) (* 2.0 d))
6.8b
(/ (* M D) (* 2.0 d))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
352×add-exp-log
173×prod-exp
125×div-exp
75×pow-exp
37×add-cbrt-cube
15×pow-to-exp
11×cbrt-undiv cbrt-unprod
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
5×pow1 times-frac associate-/r* sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num div-inv associate-/l*
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 144
Calls
4 calls:
20.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
10.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
714.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
386.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
27.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(/ (* M D) (* 2.0 d))

simplify1.1s

Counts
156 → 156
Iterations

Useful iterations: 2 (447.0ms)

IterNodesCost
02714224
18152732
225392450
done50002450

prune398.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.0b

localize17.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
6.2b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.8b
(/ (* M D) (* 2.0 d))
6.8b
(/ (* M D) (* 2.0 d))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
33×add-cbrt-cube
20×div-exp
19×prod-exp
10×cbrt-undiv
9×cbrt-unprod
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1 times-frac pow-exp associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num sqrt-prod div-inv associate-/l*
2×sqrt-div
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 92
Calls
4 calls:
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
388.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
721.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
28.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify563.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
01821988
14891820
220291382
done50011382

prune357.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.0b

regimes546.0ms

Accuracy

0% (1.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12532
done2532

end0.0ms

sample1.3s

Algorithm
intervals
Results
704.0ms9301×body80valid
168.0ms2986×body80nan