Details

Time bar (total: 16.3s)

sample43.0ms

Algorithm
intervals
Results
16.0ms304×body80valid
6.0ms101×body80nan

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317618
441318
5126318
6498018
done500018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.2b
(/ (* M D) (* 2.0 d))
3.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite36.0ms

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

series1.5s

Counts
4 → 12
Calls
4 calls:
399.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
27.0ms
(/ (* M D) (* 2.0 d))
370.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
670.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify856.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
02442427
16222198
224452040
done50002040

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize13.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* M D) (* 2.0 d))
3.5b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite37.0ms

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:
4.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
368.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
726.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
689.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify630.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (184.0ms)

IterNodesCost
02321901
15721737
223511581
done50001581

prune395.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.5b

localize21.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* M D) (* 2.0 d))
3.5b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.7b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
361×add-exp-log
180×prod-exp
125×div-exp
80×pow-exp
27×add-cbrt-cube
18×add-sqr-sqrt
16×pow-to-exp
12×*-un-lft-identity
10×add-cube-cbrt
9×associate-*l*
8×cbrt-unprod
7×cbrt-undiv
6×unpow-prod-down
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×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 → 154
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
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)))
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
17.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.8s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
374.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
731.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
695.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify802.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (257.0ms)

IterNodesCost
03254571
19163044
229882800
done50002800

prune434.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.5b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h)) l)
18.7b
(cbrt (/ (* M D) (* 2.0 d)))
18.7b
(cbrt (/ (* M D) (* 2.0 d)))
18.7b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
223×add-exp-log
122×prod-exp
67×div-exp
51×pow-exp
15×cbrt-prod
13×pow-to-exp add-cbrt-cube
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×times-frac
4×pow1 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv cbrt-div pow1/3 associate-/r* cbrt-unprod
1×frac-2neg clear-num associate-/l*
Counts
4 → 113
Calls
4 calls:
24.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h)) l)
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* (cbrt (/ (* M D) (* 2.0 d))) (cbrt (/ (* M D) (* 2.0 d)))) (cbrt (/ (* M D) (* 2.0 d)))) (/ 2.0 2)) h)) l)
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))
104.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify485.0ms

Counts
125 → 125
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
02414412
16333867
217602698
done50002695

prune471.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.5b

regimes819.0ms

Accuracy

0% (1.3b remaining)

Error of 9.1b against oracle of 7.8b and baseline of 9.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02032
12532
done2532

end0.0ms

sample1.1s

Algorithm
intervals
Results
489.0ms9409×body80valid
171.0ms3188×body80nan