Details

Time bar (total: 18.0s)

sample119.0ms

Algorithm
intervals
Results
56.0ms297×body80valid
30.0ms98×body80nan

simplify457.0ms

Counts
1 → 1
Iterations
IterNodes
done2000
3592
295
138
017

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize27.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) (* 2 d))
4.6b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
11.5b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
368×add-cbrt-cube add-exp-log
190×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
16×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac add-cube-cbrt
10×pow1
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 198
Calls
4 calls:
21.0ms
(/ (* M D) (* 2 d))
14.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
135.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series352.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))
178.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
107.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify611.0ms

Counts
210 → 210
Iterations
IterNodes
done2002
1961
0321

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

localize47.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))
4.6b
(/ (/ (* M D) 2) d)
4.6b
(/ (/ (* M D) 2) d)
4.7b
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
145×times-frac
110×add-sqr-sqrt
76×*-un-lft-identity add-cube-cbrt
54×add-exp-log
46×add-cbrt-cube
44×cbrt-prod
40×associate-*l*
25×associate-*r*
24×cbrt-undiv div-exp
15×div-inv
14×associate-/l*
12×prod-exp cbrt-unprod
10×unswap-sqr
7×pow1
6×associate-/r*
4×insert-posit16 add-log-exp
3×sqrt-prod
2×clear-num frac-2neg sqrt-div associate-/l/
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 218
Calls
4 calls:
30.0ms
(* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))
20.0ms
(/ (/ (* M D) 2) d)
27.0ms
(/ (/ (* M D) 2) d)
8.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l)))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))
39.0ms
(/ (/ (* M D) 2) d)
35.0ms
(/ (/ (* M D) 2) d)
180.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l)))))

simplify992.0ms

Counts
230 → 230
Iterations
IterNodes
done2001
1884
0301

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize124.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (* (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))))) (/ (cbrt h) (cbrt l)))))
18.7b
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
18.7b
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
18.7b
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*l/ associate-*r/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 55
Calls
4 calls:
4.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (* (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))))) (/ (cbrt h) (cbrt l)))))
11.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
16.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
20.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))

series1.1s

Counts
4 → 12
Calls
4 calls:
309.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)) (* (* (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))) (cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))))) (/ (cbrt h) (cbrt l)))))
271.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
246.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
288.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))

simplify817.0ms

Counts
67 → 67
Iterations
IterNodes
done2001
2768
1261
0128

prune855.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.3b

localize169.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-div
4×cbrt-prod add-sqr-sqrt frac-times pow1 *-un-lft-identity add-cbrt-cube pow1/3 associate-*l/ associate-*r/ add-exp-log add-cube-cbrt insert-posit16 add-log-exp
Counts
4 → 52
Calls
4 calls:
12.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
11.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
12.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
11.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))

series1.4s

Counts
4 → 12
Calls
4 calls:
604.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
293.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
263.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))
287.0ms
(cbrt (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d)))

simplify910.0ms

Counts
64 → 64
Iterations
IterNodes
done2006
31150
2417
1181
094

prune873.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.3b

regimes1.8s

Accuracy

0% (1.5b remaining)

Error of 8.0b against oracle of 6.6b and baseline of 8.0b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done35
135
026

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.9s9286×body80valid
638.0ms3280×body80nan