Details

Time bar (total: 30.2s)

sample128.0ms

Algorithm
intervals
Results
78.0ms300×body80valid
19.0ms89×body80nan

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
44673
3593
293
136
017

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize38.0ms

Local error

Found 4 expressions with local error:

5.4b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
8.0b
(/ (* M D) (* 2 d))
8.0b
(/ (* M D) (* 2 d))
11.4b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite247.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 206
Calls
4 calls:
11.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
23.0ms
(/ (* M D) (* 2 d))
26.0ms
(/ (* M D) (* 2 d))
174.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series378.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
31.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))
146.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.3s

Counts
218 → 218
Iterations
IterNodes
24014
1934
0327

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.6b

localize66.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l))))) w0)
5.4b
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l)))))
8.0b
(/ (* M D) (* 2 d))
8.0b
(/ (* M D) (* 2 d))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×clear-num associate-/r* frac-2neg times-frac flip3-- associate-*l/ div-inv flip-- associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 93
Calls
4 calls:
28.0ms
(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l))))) w0)
11.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l)))))
11.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))

series666.0ms

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l))))) w0)
194.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l)))))
48.0ms
(/ (* M D) (* 2 d))
46.0ms
(/ (* M D) (* 2 d))

simplify6.5s

Counts
105 → 105
Iterations
IterNodes
312185
21434
1323
0133

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize102.0ms

Local error

Found 4 expressions with local error:

8.0b
(/ (* M D) (* 2 d))
19.7b
(cbrt (/ (* M D) (* 2 d)))
19.7b
(cbrt (/ (* M D) (* 2 d)))
19.7b
(cbrt (/ (* M D) (* 2 d)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
15×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 cbrt-undiv times-frac div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 75
Calls
4 calls:
11.0ms
(/ (* M D) (* 2 d))
4.0ms
(cbrt (/ (* M D) (* 2 d)))
14.0ms
(cbrt (/ (* M D) (* 2 d)))
9.0ms
(cbrt (/ (* M D) (* 2 d)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2 d))
152.0ms
(cbrt (/ (* M D) (* 2 d)))
154.0ms
(cbrt (/ (* M D) (* 2 d)))
130.0ms
(cbrt (/ (* M D) (* 2 d)))

simplify3.3s

Counts
87 → 87
Iterations
IterNodes
37259
21000
1245
0107

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.6b

localize88.0ms

Local error

Found 4 expressions with local error:

8.0b
(/ (* M D) (* 2 d))
8.0b
(/ (* M D) (* 2 d))
8.0b
(/ (* M D) (* 2 d))
8.0b
(/ (* M D) (* 2 d))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
16×cbrt-undiv div-exp prod-exp cbrt-unprod
4×add-sqr-sqrt expm1-log1p-u pow1 clear-num associate-/r* frac-2neg *-un-lft-identity times-frac add-cube-cbrt insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
4 → 96
Calls
4 calls:
18.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
17.0ms
(/ (* M D) (* 2 d))

series155.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (* M D) (* 2 d))
52.0ms
(/ (* M D) (* 2 d))
33.0ms
(/ (* M D) (* 2 d))
35.0ms
(/ (* M D) (* 2 d))

simplify3.0s

Counts
108 → 108
Iterations
IterNodes
36794
2842
1163
059

prune2.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.6b

regimes1.4s

Accuracy

0% (1.1b remaining)

Error of 8.3b against oracle of 7.2b and baseline of 8.3b

bsearch0.0ms

simplify12.0ms

Iterations
IterNodes
232
132
024

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.4s9336×body80valid
693.0ms3055×body80nan