Details

Time bar (total: 1.9m)

sample112.0ms

Algorithm
intervals
Results
71.0ms299×body80valid
15.0ms76×body80nan

simplify125.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
125.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize29.0ms

Local error

Found 4 expressions with local error:

10.9b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
5.7b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
5.3b
(/ (* M D) (* 2 d))
5.3b
(/ (* M D) (* 2 d))

rewrite164.0ms

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:
Slowest
132.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
10.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
118.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
48.0ms
(/ (* M D) (* 2 d))
47.0ms
(/ (* M D) (* 2 d))

simplify49.0s

Counts
172 → 210
Calls
172 calls:
Slowest
2.8s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.6s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.4s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.2s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.3b

localize53.0ms

Local error

Found 4 expressions with local error:

9.3b
(* (/ (* M D) (* 2 d)) (/ h l))
5.7b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))
5.3b
(/ (* M D) (* 2 d))
5.3b
(/ (* M D) (* 2 d))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
19×add-sqr-sqrt
13×*-un-lft-identity times-frac associate-*r* add-cube-cbrt
7×pow1
5×associate-*l*
4×insert-posit16 div-inv add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 113
Calls
4 calls:
Slowest
33.0ms
(* (/ (* M D) (* 2 d)) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* M D) (* 2 d))
9.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))
82.0ms
(* (/ (* M D) (* 2 d)) (/ h l))
49.0ms
(/ (* M D) (* 2 d))
33.0ms
(/ (* M D) (* 2 d))

simplify24.6s

Counts
84 → 125
Calls
84 calls:
Slowest
1.4s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ h l) (/ h l)) (/ h l)))
1.4s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (* (* (/ h l) (/ h l)) (/ h l)))
1.4s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* h h) h) (* (* l l) l)))
1.4s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* h h) h) (* (* l l) l)))
1.3s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* h h) h) (* (* l l) l)))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize27.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (/ (* M D) (* 2 d)) h) l))))
5.3b
(/ (* M D) (* 2 d))
5.3b
(/ (* M D) (* 2 d))
4.4b
(/ (* (/ (* M D) (* 2 d)) h) l)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
18×cbrt-undiv div-exp
17×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1 associate-/r* times-frac
4×insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod div-inv associate-/l*
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l/ flip-- associate-/l/
Counts
4 → 91
Calls
4 calls:
Slowest
27.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* (/ (* M D) (* 2 d)) h) l)
10.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (/ (* M D) (* 2 d)) h) l))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (/ (* M D) (* 2 d)) h) l))))
115.0ms
(/ (* (/ (* M D) (* 2 d)) h) l)
47.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify18.5s

Counts
61 → 103
Calls
61 calls:
Slowest
1.5s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (* (* l l) l))
1.4s
(/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (* (* l l) l))
1.2s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (* (* h h) h)) (* (* l l) l))
1.1s
(/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (* (* h h) h)) (* (* l l) l))
823.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize60.0ms

Local error

Found 4 expressions with local error:

19.4b
(cbrt (/ (* M D) (* 2 d)))
19.4b
(cbrt (/ (* M D) (* 2 d)))
19.4b
(cbrt (/ (* M D) (* 2 d)))
5.7b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-div times-frac pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 61
Calls
4 calls:
Slowest
9.0ms
(cbrt (/ (* M D) (* 2 d)))
8.0ms
(cbrt (/ (* M D) (* 2 d)))
8.0ms
(cbrt (/ (* M D) (* 2 d)))
5.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l))))
166.0ms
(cbrt (/ (* M D) (* 2 d)))
150.0ms
(cbrt (/ (* M D) (* 2 d)))
131.0ms
(cbrt (/ (* M D) (* 2 d)))

simplify5.3s

Counts
37 → 73
Calls
37 calls:
Slowest
728.0ms
(sqrt (- (* 1 1) (* (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l)) (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l)))))
615.0ms
(sqrt (- (pow 1 3) (pow (* (/ (* M D) (* 2 d)) (/ (* (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d)))) h) l)) 3)))
434.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
358.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
349.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.5b

regimes1.0s

Accuracy

0% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 8.4b

bsearch4.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.6s9315×body80valid
672.0ms3120×body80nan