Details

Time bar (total: 2.0m)

sample132.0ms

Algorithm
intervals
Results
70.0ms293×body80valid
24.0ms105×body80nan

simplify148.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
147.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
3.5b
(/ (* M D) (* 2 d))
3.5b
(/ (* M D) (* 2 d))
3.3b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite197.0ms

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
161.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
13.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
105.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
41.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify58.5s

Counts
221 → 210
Calls
221 calls:
Slowest
2.5s
(* (* (/ (* (* (* 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)))
2.2s
(* (* (/ (* (* (* 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)))
2.2s
(* (* (/ (* (* (* 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)))
2.1s
(* (* (/ (* (* (* 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)))
2.1s
(* (* (/ (* (* (* 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)))

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize79.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (/ M (* 2 d)) D)
7.1b
(* (/ M (* 2 d)) D)
3.3b
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
2.6b
(* (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
24×add-cbrt-cube add-exp-log
23×add-sqr-sqrt
20×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×pow1
9×associate-*r* prod-exp cbrt-unprod
7×sqrt-prod
6×times-frac
4×cbrt-undiv sqrt-div div-exp associate-*l/ insert-posit16 add-log-exp unswap-sqr
3×pow-prod-down *-commutative
2×flip3-- div-inv flip--
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 97
Calls
4 calls:
Slowest
34.0ms
(* (/ M (* 2 d)) D)
29.0ms
(* (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
22.0ms
(* (/ M (* 2 d)) D)
9.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series964.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
589.0ms
(* (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
289.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
44.0ms
(* (/ M (* 2 d)) D)
42.0ms
(* (/ M (* 2 d)) D)

simplify27.6s

Counts
113 → 109
Calls
113 calls:
Slowest
1.1s
(sqrt (+ (* 1 1) (+ (* (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))))
902.0ms
(* (sqrt (- (pow 1 3) (pow (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) 3))) w0)
869.0ms
(sqrt (- (pow 1 3) (pow (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) 3)))
848.0ms
(* (sqrt (- (* 1 1) (* (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))) (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))) w0)
815.0ms
(cbrt (* (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize58.0ms

Local error

Found 4 expressions with local error:

20.0b
(cbrt (* (/ M (* 2 d)) D))
20.0b
(cbrt (* (/ M (* 2 d)) D))
20.0b
(cbrt (* (/ M (* 2 d)) D))
7.1b
(* (/ M (* 2 d)) D)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity associate-*l* add-cube-cbrt
6×pow1
4×associate-*l/ prod-exp cbrt-unprod insert-posit16 add-log-exp
3×cbrt-prod cbrt-div times-frac pow1/3 associate-*r*
2×cbrt-undiv div-exp
1×pow-prod-down *-commutative div-inv unswap-sqr
Counts
4 → 61
Calls
4 calls:
Slowest
37.0ms
(* (/ M (* 2 d)) D)
27.0ms
(cbrt (* (/ M (* 2 d)) D))
21.0ms
(cbrt (* (/ M (* 2 d)) D))
20.0ms
(cbrt (* (/ M (* 2 d)) D))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(cbrt (* (/ M (* 2 d)) D))
141.0ms
(cbrt (* (/ M (* 2 d)) D))
118.0ms
(cbrt (* (/ M (* 2 d)) D))
39.0ms
(* (/ M (* 2 d)) D)

simplify8.6s

Counts
76 → 73
Calls
76 calls:
Slowest
397.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
342.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
316.0ms
(+ (- (log M) (+ (log 2) (log d))) (log D))
312.0ms
(* (/ (* (* M M) M) (* (* (* 2 2) 2) (* (* d d) d))) (* (* D D) D))
308.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

localize127.0ms

Local error

Found 4 expressions with local error:

20.0b
(cbrt (* (/ M (* 2 d)) D))
20.0b
(cbrt (* (/ M (* 2 d)) D))
20.0b
(cbrt (* (/ M (* 2 d)) D))
7.1b
(* (/ M (* 2 d)) D)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity associate-*l* add-cube-cbrt
6×pow1
4×associate-*l/ prod-exp cbrt-unprod insert-posit16 add-log-exp
3×cbrt-prod cbrt-div times-frac pow1/3 associate-*r*
2×cbrt-undiv div-exp
1×pow-prod-down *-commutative div-inv unswap-sqr
Counts
4 → 61
Calls
4 calls:
Slowest
39.0ms
(* (/ M (* 2 d)) D)
16.0ms
(cbrt (* (/ M (* 2 d)) D))
12.0ms
(cbrt (* (/ M (* 2 d)) D))
10.0ms
(cbrt (* (/ M (* 2 d)) D))

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(cbrt (* (/ M (* 2 d)) D))
132.0ms
(cbrt (* (/ M (* 2 d)) D))
127.0ms
(cbrt (* (/ M (* 2 d)) D))
36.0ms
(* (/ M (* 2 d)) D)

simplify9.1s

Counts
76 → 73
Calls
76 calls:
Slowest
523.0ms
(* 1/2 (/ (* M D) d))
391.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
381.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
346.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
290.0ms
(* (/ (* (* M M) M) (* (* (* 2 2) 2) (* (* d d) d))) (* (* D D) D))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes1.8s

Accuracy

0% (1.1b remaining)

Error of 8.1b against oracle of 7.0b and baseline of 8.1b

bsearch9.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.9s9325×body80valid
651.0ms3061×body80nan