Details

Time bar (total: 2.8m)

sample82.0ms

Algorithm
intervals
Results
44.0ms296×body80valid
13.0ms102×body80nan

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize54.0ms

Local error

Found 4 expressions with local error:

10.5b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.5b
(/ (* M D) (* 2 d))
4.5b
(/ (* M D) (* 2 d))
4.3b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite223.0ms

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
166.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
108.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
50.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify1.1m

Counts
221 → 210
Calls
221 calls:
Slowest
3.1s
(* (* (/ (* (* (* 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 h) h) (* (* l l) l)))
2.6s
(* (* (/ (* (* (* 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)))
2.4s
(* (* (/ (* (* (* 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)))
2.4s
(* (* (/ (* (* (* 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)))
2.3s
(* (* (/ (* (* (* 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

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize53.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (/ M (* 2 d)) D)
4.8b
(* (/ M (* 2 d)) D)
4.3b
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
2.8b
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log
46×add-cbrt-cube associate-*r*
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod *-un-lft-identity add-cube-cbrt
24×prod-exp cbrt-unprod
15×associate-*l*
14×pow1
12×cbrt-undiv div-exp
5×pow-prod-down associate-*l/
4×insert-posit16 add-log-exp
3×*-commutative sqrt-prod div-inv
2×sqrt-div unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r/ flip--
Counts
4 → 143
Calls
4 calls:
Slowest
57.0ms
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))
43.0ms
(* (/ M (* 2 d)) D)
33.0ms
(* (/ M (* 2 d)) D)
7.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
154.0ms
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))
34.0ms
(* (/ M (* 2 d)) D)
33.0ms
(* (/ M (* 2 d)) D)

simplify38.6s

Counts
158 → 155
Calls
158 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)))))))
922.0ms
(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))))))
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)))
843.0ms
(* (* (/ M (* 2 d)) D) (/ (cbrt 1) 1))
798.0ms
(* (* (* (* (/ M (* 2 d)) D) (* (/ M (* 2 d)) D)) (* (/ M (* 2 d)) D)) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize87.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (/ M (* 2 d)) D)
4.8b
(* (/ M (* 2 d)) D)
4.3b
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))
2.8b
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log
46×add-cbrt-cube associate-*r*
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod *-un-lft-identity add-cube-cbrt
24×prod-exp cbrt-unprod
15×associate-*l*
14×pow1
12×cbrt-undiv div-exp
5×pow-prod-down associate-*l/
4×insert-posit16 add-log-exp
3×*-commutative sqrt-prod div-inv
2×sqrt-div unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r/ flip--
Counts
4 → 143
Calls
4 calls:
Slowest
98.0ms
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))
27.0ms
(* (/ M (* 2 d)) D)
17.0ms
(* (/ M (* 2 d)) D)
8.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))
144.0ms
(* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l)))
52.0ms
(* (/ M (* 2 d)) D)
37.0ms
(* (/ M (* 2 d)) D)

simplify39.9s

Counts
158 → 155
Calls
158 calls:
Slowest
941.0ms
(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)))) (* 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))))
908.0ms
(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))))))
862.0ms
(* (cbrt (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))) (cbrt (sqrt (- 1 (* (* (* (* (/ M (* 2 d)) D) (/ (cbrt h) (cbrt l))) (/ (* (* (/ M (* 2 d)) D) (cbrt h)) (cbrt l))) (/ (cbrt h) (cbrt l)))))))
805.0ms
(* (* (/ (* (* M M) M) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* D D) D)) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
772.0ms
(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)))

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize88.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (* (/ M (* 2 d)) D))
17.9b
(cbrt (* (/ M (* 2 d)) D))
17.9b
(cbrt (* (/ M (* 2 d)) D))
4.8b
(* (/ M (* 2 d)) D)

rewrite64.0ms

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
19.0ms
(cbrt (* (/ M (* 2 d)) D))
17.0ms
(cbrt (* (/ M (* 2 d)) D))
17.0ms
(* (/ M (* 2 d)) D)
10.0ms
(cbrt (* (/ M (* 2 d)) D))

series511.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(cbrt (* (/ M (* 2 d)) D))
151.0ms
(cbrt (* (/ M (* 2 d)) D))
144.0ms
(cbrt (* (/ M (* 2 d)) D))
58.0ms
(* (/ M (* 2 d)) D)

simplify9.1s

Counts
76 → 73
Calls
76 calls:
Slowest
408.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
403.0ms
(* (/ (* (* M M) M) (* (* (* 2 2) 2) (* (* d d) d))) (* (* D D) D))
399.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
354.0ms
(* (/ (* (* M M) M) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* D D) D))
333.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

regimes1.6s

Accuracy

0% (1.0b remaining)

Error of 7.9b against oracle of 6.9b and baseline of 7.9b

bsearch10.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.3s9262×body80valid
550.0ms3132×body80nan