Details

Time bar (total: 2.4m)

sample89.0ms

Algorithm
intervals
Results
45.0ms290×body80valid
16.0ms99×body80nan

simplify157.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
157.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize55.0ms

Local error

Found 4 expressions with local error:

10.9b
(* (/ h l) (/ (* M D) (* 2 d)))
5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
4.5b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite77.0ms

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-*l* add-cube-cbrt
7×pow1
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 121
Calls
4 calls:
Slowest
39.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
17.0ms
(/ (* M D) (* 2 d))
13.0ms
(/ (* M D) (* 2 d))
6.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
97.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
48.0ms
(/ (* M D) (* 2 d))
47.0ms
(/ (* M D) (* 2 d))

simplify25.8s

Counts
84 → 133
Calls
84 calls:
Slowest
1.4s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.4s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize50.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
5.8b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
4.5b
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
127×add-exp-log
81×add-cbrt-cube
65×prod-exp
37×cbrt-unprod
34×div-exp
21×cbrt-undiv
10×pow1
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×rec-exp 1-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down sqrt-prod
2×clear-num associate-/r* frac-2neg times-frac sqrt-div div-inv associate-/l*
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r* associate-*l/ *-commutative flip--
Counts
4 → 118
Calls
4 calls:
Slowest
89.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
13.0ms
(/ (* M D) (* 2 d))
13.0ms
(/ (* M D) (* 2 d))
12.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
91.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
52.0ms
(/ (* M D) (* 2 d))
46.0ms
(/ (* M D) (* 2 d))

simplify34.0s

Counts
78 → 130
Calls
78 calls:
Slowest
1.9s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.8s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.8s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.6s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.6s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize54.0ms

Local error

Found 4 expressions with local error:

5.9b
(* (* M D) (/ 1 (* 2 d)))
5.8b
(/ (* M D) (* 2 d))
5.8b
(* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d)))))
4.5b
(sqrt (- 1 (* (* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d))))) (/ (* M D) (* 2 d)))))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
382×add-exp-log
260×prod-exp
118×add-cbrt-cube
74×div-exp
66×cbrt-unprod
35×rec-exp 1-exp
24×pow1
23×cbrt-undiv
13×pow-prod-down
10×associate-*r/
9×add-sqr-sqrt
8×*-un-lft-identity associate-*r* add-cube-cbrt
4×expm1-log1p-u times-frac associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×un-div-inv sqrt-prod
2×frac-times sqrt-div *-commutative div-inv
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 associate-*l/ flip-- associate-/l*
Counts
4 → 185
Calls
4 calls:
Slowest
316.0ms
(* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d)))))
47.0ms
(* (* M D) (/ 1 (* 2 d)))
13.0ms
(/ (* M D) (* 2 d))
6.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d))))) (/ (* M D) (* 2 d)))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d))))) (/ (* M D) (* 2 d)))))
117.0ms
(* h (* (/ 1 l) (* (* M D) (/ 1 (* 2 d)))))
49.0ms
(* (* M D) (/ 1 (* 2 d)))
33.0ms
(/ (* M D) (* 2 d))

simplify57.7s

Counts
147 → 197
Calls
147 calls:
Slowest
1.4s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* d d) d))))))
1.4s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* d d) d))))))
1.3s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* 1 1) 1) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
1.1s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* 1 1) 1) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
1.1s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* d d) d))))))

prune3.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

localize68.0ms

Local error

Found 4 expressions with local error:

18.6b
(cbrt (/ (* M D) (* 2 d)))
18.6b
(cbrt (/ (* M D) (* 2 d)))
18.6b
(cbrt (/ (* M D) (* 2 d)))
5.8b
(/ (* M D) (* 2 d))

rewrite31.0ms

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:
Slowest
13.0ms
(/ (* M D) (* 2 d))
6.0ms
(cbrt (/ (* M D) (* 2 d)))
6.0ms
(cbrt (/ (* M D) (* 2 d)))
5.0ms
(cbrt (/ (* M D) (* 2 d)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(cbrt (/ (* M D) (* 2 d)))
153.0ms
(cbrt (/ (* M D) (* 2 d)))
132.0ms
(cbrt (/ (* M D) (* 2 d)))
40.0ms
(/ (* M D) (* 2 d))

simplify6.7s

Counts
40 → 87
Calls
40 calls:
Slowest
716.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
644.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
501.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))
501.0ms
(cbrt (sqrt (/ (* M D) (* 2 d))))
496.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

regimes1.6s

Accuracy

0% (0.8b remaining)

Error of 8.5b against oracle of 7.7b and baseline of 8.5b

bsearch7.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.3s9380×body80valid
618.0ms3171×body80nan