Details

Time bar (total: 3.1m)

sample67.0ms

Algorithm
intervals
Results
33.0ms290×body80valid
19.0ms87×body80nan

simplify153.0ms

Calls
1 calls:
Slowest
152.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize47.0ms

Local error

Found 4 expressions with local error:

11.8b
(* (/ h l) (/ (* M D) (* 2 d)))
4.6b
(/ (* M D) (* 2 d))
4.6b
(/ (* M D) (* 2 d))
3.6b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite78.0ms

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--
Calls
4 calls:
Slowest
31.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
28.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series364.0ms

Calls
4 calls:
Slowest
191.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
96.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
44.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify25.6s

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

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize28.0ms

Local error

Found 4 expressions with local error:

6.4b
(* h (/ (* M D) (* 2 d)))
4.6b
(/ (* M D) (* 2 d))
4.6b
(/ (* M D) (* 2 d))
4.2b
(/ (* h (/ (* M D) (* 2 d))) l)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
71×add-cbrt-cube add-exp-log
26×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×pow1 times-frac
5×associate-/r* associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×clear-num frac-2neg associate-*l* associate-/l*
2×associate-*r/
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Calls
4 calls:
Slowest
41.0ms
(* h (/ (* M D) (* 2 d)))
22.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
11.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series225.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
49.0ms
(* h (/ (* M D) (* 2 d)))
43.0ms
(/ (* M D) (* 2 d))
28.0ms
(/ (* M D) (* 2 d))

simplify25.2s

Calls
74 calls:
Slowest
1.6s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.5s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.3s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.3s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.1s
(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize52.0ms

Local error

Found 4 expressions with local error:

6.8b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
5.4b
(* (/ 1 l) (/ (* M D) (* 2 d)))
4.6b
(/ (* M D) (* 2 d))
4.6b
(/ (* M D) (* 2 d))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
204×add-exp-log
122×add-cbrt-cube
101×prod-exp
60×div-exp
55×cbrt-unprod
34×cbrt-undiv
20×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity times-frac
13×add-cube-cbrt
11×pow1
10×rec-exp 1-exp
6×associate-*r*
5×associate-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×frac-times clear-num associate-/r* frac-2neg associate-*l/ *-commutative associate-/l*
Calls
4 calls:
Slowest
86.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
26.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
16.0ms
(/ (* M D) (* 2 d))
16.0ms
(/ (* M D) (* 2 d))

series220.0ms

Calls
4 calls:
Slowest
85.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
55.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
46.0ms
(/ (* M D) (* 2 d))
33.0ms
(/ (* M D) (* 2 d))

simplify47.5s

Calls
128 calls:
Slowest
1.7s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) 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)))))
1.5s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))

prune3.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize56.0ms

Local error

Found 4 expressions with local error:

6.8b
(* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))
4.6b
(/ (* M D) (* 2 d))
4.6b
(/ (* M D) (* 2 d))
3.6b
(sqrt (- 1 (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
975×add-exp-log
618×prod-exp
274×div-exp
218×add-cbrt-cube
140×cbrt-unprod
77×rec-exp 1-exp
69×cbrt-undiv
14×pow1
12×associate-*r/
7×add-sqr-sqrt
6×*-un-lft-identity pow-prod-down add-cube-cbrt
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* associate-*l/ sqrt-prod
2×clear-num associate-/r* frac-2neg times-frac sqrt-div div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*r* *-commutative flip--
Calls
4 calls:
Slowest
420.0ms
(* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(sqrt (- 1 (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))

series450.0ms

Calls
4 calls:
Slowest
228.0ms
(sqrt (- 1 (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))))
156.0ms
(* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))
36.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify1.1m

Calls
234 calls:
Slowest
1.9s
(sqrt (- (* 1 1) (* (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))) (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))))))
1.8s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))) (* (* (* (/ 1 (cbrt l)) (/ 1 (cbrt l))) (/ 1 (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* 1 1) 1) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))))
1.6s
(sqrt (- (pow 1 3) (pow (* (* h (* (/ 1 (* (cbrt l) (cbrt l))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))) 3)))
1.6s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* 1 1) 1) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))))

prune5.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.5b

regimes1.4s

Accuracy

0% (0.8b remaining)

Error of 8.3b against oracle of 7.6b and baseline of 8.3b

bsearch6.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.9s9305×body80valid
540.0ms3095×body80nan