Details

Time bar (total: 2.2m)

sample112.0ms

Algorithm
intervals
Results
63.0ms299×body80valid
16.0ms96×body80nan

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize26.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (/ h l) (/ (* M D) (* 2 d)))
5.5b
(/ (* M D) (* 2 d))
5.5b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite92.0ms

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
48.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
25.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
99.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
36.0ms
(/ (* M D) (* 2 d))
35.0ms
(/ (* M D) (* 2 d))

simplify26.2s

Counts
84 → 133
Calls
84 calls:
Slowest
1.6s
(* (* (* (/ 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 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))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize39.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* M D) (* 2 d))
5.5b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
4.7b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))

rewrite121.0ms

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
75.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
23.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
95.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
43.0ms
(/ (* M D) (* 2 d))
33.0ms
(/ (* M D) (* 2 d))

simplify33.5s

Counts
78 → 130
Calls
78 calls:
Slowest
1.9s
(* (* (* 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 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.8s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (* (* 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)))))

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.6b

localize61.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (/ M 2) (/ D d))
5.5b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (* (/ M 2) (/ D d)))))
4.7b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
127×add-exp-log
81×add-cbrt-cube
65×prod-exp
37×cbrt-unprod
34×div-exp
33×add-sqr-sqrt
23×times-frac
21×cbrt-undiv
20×*-un-lft-identity add-cube-cbrt
16×associate-*l*
14×associate-*r*
12×pow1
5×rec-exp 1-exp associate-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-prod div-inv
2×frac-times sqrt-div associate-*l/ *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 flip-- associate-/l*
Counts
4 → 147
Calls
4 calls:
Slowest
84.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
17.0ms
(/ (* M D) (* 2 d))
15.0ms
(* (/ M 2) (/ D d))
6.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (* (/ M 2) (/ D d)))))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (* (/ M 2) (/ D d)))))
107.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
41.0ms
(* (/ M 2) (/ D d))
33.0ms
(/ (* M D) (* 2 d))

simplify33.3s

Counts
112 → 159
Calls
112 calls:
Slowest
1.8s
(* (* (* 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)))))
1.7s
(* (* (* 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 D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.7s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))

prune2.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.6b

localize79.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (/ M 2) (/ D d))
6.9b
(/ M (/ (* 2 d) D))
4.7b
(sqrt (- 1 (* (* h (* (/ 1 l) (/ M (/ (* 2 d) D)))) (* (/ M 2) (/ D d)))))
4.7b
(* h (* (/ 1 l) (/ M (/ (* 2 d) D))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
103×add-exp-log
67×add-cbrt-cube
55×times-frac
49×add-sqr-sqrt
42×prod-exp
37×div-exp
36×*-un-lft-identity add-cube-cbrt
24×cbrt-unprod
23×cbrt-undiv
16×associate-*l*
14×associate-*r*
12×pow1
7×associate-/r* div-inv
5×associate-*r/
4×expm1-log1p-u rec-exp 1-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-prod associate-/l*
2×frac-times sqrt-div associate-*l/ *-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 associate-/r/ flip--
Counts
4 → 168
Calls
4 calls:
Slowest
88.0ms
(* h (* (/ 1 l) (/ M (/ (* 2 d) D))))
25.0ms
(* (/ M 2) (/ D d))
15.0ms
(/ M (/ (* 2 d) D))
11.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ M (/ (* 2 d) D)))) (* (/ M 2) (/ D d)))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ M (/ (* 2 d) D)))) (* (/ M 2) (/ D d)))))
109.0ms
(* h (* (/ 1 l) (/ M (/ (* 2 d) D))))
50.0ms
(/ M (/ (* 2 d) D))
32.0ms
(* (/ M 2) (/ D d))

simplify23.0s

Counts
153 → 180
Calls
153 calls:
Slowest
1.0s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* M M) M) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* D D) D)))))
947.0ms
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* M M) M) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* D D) D)))))
885.0ms
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* M M) M) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* D D) D)))))
837.0ms
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* M M) M) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* D D) D)))))
836.0ms
(sqrt (- (* 1 1) (* (* (* h (* (/ 1 l) (/ M (/ (* 2 d) D)))) (* (/ M 2) (/ D d))) (* (* h (* (/ 1 l) (/ M (/ (* 2 d) D)))) (* (/ M 2) (/ D d))))))

prune2.9s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.6b

regimes1.3s

Accuracy

0% (1.4b remaining)

Error of 7.9b against oracle of 6.5b and baseline of 7.9b

bsearch4.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.8s9289×body80valid
1.1s3233×body80nan