Details

Time bar (total: 3.7m)

sample104.0ms

Algorithm
intervals
Results
58.0ms302×body80valid
18.0ms93×body80nan

simplify198.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
198.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize48.0ms

Local error

Found 4 expressions with local error:

11.8b
(* (/ h l) (/ (* M D) (* 2 d)))
4.2b
(/ (* M D) (* 2 d))
4.2b
(/ (* M D) (* 2 d))
4.0b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite84.0ms

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
23.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
14.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
192.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
103.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
44.0ms
(/ (* M D) (* 2 d))
37.0ms
(/ (* M D) (* 2 d))

simplify25.8s

Counts
84 → 133
Calls
84 calls:
Slowest
1.5s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) 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))))
1.4s
(* (* (* (/ h l) (/ h l)) (/ h 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 2) 2) (* (* d d) d))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

localize36.0ms

Local error

Found 4 expressions with local error:

6.9b
(* (/ 1 l) (/ (* M D) (* 2 d)))
5.7b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
4.2b
(/ (* M D) (* 2 d))
4.2b
(/ (* M D) (* 2 d))

rewrite182.0ms

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*
Counts
4 → 166
Calls
4 calls:
Slowest
76.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
52.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
24.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
60.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
51.0ms
(/ (* M D) (* 2 d))
48.0ms
(/ (* M D) (* 2 d))

simplify49.3s

Counts
128 → 178
Calls
128 calls:
Slowest
2.2s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.9s
(* (* (* 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 M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.7s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

localize32.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (/ 1 l) (* M D))
5.7b
(* h (/ (* (/ 1 l) (* M D)) (* 2 d)))
4.6b
(/ (* (/ 1 l) (* M D)) (* 2 d))
4.2b
(/ (* M D) (* 2 d))

rewrite180.0ms

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
16×associate-*l*
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
11×pow1
10×rec-exp 1-exp
6×associate-*r*
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num associate-/r* frac-2neg associate-*l/ *-commutative associate-/l*
1×associate-*r/ unswap-sqr associate-/l/
Counts
4 → 161
Calls
4 calls:
Slowest
89.0ms
(* h (/ (* (/ 1 l) (* M D)) (* 2 d)))
39.0ms
(/ (* (/ 1 l) (* M D)) (* 2 d))
38.0ms
(* (/ 1 l) (* M D))
11.0ms
(/ (* M D) (* 2 d))

series199.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(* h (/ (* (/ 1 l) (* M D)) (* 2 d)))
51.0ms
(/ (* (/ 1 l) (* M D)) (* 2 d))
37.0ms
(/ (* M D) (* 2 d))
33.0ms
(* (/ 1 l) (* M D))

simplify56.6s

Counts
121 → 173
Calls
121 calls:
Slowest
2.4s
(* (* (* h h) h) (/ (* (/ (* (* 1 1) 1) (* (* l l) l)) (* (* (* M M) M) (* (* D D) D))) (* (* (* 2 d) (* 2 d)) (* 2 d))))
2.3s
(* (* (* h h) h) (/ (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (* (* (* M M) M) (* (* D D) D))) (* (* (* 2 d) (* 2 d)) (* 2 d))))
2.2s
(* (* (* h h) h) (/ (* (* (* (/ 1 l) (* M D)) (* (/ 1 l) (* M D))) (* (/ 1 l) (* M D))) (* (* (* 2 d) (* 2 d)) (* 2 d))))
2.2s
(* (* (* h h) h) (/ (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (* (* (* M M) M) (* (* D D) D))) (* (* (* 2 2) 2) (* (* d d) d))))
2.2s
(* (* (* h h) h) (/ (* (* (* (/ 1 l) (* M D)) (* (/ 1 l) (* M D))) (* (/ 1 l) (* M D))) (* (* (* 2 2) 2) (* (* d d) d))))

prune3.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize82.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))))
4.2b
(/ (* M D) (* 2 d))
4.2b
(/ (* M D) (* 2 d))
4.0b
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
381×add-exp-log
243×add-cbrt-cube
197×prod-exp cbrt-unprod
117×cbrt-undiv div-exp
17×frac-times pow1
11×associate-*l/ associate-*r/
8×pow-prod-down
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×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* associate-*l* *-commutative flip--
Counts
4 → 208
Calls
4 calls:
Slowest
111.0ms
(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))))
22.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
12.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
221.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
100.0ms
(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))))
45.0ms
(/ (* M D) (* 2 d))
39.0ms
(/ (* M D) (* 2 d))

simplify1.1m

Counts
179 → 220
Calls
179 calls:
Slowest
1.9s
(* (* (/ h l) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (/ h l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.7s
(* (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l)))) (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l)))) (* (/ h l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.6s
(* (* (/ h l) (/ h l)) (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.6s
(* (* (/ h l) (/ h l)) (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.5s
(sqrt (- (pow 1 3) (pow (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d))) 3)))

prune4.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

regimes1.7s

Accuracy

0% (1.4b remaining)

Error of 7.6b against oracle of 6.2b and baseline of 7.6b

bsearch4.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.4s9324×body80valid
688.0ms3022×body80nan