Details

Time bar (total: 2.8m)

sample131.0ms

Algorithm
intervals
Results
79.0ms304×body80valid
25.0ms109×body80nan

simplify153.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(* 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: 15.5b

localize42.0ms

Local error

Found 4 expressions with local error:

11.4b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
5.6b
(/ (* M D) (* 2 d))
5.6b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite276.0ms

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
216.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
114.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
50.0ms
(/ (* M D) (* 2 d))
34.0ms
(/ (* M D) (* 2 d))

simplify51.2s

Counts
172 → 210
Calls
172 calls:
Slowest
2.9s
(* (* (/ (* (* (* 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)))
2.5s
(* (* (/ (* (* (* 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 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)))

prune3.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.6b

localize54.0ms

Local error

Found 4 expressions with local error:

9.6b
(* (/ (* M D) (* 2 d)) (/ h l))
5.6b
(/ (* M D) (* 2 d))
5.6b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))

rewrite74.0ms

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-*r* add-cube-cbrt
7×pow1
5×associate-*l*
4×insert-posit16 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 → 113
Calls
4 calls:
Slowest
41.0ms
(* (/ (* M D) (* 2 d)) (/ h l))
15.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) (/ h l)))))
95.0ms
(* (/ (* M D) (* 2 d)) (/ h l))
54.0ms
(/ (* M D) (* 2 d))
35.0ms
(/ (* M D) (* 2 d))

simplify25.4s

Counts
84 → 125
Calls
84 calls:
Slowest
1.5s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* h h) h) (* (* l l) l)))
1.4s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* h h) h) (* (* l l) l)))
1.3s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ h l) (/ h l)) (/ h l)))
1.3s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* h h) h) (* (* l l) l)))
1.2s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ h l) (/ h l)) (/ h l)))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.6b

localize44.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (/ (* M D) (* 2 d)) h) (/ 1 l))
5.6b
(/ (* M D) (* 2 d))
5.6b
(/ (* M D) (* 2 d))
5.1b
(* (/ (* M D) (* 2 d)) h)

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
102×add-cbrt-cube
77×prod-exp
47×cbrt-unprod
40×div-exp
26×cbrt-undiv
16×associate-*r*
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
11×pow1
6×rec-exp 1-exp associate-*l*
4×pow-prod-down associate-*l/ insert-posit16 div-inv add-log-exp
2×clear-num associate-/r* frac-2neg *-commutative associate-/l*
1×frac-times associate-*r/ un-div-inv unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
112.0ms
(* (* (/ (* M D) (* 2 d)) h) (/ 1 l))
33.0ms
(* (/ (* M D) (* 2 d)) h)
21.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))

series264.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(* (* (/ (* M D) (* 2 d)) h) (/ 1 l))
68.0ms
(* (/ (* M D) (* 2 d)) h)
49.0ms
(/ (* M D) (* 2 d))
37.0ms
(/ (* M D) (* 2 d))

simplify39.4s

Counts
107 → 151
Calls
107 calls:
Slowest
1.7s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (/ (* (* 1 1) 1) (* (* l l) l)))
1.7s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (/ (* (* 1 1) 1) (* (* l l) l)))
1.6s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (* (* h h) h)) (/ (* (* 1 1) 1) (* (* l l) l)))
1.5s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
1.4s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h)) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.6b

localize53.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (/ M 2) (* (/ D d) h)) (/ 1 l))
5.6b
(/ (* M D) (* 2 d))
5.3b
(* (/ M 2) (* (/ D d) h))
4.9b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l)))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
160×add-exp-log
102×add-cbrt-cube
82×prod-exp
48×cbrt-unprod
43×div-exp
26×cbrt-undiv
20×add-sqr-sqrt
19×pow1 *-un-lft-identity times-frac add-cube-cbrt
14×associate-*r* associate-*l*
12×associate-*l/
9×pow-prod-down
7×rec-exp 1-exp
6×frac-times
4×associate-*r/ insert-posit16 add-log-exp
3×sqrt-prod div-inv
2×sqrt-div *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 un-div-inv flip-- associate-/l*
Counts
4 → 154
Calls
4 calls:
Slowest
103.0ms
(* (* (/ M 2) (* (/ D d) h)) (/ 1 l))
24.0ms
(* (/ M 2) (* (/ D d) h))
12.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l)))))
73.0ms
(* (* (/ M 2) (* (/ D d) h)) (/ 1 l))
63.0ms
(* (/ M 2) (* (/ D d) h))
44.0ms
(/ (* M D) (* 2 d))

simplify33.9s

Counts
125 → 166
Calls
125 calls:
Slowest
1.1s
(sqrt (- (pow 1 3) (pow (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l))) 3)))
1.0s
(* (* (* (* (/ M 2) (/ M 2)) (/ M 2)) (* (* (* (/ D d) h) (* (/ D d) h)) (* (/ D d) h))) (/ (* (* 1 1) 1) (* (* l l) l)))
1.0s
(sqrt (- (* 1 1) (* (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l))) (* (/ (* M D) (* 2 d)) (* (* (/ M 2) (* (/ D d) h)) (/ 1 l))))))
995.0ms
(* (* (/ (* (* M M) M) (* (* 2 2) 2)) (* (/ (* (* D D) D) (* (* d d) d)) (* (* h h) h))) (/ (* (* 1 1) 1) (* (* l l) l)))
806.0ms
(* (* (/ (* (* M M) M) (* (* 2 2) 2)) (* (/ (* (* D D) D) (* (* d d) d)) (* (* h h) h))) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.1b

regimes1.4s

Accuracy

0% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 8.4b

bsearch7.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s9390×body80valid
1.1s3105×body80nan