Details

Time bar (total: 2.3m)

sample74.0ms

Algorithm
intervals
Results
42.0ms295×body80valid
12.0ms102×body80nan

simplify177.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
177.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize43.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (/ h l) (/ (* M D) (* 2 d)))
4.7b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
4.1b
(/ (* M D) (* 2 d))
4.1b
(/ (* M D) (* 2 d))

rewrite73.0ms

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
43.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
12.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
106.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
51.0ms
(/ (* M D) (* 2 d))
48.0ms
(/ (* M D) (* 2 d))

simplify25.8s

Counts
84 → 133
Calls
84 calls:
Slowest
1.8s
(* (/ (* (* 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 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 2) 2) (* (* d d) d))))
1.2s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.8b

localize54.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ (* h (/ (* M D) (* 2 d))) l)
4.7b
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
4.3b
(* h (/ (* M D) (* 2 d)))
4.1b
(/ (* M D) (* 2 d))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
59×add-cbrt-cube add-exp-log
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×pow1
5×times-frac associate-*r*
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* sqrt-prod div-inv
2×clear-num frac-2neg sqrt-div associate-*r/ associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down *-commutative flip-- unswap-sqr associate-/l/
Counts
4 → 107
Calls
4 calls:
Slowest
27.0ms
(* h (/ (* M D) (* 2 d)))
27.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
11.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
343.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
106.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
57.0ms
(* h (/ (* M D) (* 2 d)))
43.0ms
(/ (* M D) (* 2 d))

simplify24.9s

Counts
71 → 119
Calls
71 calls:
Slowest
1.5s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.4s
(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.4s
(/ (* (* (* 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))))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize47.0ms

Local error

Found 4 expressions with local error:

5.6b
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
5.3b
(* (/ 1 l) (/ (* M D) (* 2 d)))
4.7b
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
4.1b
(/ (* M D) (* 2 d))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
192×add-exp-log
110×add-cbrt-cube
97×prod-exp
56×div-exp
51×cbrt-unprod
30×cbrt-undiv
22×add-sqr-sqrt
16×associate-*l*
15×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
12×pow1
10×rec-exp 1-exp
6×associate-*r*
5×associate-*r/
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
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 → 160
Calls
4 calls:
Slowest
66.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
26.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
15.0ms
(/ (* M D) (* 2 d))
5.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(sqrt (- 1 (* (* h (* (/ 1 l) (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
114.0ms
(* h (* (/ 1 l) (/ (* M D) (* 2 d))))
51.0ms
(* (/ 1 l) (/ (* M D) (* 2 d)))
37.0ms
(/ (* M D) (* 2 d))

simplify48.3s

Counts
125 → 172
Calls
125 calls:
Slowest
2.0s
(* (* (* h h) h) (* (* (* (/ 1 l) (/ 1 l)) (/ 1 l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.8s
(* (* (* (/ 1 l) (/ 1 l)) (/ 1 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 1) 1) (* (* l l) 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 2) 2) (* (* d d) d)))))

prune3.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

localize48.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ (* h (/ (* M D) (* 2 d))) l)
6.1b
(/ M (/ (* 2 d) D))
4.7b
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ M (/ (* 2 d) D)))))
4.3b
(* h (/ (* M D) (* 2 d)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
56×add-cbrt-cube add-exp-log
37×times-frac
28×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
19×cbrt-undiv div-exp prod-exp cbrt-unprod
10×associate-/r*
7×pow1 div-inv
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-*l* sqrt-prod
2×clear-num frac-2neg sqrt-div associate-*r/
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-/r/ *-commutative flip-- unswap-sqr associate-/l/
Counts
4 → 134
Calls
4 calls:
Slowest
45.0ms
(* h (/ (* M D) (* 2 d)))
30.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
9.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ M (/ (* 2 d) D)))))
7.0ms
(/ M (/ (* 2 d) D))

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
383.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ M (/ (* 2 d) D)))))
94.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
61.0ms
(* h (/ (* M D) (* 2 d)))
40.0ms
(/ M (/ (* 2 d) D))

simplify25.4s

Counts
118 → 146
Calls
118 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 D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.3s
(/ (* (* (* h (/ (* M D) (* 2 d))) (* h (/ (* M D) (* 2 d)))) (* h (/ (* M 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))

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.6b

regimes1.1s

Accuracy

0% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 8.3b

bsearch7.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.2s9348×body80valid
604.0ms3118×body80nan