Details

Time bar (total: 2.4m)

sample101.0ms

Algorithm
intervals
Results
60.0ms290×body80valid
15.0ms89×body80nan

simplify146.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
146.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize58.0ms

Local error

Found 4 expressions with local error:

11.9b
(* (/ h l) (/ (* M D) (* 2 d)))
4.3b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
4.1b
(/ (* M D) (* 2 d))
4.1b
(/ (* M D) (* 2 d))

rewrite123.0ms

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
60.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
24.0ms
(/ (* M D) (* 2 d))
24.0ms
(/ (* M D) (* 2 d))
12.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
102.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
47.0ms
(/ (* M D) (* 2 d))
40.0ms
(/ (* M D) (* 2 d))

simplify25.4s

Counts
84 → 133
Calls
84 calls:
Slowest
1.6s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) 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 d) (* 2 d)) (* 2 d))))
1.3s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize40.0ms

Local error

Found 4 expressions with local error:

8.0b
(* h (/ (* M D) (* 2 d)))
5.3b
(/ (* h (/ (* M D) (* 2 d))) l)
4.3b
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
4.1b
(/ (* M D) (* 2 d))

rewrite80.0ms

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
30.0ms
(* h (/ (* M D) (* 2 d)))
26.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
12.0ms
(/ (* M D) (* 2 d))
10.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series490.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
82.0ms
(/ (* h (/ (* M D) (* 2 d))) l)
54.0ms
(* h (/ (* M D) (* 2 d)))
30.0ms
(/ (* M D) (* 2 d))

simplify24.0s

Counts
71 → 119
Calls
71 calls:
Slowest
1.6s
(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.6s
(/ (* (* (* 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))))

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize101.0ms

Local error

Found 4 expressions with local error:

8.0b
(* h (/ (* M D) (* 2 d)))
8.0b
(* h (/ (* M D) (* 2 d)))
8.0b
(* h (/ (* M D) (* 2 d)))
6.0b
(cbrt (* (* (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
58×add-cbrt-cube add-exp-log
54×sqrt-div
28×frac-times
27×flip3-- prod-exp cbrt-unprod flip--
26×cbrt-div
16×add-sqr-sqrt
15×associate-*r*
14×associate-*l/
12×cbrt-undiv div-exp
11×associate-*r/
10×pow1 *-un-lft-identity add-cube-cbrt
9×associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac pow-prod-down *-commutative div-inv unswap-sqr
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 135
Calls
4 calls:
Slowest
54.0ms
(cbrt (* (* (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))))
44.0ms
(* h (/ (* M D) (* 2 d)))
43.0ms
(* h (/ (* M D) (* 2 d)))
43.0ms
(* h (/ (* M D) (* 2 d)))

series575.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
373.0ms
(cbrt (* (* (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))))
88.0ms
(* h (/ (* M D) (* 2 d)))
62.0ms
(* h (/ (* M D) (* 2 d)))
53.0ms
(* h (/ (* M D) (* 2 d)))

simplify54.4s

Counts
103 → 147
Calls
103 calls:
Slowest
1.5s
(cbrt (* (* (sqrt (- (pow 1 3) (pow (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) 3))) (sqrt (- (* 1 1) (* (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))))
1.5s
(cbrt (* (* (sqrt (- (pow 1 3) (pow (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) 3))) (sqrt (- (* 1 1) (* (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))))) (sqrt (- (pow 1 3) (pow (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) 3)))))
1.5s
(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.5s
(cbrt (* (* (sqrt (- (* 1 1) (* (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))) (sqrt (- (pow 1 3) (pow (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) 3)))) (sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))))
1.4s
(cbrt (* (* (sqrt (- (* 1 1) (* (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))) (sqrt (- (* 1 1) (* (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))))))) (sqrt (- (pow 1 3) (pow (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d))) 3)))))

prune3.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.2b

localize80.0ms

Local error

Found 4 expressions with local error:

11.9b
(* (/ h l) (* (/ M 2) (/ D d)))
5.3b
(* (/ M 2) (/ D d))
4.3b
(sqrt (- 1 (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d)))))
4.1b
(/ (* M D) (* 2 d))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
39×add-sqr-sqrt
32×times-frac
26×*-un-lft-identity associate-*l* prod-exp add-cube-cbrt cbrt-unprod
21×cbrt-undiv div-exp
14×associate-*r*
12×pow1
6×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×sqrt-prod
2×sqrt-div *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 flip-- associate-/l*
Counts
4 → 149
Calls
4 calls:
Slowest
57.0ms
(* (/ h l) (* (/ M 2) (/ D d)))
18.0ms
(* (/ M 2) (/ D d))
12.0ms
(/ (* M D) (* 2 d))
9.0ms
(sqrt (- 1 (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d)))))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
201.0ms
(sqrt (- 1 (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d)))))
79.0ms
(* (/ h l) (* (/ M 2) (/ D d)))
45.0ms
(/ (* M D) (* 2 d))
32.0ms
(* (/ M 2) (/ D d))

simplify19.8s

Counts
115 → 161
Calls
115 calls:
Slowest
1.2s
(sqrt (- (* 1 1) (* (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d))) (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d))))))
872.0ms
(sqrt (- (pow 1 3) (pow (* (* (/ h l) (* (/ M 2) (/ D d))) (/ (* M D) (* 2 d))) 3)))
673.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
671.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
649.0ms
(+ (log (/ h l)) (+ (log (/ M 2)) (- (log D) (log d))))

prune2.9s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.5b

regimes1.3s

Accuracy

-16.6% (1.3b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.0b

bsearch252.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.8s9286×body80valid
996.0ms3082×body80nan