Details

Time bar (total: 1.8m)

sample735.0ms

Algorithm
intervals
Results
451.0ms1281×body80nan
189.0ms402×body80valid

simplify339.0ms

Calls
1 calls:
Slowest
339.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.6b

localize82.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
11.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.6b
(pow (/ d h) (/ 1 2))
8.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
28×prod-exp
14×add-cbrt-cube
10×add-sqr-sqrt pow1 *-un-lft-identity pow-exp add-cube-cbrt
9×pow-to-exp
8×pow-unpow unpow-prod-down
7×associate-*r*
6×cbrt-unprod
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- div-exp flip--
Calls
4 calls:
Slowest
35.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
22.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.0ms
(pow (/ d h) (/ 1 2))
2.0ms
(pow (/ d l) (/ 1 2))

series710.0ms

Calls
4 calls:
Slowest
418.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
118.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
91.0ms
(pow (/ d h) (/ 1 2))
83.0ms
(pow (/ d l) (/ 1 2))

simplify12.4s

Calls
71 calls:
Slowest
664.0ms
(+ 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))
656.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
549.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
470.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
458.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.8b

localize46.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
10.6b
(pow (/ d h) (/ 1 2))
8.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
7.5b
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
26×associate-*l/
19×prod-exp
17×frac-times
15×associate-/l/
13×associate-*r/
11×add-cbrt-cube
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow-to-exp pow1 pow-unpow unpow-prod-down pow-exp
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in
1×cbrt-undiv clear-num associate-/r* frac-2neg times-frac flip3-- div-exp associate-*l* pow-prod-down *-commutative flip-- associate-/l*
Calls
4 calls:
Slowest
61.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
23.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
2.0ms
(pow (/ d l) (/ 1 2))
2.0ms
(pow (/ d h) (/ 1 2))

series692.0ms

Calls
4 calls:
Slowest
364.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
129.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
101.0ms
(pow (/ d h) (/ 1 2))
98.0ms
(pow (/ d l) (/ 1 2))

simplify16.8s

Calls
75 calls:
Slowest
1.9s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
743.0ms
(+ (* 1 1) (+ (* (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (* 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
528.0ms
(* (* (* (/ M d) D) (* (/ M d) (/ D 2))) h)
518.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
512.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.6b

localize38.0ms

Local error

Found 4 expressions with local error:

14.0b
(sqrt (/ (/ -1 l) (/ -1 d)))
10.6b
(pow (/ d h) (/ 1 2))
8.6b
(* (* (pow (/ d h) (/ 1 2)) (sqrt (/ (/ -1 l) (/ -1 d)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
7.5b
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-*l/
21×sqrt-prod
19×add-sqr-sqrt frac-times
18×times-frac
17×add-exp-log
16×*-un-lft-identity associate-*r/ add-cube-cbrt
15×associate-/l/
12×div-inv
11×add-cbrt-cube
7×pow1 prod-exp
4×expm1-log1p-u pow-unpow unpow-prod-down sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod
2×distribute-rgt-in pow-to-exp rem-sqrt-square sub-neg distribute-lft-in flip3-- pow-exp flip--
1×cbrt-undiv clear-num associate-/r* pow-pow frac-2neg pow1/2 div-exp associate-*l* pow-prod-down associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
64.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
37.0ms
(* (* (pow (/ d h) (/ 1 2)) (sqrt (/ (/ -1 l) (/ -1 d)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
4.0ms
(pow (/ d h) (/ 1 2))
4.0ms
(sqrt (/ (/ -1 l) (/ -1 d)))

series590.0ms

Calls
4 calls:
Slowest
366.0ms
(* (* (pow (/ d h) (/ 1 2)) (sqrt (/ (/ -1 l) (/ -1 d)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
115.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
67.0ms
(pow (/ d h) (/ 1 2))
43.0ms
(sqrt (/ (/ -1 l) (/ -1 d)))

simplify18.9s

Calls
88 calls:
Slowest
1.9s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
917.0ms
(* (sqrt (/ -1 d)) (+ (* 1 1) (+ (* (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (* 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))))
739.0ms
(+ (* 1 1) (+ (* (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (* 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
730.0ms
(* (* (pow (/ d h) (/ 1 2)) (sqrt (/ -1 l))) (- (* 1 1) (* (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
685.0ms
(* (* (pow (/ d h) (/ 1 2)) (sqrt (/ -1 l))) (- (pow 1 3) (pow (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) 3)))

prune2.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.1b

localize46.0ms

Local error

Found 4 expressions with local error:

10.6b
(pow (/ d h) (/ 1 2))
8.6b
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
7.5b
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
6.4b
(* (/ M d) (/ D 2))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
28×associate-*l/
20×frac-times associate-*r/
17×add-cbrt-cube prod-exp
15×associate-/l/
9×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
7×associate-*r* cbrt-unprod
5×associate-*l* div-inv
4×expm1-log1p-u pow-unpow unpow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- pow-prod-down *-commutative flip--
1×cbrt-undiv clear-num associate-/r* pow-pow frac-2neg times-frac div-exp associate-/l*
Calls
4 calls:
Slowest
73.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
51.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
8.0ms
(* (/ M d) (/ D 2))
4.0ms
(pow (/ d h) (/ 1 2))

series1.0s

Calls
4 calls:
Slowest
818.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))))
114.0ms
(/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))
77.0ms
(pow (/ d h) (/ 1 2))
37.0ms
(* (/ M d) (/ D 2))

simplify22.3s

Calls
80 calls:
Slowest
2.0s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
1.1s
(* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (cbrt (/ -1 l))))) (- (pow 1 3) (pow (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)) 3)))
950.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))))) (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))))) (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))))) (* (* (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
930.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))))) (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))))) (* (* (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))
899.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))) (fabs (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))) (* (* (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))) (sqrt (/ (cbrt (/ -1 l)) (cbrt (/ -1 d))))))) (* (* (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))) (- 1 (/ (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* 2 l)))))

prune2.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.7b

regimes2.2s

Accuracy

40.6% (6.0b remaining)

Error of 16.4b against oracle of 10.5b and baseline of 20.5b

bsearch30.0ms

end0.0ms

sample22.7s

Algorithm
intervals
Results
14.7s37967×body80nan
6.2s12823×body80valid