Details

Time bar (total: 4.1m)

sample650.0ms

Algorithm
intervals
Results
398.0ms1281×body80nan
190.0ms402×body80valid

simplify359.0ms

Calls
1 calls:
Slowest
359.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize80.0ms

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))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×insert-posit16 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 sqr-pow
1×frac-times flip3-- flip--
Calls
4 calls:
Slowest
59.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
48.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms
(pow (/ d l) (/ 1 2))
5.0ms
(pow (/ d h) (/ 1 2))

series661.0ms

Calls
4 calls:
Slowest
394.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
110.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
84.0ms
(pow (/ d h) (/ 1 2))
74.0ms
(pow (/ d l) (/ 1 2))

simplify41.8s

Calls
182 calls:
Slowest
1.3s
(* (* (* (* (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)))))
850.0ms
(* (* (* (* (/ 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 h) h) (* (* l l) l)))
799.0ms
(* (* (* (* (/ 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)))
713.0ms
(* (* (* (* (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)))))
702.0ms
(+ (+ (- 0 (log 2)) (* (log (/ (* M D) (* 2 d))) 2)) (log (/ h l)))

prune4.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.5b

localize124.0ms

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))
8.6b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.5b
(/ (* M D) (* 2 d))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
368×add-exp-log
207×prod-exp
103×div-exp
60×pow-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
4×insert-posit16 div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Calls
4 calls:
Slowest
144.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
85.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(pow (/ d l) (/ 1 2))

series1.5s

Calls
4 calls:
Slowest
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
93.0ms
(pow (/ d l) (/ 1 2))
85.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
41.0ms
(/ (* M D) (* 2 d))

simplify46.0s

Calls
168 calls:
Slowest
1.2s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt 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)))))
1.1s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt 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)))))
1.1s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ (cbrt d) (cbrt 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)))))
1.0s
(* (* (* (* (/ 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 h) h) (* (* l l) l)))
883.0ms
(+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))

prune4.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 11.5b

localize107.0ms

Local error

Found 4 expressions with local error:

11.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.6b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.5b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
404×add-exp-log
241×prod-exp
103×div-exp
60×pow-exp
55×add-cbrt-cube
27×cbrt-unprod
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×pow1
10×times-frac
9×cbrt-undiv
4×pow-prod-down insert-posit16 add-log-exp
3×cbrt-prod associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- pow1/3 flip-- associate-/l*
Calls
4 calls:
Slowest
226.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
51.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

series2.0s

Calls
4 calls:
Slowest
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
286.0ms
(cbrt l)
115.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
41.0ms
(/ (* M D) (* 2 d))

simplify47.9s

Calls
150 calls:
Slowest
1.0s
(* (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))))
999.0ms
(* (* (* (* (/ 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 h) h) (* (* l l) l)))
897.0ms
(* (* (* (* (/ 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)))
761.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
728.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune5.3s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 7.7b

localize116.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
5.5b
(/ (* M D) (* d 2))
5.5b
(/ (* M D) (* d 2))
5.4b
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
359×add-exp-log
260×add-cbrt-cube
192×prod-exp
114×cbrt-unprod
111×div-exp
101×cbrt-undiv
35×times-frac
32×add-sqr-sqrt
26×associate-*l*
24×*-un-lft-identity
20×pow-exp add-cube-cbrt
11×pow1 associate-*r*
10×pow-to-exp
6×div-inv
4×pow-prod-down insert-posit16 add-log-exp difference-of-squares
3×unswap-sqr
2×distribute-rgt-in clear-num associate-/r* sub-neg frac-2neg distribute-lft-in associate-*r/ *-commutative associate-/l* sqr-pow
1×flip3-- associate-*l/ flip-- distribute-lft-out--
Calls
4 calls:
Slowest
218.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
190.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
22.0ms
(/ (* M D) (* d 2))
22.0ms
(/ (* M D) (* d 2))

series1.8s

Calls
4 calls:
Slowest
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
118.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
53.0ms
(/ (* M D) (* d 2))
47.0ms
(/ (* M D) (* d 2))

simplify54.2s

Calls
170 calls:
Slowest
1.3s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2))) (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
1.3s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
932.0ms
(+ (+ (+ (log (fabs (/ (cbrt d) (cbrt h)))) (log (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (+ (log (fabs (/ (cbrt d) (cbrt l)))) (* (log (/ (cbrt d) (cbrt l))) (/ 1 2)))) (log (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1))))
878.0ms
(* (/ (* (* (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)) (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)) (* (* l l) l)) (* (* h h) h))
751.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* d 2) (* d 2)) (* d 2)))

prune5.6s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 6.0b

regimes3.8s

Accuracy

0% (4.0b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 9.5b

bsearch1.3s

end0.0ms

sample22.6s

Algorithm
intervals
Results
15.5s37967×body80nan
5.3s12823×body80valid