Details

Time bar (total: 6.2m)

sample847.0ms

Algorithm
intervals
Results
587.0ms1500×body80nan
182.0ms416×body80valid

simplify439.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
438.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize68.0ms

Local error

Found 4 expressions with local error:

13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.7b
(pow (/ d h) (/ 1 2))
10.1b
(pow (/ d l) (/ 1 2))
7.8b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
42×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
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 222
Calls
4 calls:
Slowest
81.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
55.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms
(pow (/ d h) (/ 1 2))
9.0ms
(pow (/ d l) (/ 1 2))

series736.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
389.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
147.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
110.0ms
(pow (/ d h) (/ 1 2))
90.0ms
(pow (/ d l) (/ 1 2))

simplify44.4s

Counts
188 → 234
Calls
188 calls:
Slowest
1.1s
(* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
984.0ms
(* (* (* (* (/ 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)))
769.0ms
(* (* (* (* (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)))))
750.0ms
(* (* (* (* (/ 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)))
734.0ms
(* (* (* (* (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)))))

prune4.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 13.4b

localize91.0ms

Local error

Found 4 expressions with local error:

13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.1b
(pow (/ d l) (/ 1 2))
7.8b
(* (* (* (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))))
5.3b
(/ (* M D) (* 2 d))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
368×add-exp-log
207×prod-exp
103×div-exp
60×pow-exp
46×add-cbrt-cube
28×add-sqr-sqrt *-un-lft-identity times-frac 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
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 210
Calls
4 calls:
Slowest
159.0ms
(* (* (* (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))))
86.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
19.0ms
(/ (* M D) (* 2 d))
11.0ms
(pow (/ d l) (/ 1 2))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(* (* (* (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))))
120.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
94.0ms
(pow (/ d l) (/ 1 2))
44.0ms
(/ (* M D) (* 2 d))

simplify49.4s

Counts
174 → 222
Calls
174 calls:
Slowest
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)))))
1.0s
(* (* (* (* (* (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)))))
948.0ms
(* (* (* (* (* (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)))))
927.0ms
(* (* (* (* (/ 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)))
780.0ms
(* (* (* (* (/ 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)))

prune5.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.9b

localize142.0ms

Local error

Found 4 expressions with local error:

13.5b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.8b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.3b
(/ (* M D) (* 2 d))
3.7b
(pow (/ d (cbrt l)) (/ 1 2))

rewrite718.0ms

Algorithm
rewrite-expression-head
Rules
407×add-exp-log
241×prod-exp
104×div-exp
62×pow-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-unprod
22×unpow-prod-down
19×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow
12×pow1
9×cbrt-prod cbrt-undiv
7×associate-*l/
6×prod-diff associate-*r/
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×frac-times sqrt-div
2×sub-neg flip3-- associate-*l* *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 230
Calls
4 calls:
Slowest
599.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
72.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
24.0ms
(/ (* M D) (* 2 d))
12.0ms
(pow (/ d (cbrt l)) (/ 1 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
203.0ms
(pow (/ d (cbrt l)) (/ 1 2))
142.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
49.0ms
(/ (* M D) (* 2 d))

simplify58.1s

Counts
196 → 242
Calls
196 calls:
Slowest
1.0s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt 1) (pow (/ d (cbrt l)) (/ 1 2)))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))
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)))
955.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
842.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt 1) (pow (/ d (cbrt l)) (/ 1 2)))) (- (* 1 1) (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
822.0ms
(* (* (* (* (/ 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)))

prune7.3s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 8.4b

localize165.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
6.4b
(* (* (/ D d) (/ M 2)) h)
5.2b
(* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l))
4.9b
(* (/ D d) (/ M 2))

rewrite6.1s

Algorithm
rewrite-expression-head
Rules
1956×add-cbrt-cube add-exp-log
1279×prod-exp cbrt-unprod
467×cbrt-undiv div-exp
87×associate-*l/
58×associate-*r/
56×frac-times
35×add-sqr-sqrt
31×associate-/l/
28×times-frac
24×sqrt-div
23×*-un-lft-identity associate-*r* add-cube-cbrt
16×pow1
15×associate-*l*
7×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×associate-/r* *-commutative
1×clear-num frac-2neg associate-/l*
Counts
4 → 556
Calls
4 calls:
Slowest
4.5s
(* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l))
1.5s
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
48.0ms
(* (* (/ D d) (/ M 2)) h)
13.0ms
(* (/ D d) (/ M 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
706.0ms
(* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l))
409.0ms
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
69.0ms
(* (* (/ D d) (/ M 2)) h)
34.0ms
(* (/ D d) (/ M 2))

simplify2.6m

Counts
527 → 568
Calls
527 calls:
Slowest
2.7s
(/ (* (* (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (* (* l l) l))
1.1s
(* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (* (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)))
1.0s
(* (* (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ d (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (* (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)))
841.0ms
(- (+ (+ (log -1/2) (+ (+ (log (/ D d)) (- (log M) (log 2))) (+ (+ (log (/ D d)) (log (/ M 2))) (log h)))) (log (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (log l))
841.0ms
(+ (+ (log (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (log (sqrt (/ d (cbrt l))))) (- (+ (+ (log -1/2) (+ (+ (- (log D) (log d)) (- (log M) (log 2))) (+ (+ (- (log D) (log d)) (- (log M) (log 2))) (log h)))) (+ (log (sqrt (/ (cbrt d) (cbrt h)))) (log (fabs (/ (cbrt d) (cbrt h)))))) (log l)))

prune11.6s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 6.2b

regimes2.8s

Accuracy

24.9% (5.7b remaining)

Error of 10.4b against oracle of 4.7b and baseline of 12.3b

bsearch47.0ms

end0.0ms

sample14.8s

Algorithm
intervals
Results
10.0s39025×body80nan
3.4s12826×body80valid