Details

Time bar (total: 6.1m)

sample838.0ms

Algorithm
intervals
Results
556.0ms1500×body80nan
155.0ms416×body80valid

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.8b

localize53.0ms

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))))

rewrite136.0ms

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--
Counts
4 → 208
Calls
4 calls:
Slowest
62.0ms
(* (* (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))
4.0ms
(pow (/ d l) (/ 1 2))
4.0ms
(pow (/ d h) (/ 1 2))

series618.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
106.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
81.0ms
(pow (/ d l) (/ 1 2))
69.0ms
(pow (/ d h) (/ 1 2))

simplify40.4s

Counts
182 → 220
Calls
182 calls:
Slowest
886.0ms
(* (* (* (* (/ 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)))
879.0ms
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (log (/ h l)))
842.0ms
(+ (+ (* (log (/ d h)) (/ 1 2)) (log (pow (/ d l) (/ 1 2)))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
801.0ms
(* (* (* (* (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)))))
697.0ms
(* (* (/ (* (* 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)))

prune4.3s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 14.3b

localize100.0ms

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))

rewrite308.0ms

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
Counts
4 → 196
Calls
4 calls:
Slowest
204.0ms
(* (* (* (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))))
69.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
4.0ms
(pow (/ d l) (/ 1 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(* (* (* (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))))
122.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
74.0ms
(pow (/ d l) (/ 1 2))
30.0ms
(/ (* M D) (* 2 d))

simplify44.7s

Counts
168 → 208
Calls
168 calls:
Slowest
1.4s
(* (* (* (* (* (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))) (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)))))
1.0s
(* (* (* (* (* (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)))))
915.0ms
(* (* (* (* (/ 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)))
855.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (log (/ h l)))

prune5.1s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 11.8b

localize113.0ms

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))

rewrite593.0ms

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
32×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×associate-*r/
4×pow-prod-down insert-posit16 div-inv add-log-exp
3×frac-times sqrt-div
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-*l* *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 216
Calls
4 calls:
Slowest
514.0ms
(* (* (* (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))))
50.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
7.0ms
(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))))
219.0ms
(pow (/ d (cbrt l)) (/ 1 2))
126.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
30.0ms
(/ (* M D) (* 2 d))

simplify54.1s

Counts
190 → 228
Calls
190 calls:
Slowest
1.1s
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))
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)))
928.0ms
(* (* (* (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)))))
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 h) h) (* (* l l) l)))
873.0ms
(* (* (* (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 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune6.7s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 9.3b

localize196.0ms

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))

rewrite5.8s

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×insert-posit16 div-inv add-log-exp unswap-sqr
3×associate-/r* *-commutative
1×clear-num frac-2neg associate-/l*
Counts
4 → 548
Calls
4 calls:
Slowest
4.2s
(* (* (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))
1.4s
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
46.0ms
(* (* (/ D d) (/ M 2)) h)
24.0ms
(* (/ D d) (/ M 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
823.0ms
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
686.0ms
(* (* (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))
64.0ms
(* (* (/ D d) (/ M 2)) h)
37.0ms
(* (/ D d) (/ M 2))

simplify2.8m

Counts
527 → 560
Calls
527 calls:
Slowest
2.6s
(/ (* (* (* (* -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))
1.4s
(* (* (* (* (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)))
1.4s
(+ (+ (log (sqrt (/ 1 (* (cbrt l) (cbrt l))))) (log (sqrt (/ d (cbrt l))))) (- (+ (+ (log -1/2) (+ (+ (log (/ D d)) (log (/ M 2))) (+ (+ (- (log D) (log d)) (- (log M) (log 2))) (log h)))) (log (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (log 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)))
959.0ms
(+ (+ (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 d)) (- (log M) (log 2))) (log h)))) (log (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))))) (log l)))

prune10.7s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 6.2b

regimes2.6s

Accuracy

10% (6.6b remaining)

Error of 11.6b against oracle of 5.0b and baseline of 12.3b

bsearch26.0ms

end0.0ms

sample14.6s

Algorithm
intervals
Results
9.9s39025×body80nan
3.3s12826×body80valid