Details

Time bar (total: 4.6m)

sample738.0ms

Algorithm
intervals
Results
495.0ms1297×body80nan
160.0ms426×body80valid

simplify356.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
356.0ms
(* (* (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: 22.5b

localize71.0ms

Local error

Found 4 expressions with local error:

13.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.3b
(pow (/ d l) (/ 1 2))
8.3b
(pow (/ d h) (/ 1 2))
4.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite154.0ms

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
75.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
62.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
4.0ms
(pow (/ d l) (/ 1 2))
4.0ms
(pow (/ d h) (/ 1 2))

series699.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
104.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
98.0ms
(pow (/ d h) (/ 1 2))
85.0ms
(pow (/ d l) (/ 1 2))

simplify41.1s

Counts
182 → 220
Calls
182 calls:
Slowest
986.0ms
(* (* (* (* (/ 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)))
890.0ms
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (log (/ h l)))
808.0ms
(* (* (* (* (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)))))
761.0ms
(* (* (* (* (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)))))
743.0ms
(* (* (* (* (/ 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)))

prune4.4s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 10.9b

localize100.0ms

Local error

Found 4 expressions with local error:

13.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.3b
(pow (/ d l) (/ 1 2))
4.6b
(* (* (* (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))))
3.9b
(/ (* M D) (* 2 d))

rewrite263.0ms

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
182.0ms
(* (* (* (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))))
56.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
9.0ms
(pow (/ d l) (/ 1 2))

series1.5s

Counts
4 → 12
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))))
89.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
77.0ms
(pow (/ d l) (/ 1 2))
47.0ms
(/ (* M D) (* 2 d))

simplify45.6s

Counts
168 → 208
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)))))
1.2s
(* (* (* (* (* (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))) (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)))))
882.0ms
(* (* (* (* (/ 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)))
842.0ms
(* (* (* (* (/ 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)))

prune4.9s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 9.9b

localize152.0ms

Local error

Found 4 expressions with local error:

13.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
4.6b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
3.9b
(/ (* M D) (* 2 d))
3.6b
(pow (/ (cbrt d) l) (/ 1 2))

rewrite328.0ms

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
4×pow-prod-down insert-posit16 div-inv add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 213
Calls
4 calls:
Slowest
224.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
83.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ (cbrt d) l) (/ 1 2))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
224.0ms
(pow (/ (cbrt d) l) (/ 1 2))
111.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
40.0ms
(/ (* M D) (* 2 d))

simplify51.4s

Counts
185 → 225
Calls
185 calls:
Slowest
1.6s
(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2))))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt 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)))))
862.0ms
(* (* (* (* (/ 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)))
860.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
859.0ms
(+ (+ (log (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (+ (log (fabs (cbrt d))) (* (- (log (cbrt d)) (log l)) (/ 1 2)))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
815.0ms
(* (* (* (* (/ 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)))

prune5.7s

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 8.0b

localize143.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
5.6b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
4.6b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
3.9b
(/ (* M D) (* 2 d))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
892×add-exp-log
580×prod-exp
224×div-exp
120×pow-exp
75×add-cbrt-cube
65×rec-exp 1-exp
40×cbrt-unprod
30×pow-to-exp
19×associate-*r*
16×pow1
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cbrt-undiv
10×times-frac
7×pow-prod-down associate-*l/
4×insert-posit16 add-log-exp
3×associate-*l* associate-*r/ *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- un-div-inv flip-- associate-/l*
Counts
4 → 278
Calls
4 calls:
Slowest
182.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
149.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
40.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
18.0ms
(/ (* M D) (* 2 d))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
146.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
122.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
38.0ms
(/ (* M D) (* 2 d))

simplify1.3m

Counts
249 → 290
Calls
249 calls:
Slowest
1.1s
(* (* (* (* (* (/ 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)) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
1.1s
(* (* (* (* (* (/ 1 2) (/ 1 2)) (/ 1 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (* (* h h) h)) (/ (* (* 1 1) 1) (* (* l l) l)))
950.0ms
(* (* (* (* (* (/ 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)) (/ (* (* 1 1) 1) (* (* l l) l)))
842.0ms
(* (- (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))))
825.0ms
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)) (/ (* (* 1 1) 1) (* (* l l) l)))

prune7.2s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 7.3b

regimes3.4s

Accuracy

1.2% (6.6b remaining)

Error of 15.4b against oracle of 8.8b and baseline of 15.5b

bsearch1.3s

end0.0ms

sample23.9s

Algorithm
intervals
Results
15.9s38190×body80nan
6.2s12604×body80valid