Details

Time bar (total: 7.4m)

sample1.0s

Algorithm
intervals
Results
418.0ms1139×body80nan
180.0ms389×body80valid

simplify357.0ms

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))))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.8b

localize113.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.3b
(pow (/ d h) (/ 1 2))
5.9b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite124.0ms

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
61.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
43.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
9.0ms
(pow (/ d l) (/ 1 2))
6.0ms
(pow (/ d h) (/ 1 2))

series715.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
376.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
145.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
109.0ms
(pow (/ d h) (/ 1 2))
84.0ms
(pow (/ d l) (/ 1 2))

simplify44.7s

Counts
188 → 234
Calls
188 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 l) (/ h l)) (/ h l)))
981.0ms
(* (* (* (* (/ 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)))
874.0ms
(* (* (* (* (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)))))
739.0ms
(* (* (* (* (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)))))
717.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log h) (log l)))

prune4.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.1b

localize86.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.3b
(pow (/ d h) (/ 1 2))
5.9b
(* (* (pow (/ d 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))))
3.5b
(/ (* M D) (* 2 d))

rewrite198.0ms

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
114.0ms
(* (* (pow (/ d 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))))
48.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
23.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d h) (/ 1 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
887.0ms
(* (* (pow (/ d 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))))
111.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
69.0ms
(pow (/ d h) (/ 1 2))
32.0ms
(/ (* M D) (* 2 d))

simplify50.1s

Counts
174 → 222
Calls
174 calls:
Slowest
1.2s
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt d) (cbrt l))) (fabs (/ (cbrt d) (cbrt l)))) (fabs (/ (cbrt d) (cbrt l)))) (* (* (pow (/ (cbrt d) (cbrt l)) (/ 1 2)) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))) (pow (/ (cbrt d) (cbrt 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
(* (* (* (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))))) (* (pow (/ d 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))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
1.0s
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 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))) (- 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)))
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)))

prune5.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.4b

localize114.0ms

Local error

Found 4 expressions with local error:

11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.9b
(* (* (* (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))))
3.5b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite306.0ms

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*
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×rec-exp 1-exp
11×pow1
10×times-frac
9×cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod associate-*l/ associate-*r/
2×sub-neg associate-*l* *-commutative div-inv
1×frac-times clear-num associate-/r* frac-2neg flip3-- pow1/3 flip-- associate-/l*
Counts
4 → 191
Calls
4 calls:
Slowest
215.0ms
(* (* (* (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))))
56.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
24.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (* (* (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))))
355.0ms
(cbrt l)
139.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
44.0ms
(/ (* M D) (* 2 d))

simplify53.3s

Counts
156 → 203
Calls
156 calls:
Slowest
1.0s
(* (* (* (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))))
860.0ms
(* (* (* (* (/ 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)))
815.0ms
(+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (log (/ h l)))
809.0ms
(* (* (* (* (/ 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)))
763.0ms
(* (- (* (* (/ 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)))))

prune5.7s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 6.9b

localize102.0ms

Local error

Found 4 expressions with local error:

5.9b
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
5.4b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
5.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
3.5b
(/ (* M D) (* 2 d))

rewrite639.0ms

Algorithm
rewrite-expression-head
Rules
3723×add-exp-log
2297×prod-exp
1196×div-exp
440×pow-exp
321×rec-exp 1-exp
146×add-cbrt-cube
94×pow-to-exp
91×cbrt-unprod
41×cbrt-undiv
32×associate-*r*
22×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
16×pow1
13×associate-*l/
9×cbrt-prod
7×frac-times pow-prod-down
6×prod-diff associate-*r/
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* un-div-inv *-commutative div-inv
2×sub-neg
1×clear-num associate-/r* frac-2neg flip3-- flip-- associate-/l*
Counts
4 → 793
Calls
4 calls:
Slowest
288.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
207.0ms
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
72.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
18.0ms
(/ (* M D) (* 2 d))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (* (* (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)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))))
313.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l))))
210.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ 1 (* (cbrt l) (cbrt l)))) (/ h (cbrt l)))
50.0ms
(/ (* M D) (* 2 d))

simplify3.9m

Counts
763 → 805
Calls
763 calls:
Slowest
1.5s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l))))) (/ (* (* h h) h) l))
1.4s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l))))) (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))))
1.4s
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))))
1.4s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ 1 (* (cbrt l) (cbrt l))) (/ 1 (* (cbrt l) (cbrt l)))) (/ 1 (* (cbrt l) (cbrt l))))) (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))))
1.2s
(* (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ 1 (* (cbrt l) (cbrt l))) (/ 1 (* (cbrt l) (cbrt l)))) (/ 1 (* (cbrt l) (cbrt l))))) (/ (* (* h h) h) l))

prune19.4s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 4.4b

regimes2.1s

Accuracy

0% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 10.4b

bsearch11.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.8s38369×body80nan
4.3s12705×body80valid