Details

Time bar (total: 4.7m)

sample696.0ms

Algorithm
intervals
Results
460.0ms1148×body80nan
151.0ms400×body80valid

simplify381.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
381.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.8b

localize90.0ms

Local error

Found 4 expressions with local error:

12.7b
(pow (/ d l) (/ 1 2))
12.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.2b
(pow (/ d h) (/ 1 2))
8.4b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite130.0ms

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
69.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
42.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.0ms
(pow (/ d l) (/ 1 2))
5.0ms
(pow (/ d h) (/ 1 2))

series720.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
384.0ms
(* (* (pow (/ d 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))
111.0ms
(pow (/ d l) (/ 1 2))
105.0ms
(pow (/ d h) (/ 1 2))

simplify41.1s

Counts
182 → 220
Calls
182 calls:
Slowest
936.0ms
(* (* (* (* (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)))))
906.0ms
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (log (/ h l)))
784.0ms
(* (* (* (* (/ 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)))
733.0ms
(* (* (* (* (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)))))
718.0ms
(* (* (* (* (/ 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)))

prune4.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 13.3b

localize73.0ms

Local error

Found 4 expressions with local error:

12.7b
(pow (/ d l) (/ 1 2))
12.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.4b
(* (* (* (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))))
1.9b
(/ (* M D) (* 2 d))

rewrite235.0ms

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
155.0ms
(* (* (* (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))))
50.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
21.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d l) (/ 1 2))

series1.7s

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))))
118.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
84.0ms
(pow (/ d l) (/ 1 2))
46.0ms
(/ (* M D) (* 2 d))

simplify47.3s

Counts
168 → 208
Calls
168 calls:
Slowest
1.6s
(* (* (* (* (* (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)))))
1.0s
(* (* (* (* (* (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)))))
885.0ms
(* (* (* (* (/ 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)))
758.0ms
(* (* (* (* (/ 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: 11.4b

localize111.0ms

Local error

Found 4 expressions with local error:

12.4b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.4b
(* (* (* (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))))
1.9b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite362.0ms

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*
Counts
4 → 177
Calls
4 calls:
Slowest
270.0ms
(* (* (* (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))))
69.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

series2.0s

Counts
4 → 12
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))))
260.0ms
(cbrt l)
147.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
29.0ms
(/ (* M D) (* 2 d))

simplify47.6s

Counts
150 → 189
Calls
150 calls:
Slowest
924.0ms
(* (* (* (* (/ 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)))
813.0ms
(+ (+ (log (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (+ (log (fabs (/ (cbrt d) (cbrt l)))) (log (pow (/ (cbrt d) (cbrt l)) (/ 1 2))))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
758.0ms
(* (* (* (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))))
750.0ms
(* (- (* (* (/ 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)))))
717.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune5.3s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 7.7b

localize98.0ms

Local error

Found 4 expressions with local error:

8.4b
(* (* (* (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) (/ 1 l))))
5.5b
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
4.8b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
1.9b
(/ (* M D) (* 2 d))

rewrite473.0ms

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
235.0ms
(* (* (* (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) (/ 1 l))))
153.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
41.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
22.0ms
(/ (* M D) (* 2 d))

series1.9s

Counts
4 → 12
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) (/ 1 l))))
135.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h)
104.0ms
(* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))
30.0ms
(/ (* M D) (* 2 d))

simplify1.4m

Counts
249 → 290
Calls
249 calls:
Slowest
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))) (* (* h h) h)) (/ (* (* 1 1) 1) (* (* l l) 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)) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
945.0ms
(+ (+ (+ (- 0 (log 2)) (* (- (log (* M D)) (+ (log 2) (log d))) 2)) (log h)) (log (/ 1 l)))
909.0ms
(* (* (* (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) (/ 1 l))))
896.0ms
(* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))

prune8.1s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 7.0b

regimes3.1s

Accuracy

47.3% (3.5b remaining)

Error of 10.6b against oracle of 7.1b and baseline of 13.8b

bsearch1.1s

end0.0ms

sample24.7s

Algorithm
intervals
Results
16.3s38587×body80nan
5.5s12822×body80valid