Details

Time bar (total: 4.9m)

sample730.0ms

Algorithm
intervals
Results
432.0ms1348×body80nan
161.0ms444×body80valid

simplify422.0ms

Calls
1 calls:
Slowest
422.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.8b

localize103.0ms

Local error

Found 4 expressions with local error:

12.7b
(pow (/ d h) (/ 1 2))
11.4b
(pow (/ d l) (/ 1 2))
9.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.4b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite141.0ms

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--
Calls
4 calls:
Slowest
69.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
46.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms
(pow (/ d h) (/ 1 2))
9.0ms
(pow (/ d l) (/ 1 2))

series664.0ms

Calls
4 calls:
Slowest
401.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
101.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
88.0ms
(pow (/ d h) (/ 1 2))
73.0ms
(pow (/ d l) (/ 1 2))

simplify40.9s

Calls
182 calls:
Slowest
999.0ms
(* (* (* (* (/ 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)))
906.0ms
(* (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))))
802.0ms
(* (* (* (* (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)))))
740.0ms
(* (* (* (* (/ 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)))
689.0ms
(* (* (* (* (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)))))

prune4.3s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 10.2b

localize82.0ms

Local error

Found 4 expressions with local error:

11.4b
(pow (/ d l) (/ 1 2))
9.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.4b
(* (* (* (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))))
4.6b
(/ (* M D) (* 2 d))

rewrite203.0ms

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
Calls
4 calls:
Slowest
124.0ms
(* (* (* (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))))
51.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
18.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d l) (/ 1 2))

series1.7s

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))))
143.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
81.0ms
(pow (/ d l) (/ 1 2))
47.0ms
(/ (* M D) (* 2 d))

simplify46.6s

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)))))
1.1s
(* (* (* (* (* (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)))))
962.0ms
(* (* (* (* (/ 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)))
899.0ms
(+ (* 1 1) (+ (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))

prune4.7s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 9.1b

localize98.0ms

Local error

Found 4 expressions with local error:

9.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.4b
(* (* (* (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))))
4.6b
(/ (* M D) (* 2 d))
3.4b
(pow (/ (cbrt d) l) (/ 1 2))

rewrite345.0ms

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
Calls
4 calls:
Slowest
232.0ms
(* (* (* (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))))
80.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ (cbrt d) l) (/ 1 2))

series2.1s

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))))
240.0ms
(pow (/ (cbrt d) l) (/ 1 2))
106.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
47.0ms
(/ (* M D) (* 2 d))

simplify50.5s

Calls
185 calls:
Slowest
1.9s
(* (* (* (* (* (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)))))
925.0ms
(* (* (* (* (/ 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)))
835.0ms
(+ (+ (- (log 1) (log 2)) (* (- (log (* M D)) (+ (log 2) (log d))) 2)) (log (/ h l)))
744.0ms
(* (- (* (* (/ 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)) (pow (/ (cbrt d) l) (/ 1 2)))))
716.0ms
(* (* (* (* (/ 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)))

prune5.3s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 7.7b

localize145.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
4.6b
(/ (* M D) (* 2 d))
3.4b
(pow (/ (cbrt d) l) (/ 1 2))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
973×add-exp-log
576×prod-exp
281×div-exp
122×pow-exp
79×add-cbrt-cube
54×cbrt-unprod
35×rec-exp 1-exp
31×pow-to-exp
29×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
22×unpow-prod-down
21×cbrt-undiv
13×pow-unpow
12×pow1
9×cbrt-prod
8×associate-*r*
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
Calls
4 calls:
Slowest
198.0ms
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
56.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
13.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ (cbrt d) l) (/ 1 2))

series2.2s

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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
227.0ms
(pow (/ (cbrt d) l) (/ 1 2))
205.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
48.0ms
(/ (* M D) (* 2 d))

simplify1.7m

Calls
274 calls:
Slowest
2.0s
(* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))) (* (cbrt h) (cbrt h))) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))))
1.5s
(* (* (* (* (/ 1 2) (/ 1 2)) (/ 1 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))) (* (cbrt h) (cbrt h))) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))))
1.4s
(+ (* 1 1) (+ (* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))) (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))
1.4s
(* (- (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))))
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

prune7.9s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 6.0b

regimes2.4s

Accuracy

0% (4.9b remaining)

Error of 10.8b against oracle of 5.9b and baseline of 10.8b

bsearch9.0ms

end0.0ms

sample16.2s

Algorithm
intervals
Results
10.7s39322×body80nan
4.3s13045×body80valid