Details

Time bar (total: 4.5m)

sample729.0ms

Algorithm
intervals
Results
504.0ms1281×body80nan
153.0ms402×body80valid

simplify765.0ms

Calls
1 calls:
Slowest
764.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.6b

localize72.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
11.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.6b
(pow (/ d h) (/ 1 2))
8.6b
(* (* (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
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--
Calls
4 calls:
Slowest
59.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
49.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
13.0ms
(pow (/ d h) (/ 1 2))
10.0ms
(pow (/ d l) (/ 1 2))

series741.0ms

Calls
4 calls:
Slowest
420.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
140.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
106.0ms
(pow (/ d h) (/ 1 2))
75.0ms
(pow (/ d l) (/ 1 2))

simplify44.4s

Calls
188 calls:
Slowest
1.3s
(* (* (* (* (/ 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)))
853.0ms
(* (* (* (* (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)))))
829.0ms
(* (* (* (* (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)))))
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)))
680.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))

prune4.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.7b

localize79.0ms

Local error

Found 4 expressions with local error:

14.0b
(pow (/ d l) (/ 1 2))
11.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.6b
(* (* (* (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))))
5.5b
(/ (* M D) (* 2 d))

rewrite214.0ms

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
Calls
4 calls:
Slowest
134.0ms
(* (* (* (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))
15.0ms
(/ (* M D) (* 2 d))
10.0ms
(pow (/ d l) (/ 1 2))

series2.0s

Calls
4 calls:
Slowest
1.7s
(* (* (* (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))))
141.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
81.0ms
(pow (/ d l) (/ 1 2))
34.0ms
(/ (* M D) (* 2 d))

simplify49.8s

Calls
174 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) (* (* l l) 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)))))
944.0ms
(* (* (* (* (* (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)))))
937.0ms
(* (* (* (* (* (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)))))
837.0ms
(* (* (* (* (/ 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)))

prune5.4s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.4b

localize122.0ms

Local error

Found 4 expressions with local error:

11.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
8.6b
(* (* (* (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))))
5.5b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite353.0ms

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*
Calls
4 calls:
Slowest
247.0ms
(* (* (* (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))))
73.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
23.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

series2.0s

Calls
4 calls:
Slowest
1.5s
(* (* (* (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))))
306.0ms
(cbrt l)
128.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
49.0ms
(/ (* M D) (* 2 d))

simplify52.3s

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))))
989.0ms
(* (* (* (* (/ 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)))
824.0ms
(* (* (* (* (/ 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)))
762.0ms
(* (* (* (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))))
738.0ms
(* (- (* (* (/ 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

32 alts after pruning (32 fresh and 0 done)

Merged error: 7.5b

localize102.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (* (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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
5.5b
(/ (* M D) (* d 2))
5.5b
(/ (* M D) (* d 2))
5.4b
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)

rewrite475.0ms

Algorithm
rewrite-expression-head
Rules
359×add-exp-log
260×add-cbrt-cube
192×prod-exp
114×cbrt-unprod
111×div-exp
101×cbrt-undiv
48×add-sqr-sqrt
40×*-un-lft-identity
36×add-cube-cbrt
35×times-frac
30×prod-diff
26×associate-*l*
20×pow-exp
17×distribute-rgt-in distribute-lft-in
11×pow1 associate-*r*
10×pow-to-exp
8×sqr-pow
6×unpow-prod-down div-inv
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×unswap-sqr
2×clear-num associate-/r* sub-neg frac-2neg associate-*r/ *-commutative associate-/l*
1×flip3-- associate-*l/ flip-- distribute-lft-out--
Calls
4 calls:
Slowest
258.0ms
(* (* (* (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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
161.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
24.0ms
(/ (* M D) (* d 2))
23.0ms
(/ (* M D) (* d 2))

series1.9s

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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
150.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
37.0ms
(/ (* M D) (* d 2))
29.0ms
(/ (* M D) (* d 2))

simplify1.2m

Calls
200 calls:
Slowest
1.4s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2))) (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
1.2s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
846.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* d 2) (* d 2)) (* d 2)))
808.0ms
(* (fma (- (pow h 1)) (pow (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) 1) (* (pow h 1) (pow (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) 1))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))))
802.0ms
(+ (+ (+ (log (fabs (/ (cbrt d) (cbrt h)))) (* (log (/ (cbrt d) (cbrt h))) (/ 1 2))) (log (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2))))) (log (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1))))

prune6.4s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 6.0b

regimes2.7s

Accuracy

0% (4.0b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 9.5b

bsearch1.1s

end0.0ms

sample18.5s

Algorithm
intervals
Results
12.2s37967×body80nan
4.5s12823×body80valid