Details

Time bar (total: 5.1m)

sample638.0ms

Algorithm
intervals
Results
367.0ms1078×body80nan
153.0ms404×body80valid

simplify423.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
423.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.6b

localize82.0ms

Local error

Found 4 expressions with local error:

13.0b
(pow (/ d l) (/ 1 2))
12.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.1b
(pow (/ d h) (/ 1 2))
7.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite128.0ms

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
65.0ms
(* (* (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))
9.0ms
(pow (/ d h) (/ 1 2))
7.0ms
(pow (/ d l) (/ 1 2))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
395.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
109.0ms
(pow (/ d l) (/ 1 2))
104.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
80.0ms
(pow (/ d h) (/ 1 2))

simplify42.1s

Counts
188 → 234
Calls
188 calls:
Slowest
954.0ms
(* (* (* (* (/ 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)))
804.0ms
(* (* (* (* (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)))))
753.0ms
(* (* (* (* (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)))))
675.0ms
(* (* (* (* (/ 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)))
660.0ms
(+ (+ (log (/ 1 2)) (* (- (log (* M D)) (log (* 2 d))) 2)) (log (/ h l)))

prune4.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.0b

localize120.0ms

Local error

Found 4 expressions with local error:

13.0b
(pow (/ d l) (/ 1 2))
12.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.6b
(* (* (* (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))))
3.8b
(/ (* M D) (* 2 d))

rewrite193.0ms

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
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))))
42.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(pow (/ d l) (/ 1 2))
11.0ms
(/ (* M D) (* 2 d))

series1.6s

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))))
103.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
86.0ms
(pow (/ d l) (/ 1 2))
48.0ms
(/ (* M D) (* 2 d))

simplify48.8s

Counts
174 → 222
Calls
174 calls:
Slowest
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)))))
959.0ms
(* (* (* (* (* (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)))))
924.0ms
(* (* (* (* (* (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)))))
864.0ms
(* (* (* (* (/ 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)))
807.0ms
(+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log h) (log l)))

prune5.5s

Pruning

33 alts after pruning (33 fresh and 0 done)

Merged error: 9.8b

localize147.0ms

Local error

Found 4 expressions with local error:

12.2b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.6b
(* (* (* (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))))
3.8b
(/ (* M D) (* 2 d))
0.6b
(cbrt h)

rewrite261.0ms

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
192.0ms
(* (* (* (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))))
51.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt h)

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))))
266.0ms
(cbrt h)
98.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
40.0ms
(/ (* M D) (* 2 d))

simplify51.8s

Counts
156 → 203
Calls
156 calls:
Slowest
988.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log h) (log l)))
897.0ms
(* (* (* (* (/ 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)))
894.0ms
(* (* (* (* (/ 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)))
877.0ms
(+ (+ (log (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (+ (log (fabs (/ (cbrt d) (cbrt l)))) (* (log (/ (cbrt d) (cbrt l))) (/ 1 2)))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
825.0ms
(* (- (* (* (/ 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)))))

prune6.0s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 7.3b

localize100.0ms

Local error

Found 4 expressions with local error:

8.1b
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
7.6b
(* (* (* (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)))
4.8b
(/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l)
3.8b
(/ (* M D) (* d 2))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
532×add-exp-log
433×add-cbrt-cube
253×prod-exp
200×div-exp
190×cbrt-undiv
175×cbrt-unprod
67×times-frac
64×add-sqr-sqrt
56×*-un-lft-identity
52×add-cube-cbrt
30×prod-diff
26×associate-*l*
20×pow-exp
17×distribute-rgt-in distribute-lft-in
11×pow1 associate-*r*
10×pow-to-exp div-inv
8×associate-/l* sqr-pow
6×unpow-prod-down
4×expm1-log1p-u associate-/r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×unswap-sqr
2×clear-num sub-neg frac-2neg associate-*r/ *-commutative
1×flip3-- associate-*l/ flip-- distribute-lft-out-- associate-/l/
Counts
4 → 312
Calls
4 calls:
Slowest
255.0ms
(* (* (* (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)))
234.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
42.0ms
(/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l)
11.0ms
(/ (* M D) (* d 2))

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 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
126.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
111.0ms
(/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l)
31.0ms
(/ (* M D) (* d 2))

simplify1.7m

Counts
295 → 324
Calls
295 calls:
Slowest
3.9s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.4s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l))
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))
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))

prune9.1s

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 5.7b

regimes3.0s

Accuracy

0% (3.7b remaining)

Error of 10.0b against oracle of 6.3b and baseline of 10.0b

bsearch17.0ms

end0.0ms

sample23.8s

Algorithm
intervals
Results
15.2s38612×body80nan
5.8s12831×body80valid