Details

Time bar (total: 5.5m)

sample758.0ms

Algorithm
intervals
Results
522.0ms1278×body80nan
166.0ms417×body80valid

simplify766.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
765.0ms
(* (* (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: 25.0b

localize53.0ms

Local error

Found 4 expressions with local error:

13.6b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.1b
(pow (/ d h) (/ 1 2))
10.8b
(pow (/ d l) (/ 1 2))
5.6b
(/ (* M D) (* 2 d))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
293×add-exp-log
150×prod-exp
95×div-exp
46×times-frac
44×pow-exp
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
37×add-cbrt-cube
26×pow-unpow unpow-prod-down
14×rec-exp 1-exp cbrt-unprod
13×associate-*r*
10×pow-to-exp
9×cbrt-undiv
8×pow1
6×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times clear-num associate-/r* frac-2neg associate-*l* pow-prod-down associate-*r/ *-commutative associate-/l*
Counts
4 → 199
Calls
4 calls:
Slowest
53.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
24.0ms
(/ (* M D) (* 2 d))
10.0ms
(pow (/ d l) (/ 1 2))
9.0ms
(pow (/ d h) (/ 1 2))

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
107.0ms
(pow (/ d l) (/ 1 2))
74.0ms
(pow (/ d h) (/ 1 2))
46.0ms
(/ (* M D) (* 2 d))

simplify35.3s

Counts
162 → 211
Calls
162 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 l) (/ h l)) (/ h l)))
996.0ms
(* (* (* (* (/ 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)))
860.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
735.0ms
(* (* (/ (* (* 1 1) 1) (* (* 2 2) 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
689.0ms
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))

prune4.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.5b

localize78.0ms

Local error

Found 4 expressions with local error:

13.6b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.1b
(pow (/ d h) (/ 1 2))
5.6b
(/ (* M D) (* 2 d))
5.1b
(* (* (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))))

rewrite181.0ms

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
92.0ms
(* (* (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))))
68.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d h) (/ 1 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
848.0ms
(* (* (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))))
109.0ms
(pow (/ d h) (/ 1 2))
95.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
47.0ms
(/ (* M D) (* 2 d))

simplify50.6s

Counts
174 → 222
Calls
174 calls:
Slowest
1.3s
(* (* (* (* (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)))))
1.2s
(* (* (* (* (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)))))
1.1s
(* (* (* (* (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)))))
1.1s
(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log h) (log l)))
953.0ms
(* (* (* (* (/ 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)))

prune5.6s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.1b

localize119.0ms

Local error

Found 4 expressions with local error:

13.6b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
5.6b
(/ (* M D) (* 2 d))
5.1b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
3.0b
(pow (/ d (cbrt h)) (/ 1 2))

rewrite794.0ms

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
34×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
10×associate-*l/
9×cbrt-prod cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u div-inv add-log-exp
3×frac-times sqrt-div associate-*r/
2×sub-neg flip3-- associate-*l* *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 230
Calls
4 calls:
Slowest
709.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
59.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
16.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d (cbrt h)) (/ 1 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
740.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
261.0ms
(pow (/ d (cbrt h)) (/ 1 2))
114.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
51.0ms
(/ (* M D) (* 2 d))

simplify1.0m

Counts
196 → 242
Calls
196 calls:
Slowest
1.1s
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))
963.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
934.0ms
(* (* (* (* (/ 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
(* (* (* (* (/ 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)))
786.0ms
(* (sqrt (* (cbrt h) (cbrt h))) (+ (* 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))))))

prune7.2s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 7.3b

localize143.0ms

Local error

Found 4 expressions with local error:

5.9b
(/ M (/ 2 (/ D d)))
5.9b
(/ M (/ 2 (/ D d)))
5.8b
(/ (* -1/2 (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))) l)
5.7b
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
795×times-frac
378×add-sqr-sqrt
377×*-un-lft-identity add-cube-cbrt
257×add-cbrt-cube add-exp-log
127×cbrt-undiv div-exp
91×associate-/r*
84×prod-exp cbrt-unprod
35×div-inv
11×associate-*r/
10×associate-/r/
9×pow1
7×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down associate-/l/
2×frac-times associate-*l/
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 514
Calls
4 calls:
Slowest
198.0ms
(/ (* -1/2 (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))) l)
47.0ms
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))
22.0ms
(/ M (/ 2 (/ D d)))
16.0ms
(/ M (/ 2 (/ D d)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))
147.0ms
(/ (* -1/2 (* h (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d)))))) l)
43.0ms
(/ M (/ 2 (/ D d)))
41.0ms
(/ M (/ 2 (/ D d)))

simplify1.9m

Counts
737 → 526
Calls
737 calls:
Slowest
2.1s
(* (* (* h h) h) (* (/ (* (* M M) M) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d)))) (/ (* (* M M) M) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))))
1.5s
(/ (* (* (* -1/2 -1/2) -1/2) (* (* (* h h) h) (* (/ (* (* M M) M) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d)))) (/ (* (* M M) M) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d))))))) (* (* l l) l))
1.4s
(* (* (* h h) h) (* (/ (* (* M M) M) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* M M) M) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d))))))
1.3s
(/ (* (* (* -1/2 -1/2) -1/2) (* (* (* h h) h) (* (/ (* (* M M) M) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d)))) (/ (* (* M M) M) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d))))))) (* (* l l) l))
1.3s
(/ (* (* (* -1/2 -1/2) -1/2) (* (* (* h h) h) (* (/ (* (* M M) M) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* M M) M) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))))) (* (* l l) l))

prune18.5s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 5.8b

regimes3.0s

Accuracy

-12.5% (6.4b remaining)

Error of 13.5b against oracle of 7.1b and baseline of 12.8b

bsearch1.0s

end0.0ms

sample20.2s

Algorithm
intervals
Results
13.0s37815×body80nan
5.1s12847×body80valid