Details

Time bar (total: 4.5m)

sample807.0ms

Algorithm
intervals
Results
525.0ms1410×body80nan
188.0ms409×body80valid

simplify406.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
406.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.5b

localize57.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.5b
(pow (/ d h) (/ 1 2))
12.4b
(pow (/ d l) (/ 1 2))
7.2b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite148.0ms

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
76.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
49.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.0ms
(pow (/ d l) (/ 1 2))
4.0ms
(pow (/ d h) (/ 1 2))

series728.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
460.0ms
(* (* (pow (/ d 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))
87.0ms
(pow (/ d h) (/ 1 2))
78.0ms
(pow (/ d l) (/ 1 2))

simplify43.4s

Counts
188 → 234
Calls
188 calls:
Slowest
888.0ms
(* (* (* (* (/ 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)))
881.0ms
(* (* (* (* (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)))))
838.0ms
(* (* (* (* (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)))))
772.0ms
(+ (+ (- (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))
754.0ms
(* (* (* (* (/ 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)))

prune4.7s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 11.2b

localize121.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.4b
(pow (/ d l) (/ 1 2))
7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
6.1b
(/ (* M D) (* 2 d))

rewrite592.0ms

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
10×associate-*l/
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×frac-times sqrt-div associate-*r/
2×sub-neg flip3-- associate-*l* pow-prod-down *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 213
Calls
4 calls:
Slowest
505.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
48.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
22.0ms
(/ (* M D) (* 2 d))
4.0ms
(pow (/ d l) (/ 1 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
122.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
109.0ms
(pow (/ d l) (/ 1 2))
46.0ms
(/ (* M D) (* 2 d))

simplify52.2s

Counts
179 → 225
Calls
179 calls:
Slowest
1.1s
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ 1 (* (cbrt h) (cbrt h))))) (sqrt (/ 1 (* (cbrt h) (cbrt h))))) (* (* (pow (/ d (cbrt h)) (/ 1 2)) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ 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
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.0s
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2)))) (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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)))))
967.0ms
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune5.5s

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 9.6b

localize101.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
6.1b
(/ (* M D) (* 2 d))
2.9b
(pow (/ d (cbrt h)) (/ 1 2))

rewrite732.0ms

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
643.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
60.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
17.0ms
(/ (* M D) (* 2 d))
5.0ms
(pow (/ d (cbrt h)) (/ 1 2))

series2.3s

Counts
4 → 12
Calls
4 calls:
Slowest
1.9s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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))))
222.0ms
(pow (/ d (cbrt h)) (/ 1 2))
125.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
48.0ms
(/ (* M D) (* 2 d))

simplify58.0s

Counts
196 → 242
Calls
196 calls:
Slowest
965.0ms
(* (* (* (* (/ 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)))
935.0ms
(* (fma (- (/ h l)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ h l) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)))) (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))))
935.0ms
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))
820.0ms
(* (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))))))
789.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune6.6s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 8.9b

localize119.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
6.7b
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
6.1b
(/ (* M D) (* d 2))
6.1b
(/ (* M D) (* d 2))

rewrite856.0ms

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×associate-*l/ 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×sqrt-div unswap-sqr
2×frac-times clear-num associate-/r* sub-neg frac-2neg flip3-- associate-*r/ *-commutative flip-- associate-/l*
1×distribute-lft-out--
Counts
4 → 240
Calls
4 calls:
Slowest
675.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
139.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
23.0ms
(/ (* M D) (* d 2))
12.0ms
(/ (* M D) (* d 2))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
112.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
58.0ms
(/ (* M D) (* d 2))
35.0ms
(/ (* M D) (* d 2))

simplify1.1m

Counts
205 → 252
Calls
205 calls:
Slowest
1.1s
(* (/ (/ (* (* (* (/ (* 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))
999.0ms
(* (/ (/ (* (* (* (/ (* 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))
978.0ms
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow 1 3) (pow (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1) 3)))
924.0ms
(+ (+ (+ (log (sqrt (/ 1 (* (cbrt h) (cbrt h))))) (* (log (/ d (cbrt h))) (/ 1 2))) (+ (log (fabs (cbrt d))) (* (log (/ (cbrt d) l)) (/ 1 2)))) (log (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1))))
872.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))

prune4.6s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 7.1b

regimes2.3s

Accuracy

0% (5.7b remaining)

Error of 12.1b against oracle of 6.3b and baseline of 12.1b

bsearch7.0ms

end0.0ms

sample15.9s

Algorithm
intervals
Results
10.1s37737×body80nan
4.1s12649×body80valid