Details

Time bar (total: 5.0m)

sample675.0ms

Algorithm
intervals
Results
446.0ms1099×body80nan
150.0ms400×body80valid

simplify435.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
435.0ms
(* (* (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: 24.8b

localize68.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.7b
(pow (/ d l) (/ 1 2))
11.0b
(pow (/ d h) (/ 1 2))
6.4b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite152.0ms

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
72.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d 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))
8.0ms
(pow (/ d l) (/ 1 2))
5.0ms
(pow (/ d h) (/ 1 2))

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
118.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
86.0ms
(pow (/ d l) (/ 1 2))
83.0ms
(pow (/ d h) (/ 1 2))

simplify44.6s

Counts
188 → 234
Calls
188 calls:
Slowest
1.0s
(* (* (* (* (/ 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)))
912.0ms
(* (* (* (* (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)))))
887.0ms
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (log (/ h l)))
841.0ms
(* (* (* (* (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)))))
773.0ms
(* (* (* (* (/ 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)))

prune4.6s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.7b

localize93.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.7b
(pow (/ d l) (/ 1 2))
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))))
5.9b
(/ (* M D) (* 2 d))

rewrite182.0ms

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
118.0ms
(* (* (* (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))))
40.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.0ms
(/ (* M D) (* 2 d))
6.0ms
(pow (/ d l) (/ 1 2))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(* (* (* (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))))
112.0ms
(pow (/ d l) (/ 1 2))
99.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
34.0ms
(/ (* M D) (* 2 d))

simplify49.0s

Counts
174 → 222
Calls
174 calls:
Slowest
1.0s
(* (* (* (* (* (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)))))
992.0ms
(* (* (* (* (/ 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)))
885.0ms
(* (* (* (* (* (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)))))
870.0ms
(* (* (* (* (* (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
(+ (+ (- 0 (log 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (log (/ h l)))

prune5.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.5b

localize130.0ms

Local error

Found 4 expressions with local error:

13.7b
(* (* (/ 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) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.9b
(/ (* M D) (* 2 d))
0.6b
(cbrt l)

rewrite678.0ms

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
581.0ms
(* (* (* (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))))
70.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
21.0ms
(/ (* M D) (* 2 d))
1.0ms
(cbrt l)

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))))
274.0ms
(cbrt l)
96.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
32.0ms
(/ (* M D) (* 2 d))

simplify52.6s

Counts
156 → 203
Calls
156 calls:
Slowest
1.2s
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
946.0ms
(* (* (* (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))))
874.0ms
(* (* (* (* (/ 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)))
858.0ms
(* (* (* (* (/ 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)))
736.0ms
(* (* (* (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))))

prune5.4s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.8b

localize137.0ms

Local error

Found 4 expressions with local error:

7.0b
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
6.7b
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
6.4b
(* (* (* (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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
5.9b
(/ (* D M) (* 2 d))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
687×add-exp-log
588×add-cbrt-cube
395×prod-exp
317×cbrt-unprod
188×div-exp
178×cbrt-undiv
30×prod-diff
26×add-sqr-sqrt
25×*-un-lft-identity
22×add-cube-cbrt
20×pow-exp
17×distribute-rgt-in distribute-lft-in
14×pow1
10×pow-to-exp
9×associate-*r*
8×times-frac associate-*l/ div-inv
6×pow-prod-down
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l/
2×frac-times clear-num associate-/r* sub-neg frac-2neg associate-*l* *-commutative associate-/l* difference-of-squares
1×flip3-- flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 311
Calls
4 calls:
Slowest
261.0ms
(* (* (* (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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
134.0ms
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
130.0ms
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
17.0ms
(/ (* D M) (* 2 d))

series1.8s

Counts
4 → 12
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 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
106.0ms
(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
89.0ms
(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
42.0ms
(/ (* D M) (* 2 d))

simplify1.7m

Counts
274 → 323
Calls
274 calls:
Slowest
2.5s
(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
2.4s
(* (* (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))
2.2s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.2s
(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))
2.2s
(* (* (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))

prune5.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 5.1b

regimes1.7s

Accuracy

14.6% (3.6b remaining)

Error of 9.5b against oracle of 5.8b and baseline of 10.1b

bsearch1.1s

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.9s38110×body80nan
4.2s12891×body80valid