Details

Time bar (total: 3.4m)

sample113.0ms

Algorithm
intervals
Results
69.0ms301×body80valid
20.0ms96×body80nan

simplify177.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
177.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize47.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (/ h l) (/ (* M D) (* 2 d)))
6.5b
(/ (* M D) (* 2 d))
6.5b
(/ (* M D) (* 2 d))
3.1b
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
19×add-sqr-sqrt
13×*-un-lft-identity times-frac associate-*l* add-cube-cbrt
7×pow1
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 121
Calls
4 calls:
Slowest
34.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
22.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
122.0ms
(* (/ h l) (/ (* M D) (* 2 d)))
53.0ms
(/ (* M D) (* 2 d))
51.0ms
(/ (* M D) (* 2 d))

simplify24.9s

Counts
84 → 133
Calls
84 calls:
Slowest
1.4s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s
(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.3s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.2s
(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize81.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* M D) (* 2 d))
6.5b
(/ (* M D) (* 2 d))
6.2b
(* (/ h (cbrt l)) (/ (* M D) (* 2 d)))
3.1b
(* (/ 1 (* (cbrt l) (cbrt l))) (* (/ h (cbrt l)) (/ (* M D) (* 2 d))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
495×add-exp-log
262×prod-exp
219×add-cbrt-cube
156×div-exp
124×cbrt-unprod
82×cbrt-undiv
29×associate-*l*
28×add-sqr-sqrt
26×times-frac
22×rec-exp 1-exp
20×*-un-lft-identity add-cube-cbrt
11×pow1
10×cbrt-prod
6×frac-times associate-*r* associate-*r/
5×div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative associate-/l*
Counts
4 → 251
Calls
4 calls:
Slowest
120.0ms
(* (/ 1 (* (cbrt l) (cbrt l))) (* (/ h (cbrt l)) (/ (* M D) (* 2 d))))
47.0ms
(* (/ h (cbrt l)) (/ (* M D) (* 2 d)))
15.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(* (/ h (cbrt l)) (/ (* M D) (* 2 d)))
124.0ms
(* (/ 1 (* (cbrt l) (cbrt l))) (* (/ h (cbrt l)) (/ (* M D) (* 2 d))))
48.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify1.1m

Counts
216 → 263
Calls
216 calls:
Slowest
1.8s
(* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* h h) h) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.7s
(* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* h h) h) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.7s
(* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* h h) h) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.6s
(* (/ (* (* 1 1) 1) (* l l)) (* (* (* (/ h (cbrt l)) (/ h (cbrt l))) (/ h (cbrt l))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.6s
(* (/ (* (* 1 1) 1) (* l l)) (* (/ (* (* h h) h) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))

prune5.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize45.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* M D) (* 2 d))
6.5b
(/ (* M D) (* 2 d))
4.9b
(* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))
3.1b
(* (/ 1 (* (cbrt l) (cbrt l))) (* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
1091×add-exp-log
684×prod-exp
304×div-exp
271×add-cbrt-cube
172×cbrt-unprod
84×cbrt-undiv rec-exp 1-exp
18×pow1
15×associate-*r/
10×associate-*l*
9×pow-prod-down
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×frac-times
5×times-frac
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×clear-num associate-/r* frac-2neg associate-*r* *-commutative associate-/l*
Counts
4 → 319
Calls
4 calls:
Slowest
256.0ms
(* (/ 1 (* (cbrt l) (cbrt l))) (* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))
79.0ms
(* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series462.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))
118.0ms
(* (/ 1 (* (cbrt l) (cbrt l))) (* h (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))))
44.0ms
(/ (* M D) (* 2 d))
41.0ms
(/ (* M D) (* 2 d))

simplify1.4m

Counts
281 → 331
Calls
281 calls:
Slowest
1.8s
(* (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))) (* (* (* h h) h) (* (* (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d)))) (* (/ 1 (cbrt l)) (/ (* M D) (* 2 d))))))
1.6s
(* (/ (* (* 1 1) 1) (* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (* (cbrt l) (cbrt l)))) (* (* (* h h) h) (* (* (* (/ 1 (cbrt l)) (/ 1 (cbrt l))) (/ 1 (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))))))
1.6s
(* (* (* h h) h) (* (* (* (/ 1 (cbrt l)) (/ 1 (cbrt l))) (/ 1 (cbrt l))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
1.5s
(* (* (* h h) h) (* (* (* (/ 1 (cbrt l)) (/ 1 (cbrt l))) (/ 1 (cbrt l))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))))
1.5s
(* (* (* h h) h) (* (/ (* (* 1 1) 1) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))

prune7.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

localize57.0ms

Local error

Found 4 expressions with local error:

13.7b
(cbrt (/ (* M D) (* 2 d)))
13.7b
(cbrt (/ (* M D) (* 2 d)))
13.7b
(cbrt (/ (* M D) (* 2 d)))
6.5b
(/ (* M D) (* 2 d))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
15×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 cbrt-undiv times-frac div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×clear-num associate-/r* frac-2neg associate-/l*
Counts
4 → 75
Calls
4 calls:
Slowest
13.0ms
(cbrt (/ (* M D) (* 2 d)))
11.0ms
(/ (* M D) (* 2 d))
5.0ms
(cbrt (/ (* M D) (* 2 d)))
4.0ms
(cbrt (/ (* M D) (* 2 d)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(cbrt (/ (* M D) (* 2 d)))
127.0ms
(cbrt (/ (* M D) (* 2 d)))
121.0ms
(cbrt (/ (* M D) (* 2 d)))
41.0ms
(/ (* M D) (* 2 d))

simplify6.1s

Counts
40 → 87
Calls
40 calls:
Slowest
750.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
632.0ms
(/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
511.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))
404.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
390.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.3b

regimes1.4s

Accuracy

0% (0.6b remaining)

Error of 8.3b against oracle of 7.7b and baseline of 8.3b

bsearch5.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s9364×body80valid
666.0ms3142×body80nan