Details

Time bar (total: 8.7m)

sample113.0ms

Algorithm
intervals
Results
61.0ms299×body80valid
20.0ms96×body80nan

simplify156.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
156.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize55.0ms

Local error

Found 4 expressions with local error:

9.5b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
5.5b
(/ (* M D) (* 2 d))
5.5b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
368×add-cbrt-cube add-exp-log
190×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
16×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac add-cube-cbrt
10×pow1
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 198
Calls
4 calls:
Slowest
146.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
20.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
127.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
42.0ms
(/ (* M D) (* 2 d))
39.0ms
(/ (* M D) (* 2 d))

simplify49.8s

Counts
172 → 210
Calls
172 calls:
Slowest
2.9s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.8s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.5s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.4s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.3s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize86.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
5.5b
(/ (* M D) (* 2 d))
5.5b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
2201×add-exp-log
1284×prod-exp
1182×add-cbrt-cube
764×cbrt-unprod
747×div-exp
431×cbrt-undiv
104×1-exp
22×associate-*r*
20×times-frac
19×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
17×frac-times associate-*l/
14×pow1
9×cbrt-prod
7×associate-*r/
6×pow-prod-down
4×insert-posit16 add-log-exp
3×sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 530
Calls
4 calls:
Slowest
609.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
22.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* M D) (* 2 d))
10.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
187.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
47.0ms
(/ (* M D) (* 2 d))
42.0ms
(/ (* M D) (* 2 d))

simplify2.6m

Counts
506 → 542
Calls
506 calls:
Slowest
3.2s
(* (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
2.6s
(* (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
2.3s
(* (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
2.3s
(* (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
2.3s
(* (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* h h) (* (* 1 1) 1))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))

prune10.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize49.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* D (cbrt h)) (/ (* 2 d) M))
6.5b
(/ (* D (cbrt h)) (/ (* 2 d) M))
5.6b
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l))
4.7b
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l)) 1)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
814×add-exp-log
674×add-cbrt-cube
350×cbrt-undiv div-exp
348×prod-exp cbrt-unprod
46×times-frac
35×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
22×associate-*r*
14×associate-/r*
10×cbrt-prod pow1
7×div-inv
6×sqrt-prod
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ unswap-sqr
2×clear-num frac-2neg sqrt-div associate-/r/ associate-/l* difference-of-squares
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip-- distribute-lft-out--
Counts
4 → 341
Calls
4 calls:
Slowest
175.0ms
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l))
15.0ms
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l)) 1)))
11.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))
11.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))

series982.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))
257.0ms
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l)) 1)))
222.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))
220.0ms
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (cbrt h) l))

simplify1.7m

Counts
328 → 353
Calls
328 calls:
Slowest
3.0s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))) (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M)))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
2.9s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M))) (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M)))) (/ h (* (* l l) l)))
2.6s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))) (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M)))) (/ h (* (* l l) l)))
2.5s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M))) (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M)))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
2.2s
(* (* (/ (* (* (* D D) D) h) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))) (/ (* (* (* D D) D) h) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M)))) (/ h (* (* l l) l)))

prune6.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize79.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (* D (cbrt h)) (/ (* 2 d) M))
6.1b
(* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))
5.6b
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l))
4.7b
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l)) 1)))

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
2519×add-exp-log
1345×prod-exp
938×div-exp
928×add-cbrt-cube
559×cbrt-unprod
404×cbrt-undiv
90×rec-exp 1-exp
61×times-frac
48×associate-*r*
40×add-sqr-sqrt
39×*-un-lft-identity
36×add-cube-cbrt
24×pow1
13×pow-prod-down
10×associate-*r/
9×cbrt-prod frac-times
8×div-inv
7×associate-/r* associate-*l/
6×sqrt-prod
5×un-div-inv
4×insert-posit16 add-log-exp
2×sqrt-div associate-*l* associate-/r/ *-commutative difference-of-squares
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 flip-- associate-/l* distribute-lft-out--
Counts
4 → 597
Calls
4 calls:
Slowest
492.0ms
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l))
37.0ms
(* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))
16.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))
16.0ms
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l)) 1)))

series975.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
271.0ms
(* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))
241.0ms
(/ (* D (cbrt h)) (/ (* 2 d) M))
236.0ms
(* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l))
227.0ms
(sqrt (- 1 (/ (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (* (* D (cbrt h)) (/ 1 (/ (* 2 d) M)))) (/ (cbrt h) l)) 1)))

simplify2.8m

Counts
578 → 609
Calls
578 calls:
Slowest
2.3s
(* (* (/ (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (* (* (/ (* 2 d) M) (/ (* 2 d) M)) (/ (* 2 d) M))) (* (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (/ (* (* 1 1) 1) (* (* (/ (* 2 d) M) (/ (* 2 d) M)) (/ (* 2 d) M))))) (/ h (* (* l l) l)))
2.2s
(* (* (/ (* (* (* D D) D) h) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M))) (* (* (* (* D D) D) h) (/ (* (* 1 1) 1) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* M M) M))))) (/ h (* (* l l) l)))
2.2s
(* (* (/ (* (* (* D D) D) h) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))) (* (* (* (* D D) D) h) (/ (* (* 1 1) 1) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* M M) M))))) (/ h (* (* l l) l)))
2.0s
(* (* (* (* (/ (* D (cbrt h)) (/ (* 2 d) M)) (/ (* D (cbrt h)) (/ (* 2 d) M))) (/ (* D (cbrt h)) (/ (* 2 d) M))) (* (* (* (* D (cbrt h)) (* D (cbrt h))) (* D (cbrt h))) (* (* (/ 1 (/ (* 2 d) M)) (/ 1 (/ (* 2 d) M))) (/ 1 (/ (* 2 d) M))))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))
1.8s
(* (* (/ (* (* (* D D) D) h) (* (* (/ (* 2 d) M) (/ (* 2 d) M)) (/ (* 2 d) M))) (* (* (* (* D D) D) h) (* (* (/ 1 (/ (* 2 d) M)) (/ 1 (/ (* 2 d) M))) (/ 1 (/ (* 2 d) M))))) (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)))

prune12.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

regimes1.7s

Accuracy

43.3% (2.0b remaining)

Error of 8.7b against oracle of 6.7b and baseline of 10.2b

bsearch24.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.6s9289×body80valid
695.0ms3233×body80nan