Details

Time bar (total: 5.2m)

sample128.0ms

Algorithm
intervals
Results
74.0ms307×body80valid
22.0ms98×body80nan

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize45.0ms

Local error

Found 4 expressions with local error:

8.8b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.7b
(/ (* M D) (* 2 d))
4.7b
(/ (* M D) (* 2 d))
3.8b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite208.0ms

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
156.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
18.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series422.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
139.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
42.0ms
(/ (* M D) (* 2 d))
39.0ms
(/ (* M D) (* 2 d))

simplify50.6s

Counts
172 → 210
Calls
172 calls:
Slowest
2.8s
(* (* (/ (* (* (* 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)))
2.7s
(* (* (/ (* (* (* 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)))
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)))
2.2s
(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))

prune3.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.9b

localize77.0ms

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))
4.7b
(/ (* M D) (* 2 d))
4.7b
(/ (* M D) (* 2 d))
3.8b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

rewrite808.0ms

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
726.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
17.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
159.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))
41.0ms
(/ (* M D) (* 2 d))
37.0ms
(/ (* M D) (* 2 d))

simplify2.6m

Counts
506 → 542
Calls
506 calls:
Slowest
2.9s
(* (* (* (/ (* (* (* 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)))
2.6s
(* (* (* (/ (* (* (* 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)))
2.4s
(* (* (* (/ (* (* (* 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)))
2.1s
(* (* (* (/ (* (* (* 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)))

prune10.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.4b

localize61.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (* (cbrt h) (* D M)) (* 2 d))
5.7b
(/ (* (cbrt h) (* D M)) (* 2 d))
5.7b
(* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d)))
3.8b
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ 1 2))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
112×add-exp-log
88×add-cbrt-cube
50×prod-exp cbrt-unprod
34×add-sqr-sqrt
32×times-frac
31×cbrt-undiv div-exp
26×*-un-lft-identity add-cube-cbrt
22×associate-*l*
13×pow-unpow
10×cbrt-prod
7×pow1
5×associate-*r* div-inv
4×insert-posit16 add-log-exp
3×unpow-prod-down unswap-sqr
2×clear-num associate-/r* frac-2neg associate-/l*
1×frac-times pow-to-exp pow-pow pow-prod-down associate-*l/ pow-exp associate-*r/ *-commutative sqr-pow
Counts
4 → 151
Calls
4 calls:
Slowest
56.0ms
(* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d)))
40.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
26.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
6.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ 1 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
405.0ms
(* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d)))
398.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ 1 2))
292.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
266.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))

simplify51.5s

Counts
125 → 163
Calls
125 calls:
Slowest
2.6s
(* (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)) (/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 d) (* 2 d)) (* 2 d))))
2.6s
(* (* (* (/ (cbrt h) l) (/ (cbrt h) l)) (/ (cbrt h) l)) (/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 2) 2) (* (* d d) d))))
2.1s
(* (/ h (* (* l l) l)) (/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.8s
(/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.8s
(* (/ h (* (* l l) l)) (/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 2) 2) (* (* d d) d))))

prune3.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.4b

localize77.0ms

Local error

Found 4 expressions with local error:

6.5b
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))
6.5b
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))
5.7b
(/ (* (cbrt h) (* D M)) (* 2 d))
5.7b
(/ (* (cbrt h) (* D M)) (* 2 d))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
134×times-frac
86×pow-unpow
76×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×add-exp-log
38×add-cbrt-cube
18×prod-exp cbrt-unprod
12×cbrt-undiv div-exp
10×div-inv
6×pow1 unpow-prod-down
4×insert-posit16 add-log-exp
2×pow-to-exp clear-num associate-/r* pow-pow frac-2neg pow-exp associate-/l* sqr-pow
Counts
4 → 168
Calls
4 calls:
Slowest
23.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
23.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
14.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))
14.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
453.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))
426.0ms
(pow (- 1 (* (* (/ (cbrt h) l) (/ (* (cbrt h) (* D M)) (* 2 d))) (/ (* (cbrt h) (* D M)) (* 2 d)))) (/ (/ 1 2) 2))
264.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))
214.0ms
(/ (* (cbrt h) (* D M)) (* 2 d))

simplify24.5s

Counts
138 → 180
Calls
138 calls:
Slowest
1.5s
(/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.4s
(/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.2s
(/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 2) 2) (* (* d d) d)))
1.1s
(/ (* (* (* (cbrt h) (* D M)) (* (cbrt h) (* D M))) (* (cbrt h) (* D M))) (* (* (* 2 2) 2) (* (* d d) d)))
919.0ms
(/ (* h (* (* (* D D) D) (* (* M M) M))) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune3.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.4b

regimes1.8s

Accuracy

0% (2.2b remaining)

Error of 9.2b against oracle of 7.0b and baseline of 9.2b

bsearch4.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s9364×body80valid
1.0s3123×body80nan