Details

Time bar (total: 4.1m)

sample109.0ms

Algorithm
intervals
Results
67.0ms293×body80valid
17.0ms101×body80nan

simplify149.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
149.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize36.0ms

Local error

Found 4 expressions with local error:

12.1b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.8b
(/ (* M D) (* 2 d))
4.8b
(/ (* M D) (* 2 d))
4.4b
(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
152.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
17.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
104.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
49.0ms
(/ (* M D) (* 2 d))
36.0ms
(/ (* M D) (* 2 d))

simplify49.5s

Counts
172 → 210
Calls
172 calls:
Slowest
2.7s
(* (* (/ (* (* (* 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)))
2.7s
(* (* (/ (* (* (* 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)))
2.4s
(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))
2.4s
(* (* (/ (* (* (* 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)))
2.3s
(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize36.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) (/ 1 l))
5.4b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
4.8b
(/ (* M D) (* 2 d))
4.8b
(/ (* M D) (* 2 d))

rewrite946.0ms

Algorithm
rewrite-expression-head
Rules
952×add-exp-log
582×add-cbrt-cube
571×prod-exp
335×cbrt-unprod
262×div-exp
155×cbrt-undiv
27×rec-exp 1-exp
18×pow1
16×associate-*r*
15×associate-*l/
13×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×times-frac
9×pow-prod-down
6×frac-times
4×associate-*r/ insert-posit16 add-log-exp
3×div-inv
2×clear-num associate-/r* frac-2neg associate-*l* *-commutative associate-/l*
1×un-div-inv unswap-sqr
Counts
4 → 311
Calls
4 calls:
Slowest
666.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) (/ 1 l))
211.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))

series352.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) (/ 1 l))
112.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
50.0ms
(/ (* M D) (* 2 d))
49.0ms
(/ (* M D) (* 2 d))

simplify1.3m

Counts
282 → 323
Calls
282 calls:
Slowest
2.7s
(* (* (* (/ (* (* (* 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)) (* (* (/ 1 l) (/ 1 l)) (/ 1 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) h)) (* (* (/ 1 l) (/ 1 l)) (/ 1 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 h) h))
2.2s
(* (* (/ (* (* (* 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))
2.0s
(* (* (/ (* (* (* 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) h))

prune5.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize31.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) (/ 1 l))
5.0b
(* (/ (* M D) (* 2 d)) h)
4.8b
(/ (* M D) (* 2 d))
4.8b
(/ (* M D) (* 2 d))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
897×add-exp-log
537×prod-exp
487×add-cbrt-cube
277×cbrt-unprod
250×div-exp
131×cbrt-undiv
31×rec-exp 1-exp
16×associate-*r*
15×add-sqr-sqrt pow1
13×*-un-lft-identity add-cube-cbrt
12×times-frac
10×associate-*l/
7×pow-prod-down
6×associate-*l*
5×frac-times
4×insert-posit16 div-inv add-log-exp
3×associate-*r/
2×clear-num associate-/r* frac-2neg *-commutative associate-/l*
1×un-div-inv unswap-sqr
Counts
4 → 294
Calls
4 calls:
Slowest
349.0ms
(* (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) (/ 1 l))
43.0ms
(* (/ (* M D) (* 2 d)) h)
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))

series261.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(* (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) (/ 1 l))
77.0ms
(* (/ (* M D) (* 2 d)) h)
38.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify1.2m

Counts
264 → 306
Calls
264 calls:
Slowest
2.2s
(* (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (* (/ (* M D) (* 2 d)) h) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) h))) (/ (* (* 1 1) 1) (* (* l l) l)))
2.0s
(* (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (* (/ (* M D) (* 2 d)) h) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) h))) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
1.5s
(* (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* h h) h))) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
1.5s
(* (* (* (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h))) (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h))) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
1.5s
(* (* (* (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h))) (* (/ (* M D) (* 2 d)) (* (/ (* M D) (* 2 d)) h))) (/ (* (* 1 1) 1) (* (* l l) l)))

prune5.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize76.0ms

Local error

Found 4 expressions with local error:

5.0b
(* (/ (* M D) (* 2 d)) h)
4.8b
(/ (* M D) (* 2 d))
4.8b
(/ (* M D) (* 2 d))
4.4b
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l)))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
46×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
12×cbrt-undiv div-exp
10×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
5×associate-*l*
4×insert-posit16 add-log-exp
3×times-frac associate-*r* sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ *-commutative flip-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
48.0ms
(* (/ (* M D) (* 2 d)) h)
22.0ms
(/ (* M D) (* 2 d))
18.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l)))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(sqrt (- 1 (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l)))))
68.0ms
(* (/ (* M D) (* 2 d)) h)
52.0ms
(/ (* M D) (* 2 d))
50.0ms
(/ (* M D) (* 2 d))

simplify18.3s

Counts
59 → 102
Calls
59 calls:
Slowest
1.2s
(sqrt (- (pow 1 3) (pow (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l))) 3)))
1.1s
(sqrt (- (* 1 1) (* (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l))) (* (/ (* M D) (* 2 d)) (* (* (/ (* M D) (* 2 d)) h) (/ 1 l))))))
1.1s
(* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h))
1.1s
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.1s
(* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* h h) h))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.8b

regimes1.1s

Accuracy

0% (0.7b remaining)

Error of 8.0b against oracle of 7.3b and baseline of 8.0b

bsearch8.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.0s9350×body80valid
619.0ms3113×body80nan