Details

sample81.0ms

Algorithm

intervals

Results

48.0ms	290×	body	80	valid
12.0ms	89×	body	80	nan

simplify140.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

140.0ms

(* 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: 12.7b

localize39.0ms

Local error

Found 4 expressions with local error:

8.5b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.3b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.1b	(/ (* M D) (* 2 d))
4.1b	(/ (* M D) (* 2 d))

rewrite226.0ms

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

189.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
13.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
105.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
47.0ms	(/ (* M D) (* 2 d))
46.0ms	(/ (* M D) (* 2 d))

simplify48.5s

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 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)))
2.6s	(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))
2.3s	(* (* (/ (* (* (* 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)))
2.2s	(* (* (/ (* (* (* 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)))

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize33.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) l)))
4.2b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
4.1b	(/ (* M D) (* 2 d))
4.1b	(/ (* M D) (* 2 d))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

185×	`add-cbrt-cube` `add-exp-log`
99×	`prod-exp` `cbrt-unprod`
48×	`cbrt-undiv` `div-exp`
11×	`add-sqr-sqrt`
10×	`pow1`
9×	`*-un-lft-identity`
6×	`add-cube-cbrt` `sqrt-prod`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `sqrt-div` `div-inv` `associate-/l` `difference-of-squares`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `associate-r/` `-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

Slowest

133.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
16.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) l)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

176.0ms	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) l)))
109.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h)
46.0ms	(/ (* M D) (* 2 d))
36.0ms	(/ (* M D) (* 2 d))

simplify29.4s

Counts

104 → 146

Calls

104 calls:

Slowest

2.2s	(* (* (/ (* (* (* 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))
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))
2.1s	(* (* (/ (* (* (* 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))
1.8s	(* (* (/ (* (* (* 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))
861.0ms	(* 1/4 (/ (* (pow M 2) (* (pow D 2) h)) (pow d 2)))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize52.0ms

Local error

Found 4 expressions with local error:

8.5b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
8.5b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.3b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.3b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

684×	`add-cbrt-cube` `add-exp-log`
364×	`prod-exp` `cbrt-unprod`
212×	`cbrt-undiv` `div-exp`
28×	`add-sqr-sqrt`
26×	`associate-r`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`pow1`
10×	`frac-times` `associate-*l/`
6×	`pow-prod-down` `associate-*r/` `sqrt-prod`
4×	`sqrt-div` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `*-commutative` `div-inv` `flip--`

Counts

4 → 308

Calls

4 calls:

Slowest

186.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
170.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
7.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

195.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
171.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
118.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
101.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.4m

Counts

292 → 320

Calls

292 calls:

Slowest

2.8s	(* (* (/ (* (* (* 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 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)))
2.6s	(* (* (/ (* (* (* 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)))
2.5s	(* (* (/ (* (* (* 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 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)))

prune8.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize55.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))
6.6b	(* (* (/ (* M D) (* 2 d)) (* M D)) h)
4.3b	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))))
4.1b	(/ (* M D) (* 2 d))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

303×	`add-cbrt-cube` `add-exp-log`
176×	`prod-exp` `cbrt-unprod`
72×	`cbrt-undiv` `div-exp`
14×	`pow1`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
6×	`pow-prod-down` `add-cube-cbrt` `sqrt-prod`
4×	`associate-*l/` `insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `sqrt-div` `div-inv` `associate-/l` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 167

Calls

4 calls:

Slowest

135.0ms	(/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))
102.0ms	(* (* (/ (* M D) (* 2 d)) (* M D)) h)
45.0ms	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))))
10.0ms	(/ (* M D) (* 2 d))

series420.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(sqrt (- 1 (/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))))
114.0ms	(/ (* (* (/ (* M D) (* 2 d)) (* M D)) h) (* (* 2 d) l))
91.0ms	(* (* (/ (* M D) (* 2 d)) (* M D)) h)
29.0ms	(/ (* M D) (* 2 d))

simplify43.8s

Counts

137 → 179

Calls

137 calls:

Slowest

2.3s	(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (* M M) M) (* (* D D) D))) (* (* h h) h))
1.9s	(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (* M M) M) (* (* D D) D))) (* (* h h) h))
1.7s	(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (* (* (* M M) M) (* (* D D) D))) (* (* h h) h))
1.6s	(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (* M D) (* M D)) (* M D))) (* (* h h) h))
1.6s	(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (* M D) (* M D)) (* M D))) (* (* h h) h))

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

regimes1.8s

Accuracy

57.6% (1.7b remaining)

Error of 9.2b against oracle of 7.5b and baseline of 11.6b

bsearch26.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	9286×	body	80	valid
658.0ms	3082×	body	80	nan