Details

sample81.0ms

Algorithm

intervals

Results

44.0ms	317×	body	80	valid
12.0ms	90×	body	80	nan

simplify230.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

230.0ms

(* 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: 13.8b

localize45.0ms

Local error

Found 4 expressions with local error:

10.6b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.7b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.1b	(/ (* M D) (* 2 d))
4.1b	(/ (* M D) (* 2 d))

rewrite196.0ms

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

151.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
17.0ms	(/ (* M D) (* 2 d))
12.0ms	(/ (* M D) (* 2 d))
4.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
130.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
50.0ms	(/ (* M D) (* 2 d))
49.0ms	(/ (* M D) (* 2 d))

simplify49.5s

Counts

172 → 210

Calls

172 calls:

Slowest

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) 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 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)))
2.1s	(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize64.0ms

Local error

Found 4 expressions with local error:

7.5b	(/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))
5.8b	(* (* (* M D) (/ (* M D) (* 2 d))) h)
4.7b	(sqrt (- 1 (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))))
4.1b	(/ (* M D) (* 2 d))

rewrite356.0ms

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×	`insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `sqrt-div` `associate-l/` `associate-r/` `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

139.0ms	(/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))
117.0ms	(* (* (* M D) (/ (* M D) (* 2 d))) h)
69.0ms	(sqrt (- 1 (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))))
22.0ms	(/ (* M D) (* 2 d))

series419.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(sqrt (- 1 (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))))
109.0ms	(/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l))
103.0ms	(* (* (* M D) (/ (* M D) (* 2 d))) h)
29.0ms	(/ (* M D) (* 2 d))

simplify44.9s

Counts

137 → 179

Calls

137 calls:

Slowest

2.3s	(* (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.1s	(* (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.0s	(* (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
1.8s	(* (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
1.6s	(sqrt (- (* 1 1) (* (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l)) (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* (* 2 d) l)))))

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize46.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (* (* M D) (/ (* M D) (* 2 d))) h)
5.2b	(/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)
4.7b	(sqrt (- 1 (/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)))
4.1b	(/ (* M D) (* 2 d))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

239×	`add-cbrt-cube` `add-exp-log`
118×	`prod-exp` `cbrt-unprod`
77×	`cbrt-undiv` `div-exp`
25×	`add-sqr-sqrt`
22×	`times-frac`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`pow1`
8×	`sqrt-prod`
6×	`pow-prod-down` `div-inv` `associate-/l*`
4×	`associate-/r*` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`associate-r`
2×	`clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 167

Calls

4 calls:

Slowest

139.0ms	(* (* (* M D) (/ (* M D) (* 2 d))) h)
105.0ms	(/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)
23.0ms	(sqrt (- 1 (/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)))
12.0ms	(/ (* M D) (* 2 d))

series465.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(sqrt (- 1 (/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)))
124.0ms	(/ (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) l)
87.0ms	(* (* (* M D) (/ (* M D) (* 2 d))) h)
48.0ms	(/ (* M D) (* 2 d))

simplify48.7s

Counts

150 → 179

Calls

150 calls:

Slowest

2.1s	(* (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
1.9s	(* (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
1.9s	(* (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))
1.8s	(/ (* (* (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d)) (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d))) (/ (* (* (* M D) (/ (* M D) (* 2 d))) h) (* 2 d))) (* (* l l) l))
1.8s	(* (* (* (* (* M D) (* M D)) (* M D)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))

prune3.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize47.0ms

Local error

Found 4 expressions with local error:

6.8b	(* h (/ (* D M) (* 2 d)))
6.7b	(/ (/ (* D M) (* 2 d)) l)
4.7b	(pow (- 1 (* (* h (/ (* D M) (* 2 d))) (/ (/ (* D M) (* 2 d)) l))) (/ 1 2))
4.1b	(/ (* D M) (* 2 d))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
52×	`add-cbrt-cube`
30×	`times-frac`
26×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
13×	`pow-unpow`
8×	`div-inv`
7×	`pow1`
6×	`associate-/l*`
5×	`associate-r`
4×	`associate-/r*` `insert-posit16` `add-log-exp`
3×	`unpow-prod-down` `associate-l`
2×	`clear-num` `frac-2neg`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `unswap-sqr` `sqr-pow` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

Slowest

26.0ms	(/ (/ (* D M) (* 2 d)) l)
20.0ms	(* h (/ (* D M) (* 2 d)))
11.0ms	(/ (* D M) (* 2 d))
7.0ms	(pow (- 1 (* (* h (/ (* D M) (* 2 d))) (/ (/ (* D M) (* 2 d)) l))) (/ 1 2))

series458.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

291.0ms	(pow (- 1 (* (* h (/ (* D M) (* 2 d))) (/ (/ (* D M) (* 2 d)) l))) (/ 1 2))
78.0ms	(* h (/ (* D M) (* 2 d)))
51.0ms	(/ (/ (* D M) (* 2 d)) l)
38.0ms	(/ (* D M) (* 2 d))

simplify21.9s

Counts

108 → 137

Calls

108 calls:

Slowest

1.1s	(* (* (* h h) h) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s	(* (* (* h h) h) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
990.0ms	(/ (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* l l) l))
965.0ms	(* (* (* h h) h) (/ (* (* (* D M) (* D M)) (* D M)) (* (* (* 2 2) 2) (* (* d d) d))))
795.0ms	(/ (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* l l) l))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

regimes1.7s

Accuracy

0% (1.0b remaining)

Error of 8.2b against oracle of 7.2b and baseline of 8.2b

bsearch4.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.2s	9315×	body	80	valid
688.0ms	3161×	body	80	nan