Details

sample134.0ms

Algorithm

intervals

Results

61.0ms	292×	body	80	valid
36.0ms	87×	body	80	nan

simplify1.8s

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize40.0ms

Local error

Found 4 expressions with local error:

13.1b	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.9b	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.5b	(/ (* M D) (* 2 d))
4.5b	(/ (* M D) (* 2 d))

rewrite254.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 206

Calls

4 calls:

Slowest

216.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
12.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
91.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
51.0ms	(/ (* M D) (* 2 d))
44.0ms	(/ (* M D) (* 2 d))

simplify2.0s

Counts: 218 → 218

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.8b

localize79.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.5b	(/ (* M D) (* 2 d))
4.5b	(/ (* M D) (* 2 d))
2.6b	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `flip3--` `associate-l/` `div-inv` `flip--` `associate-/l*` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`

Counts

4 → 93

Calls

4 calls:

Slowest

19.0ms	(/ (* M D) (* 2 d))
19.0ms	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
15.0ms	(/ (* M D) (* 2 d))
10.0ms	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

317.0ms	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
187.0ms	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
52.0ms	(/ (* M D) (* 2 d))
43.0ms	(/ (* M D) (* 2 d))

simplify6.7s

Counts: 105 → 105

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.4b

localize65.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.5b	(/ (/ (* M D) 2) d)
4.5b	(/ (* M D) (* 2 d))
2.6b	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
29×	`add-sqr-sqrt`
27×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `prod-exp` `cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*l/` `flip--` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

Slowest

17.0ms	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
17.0ms	(/ (* M D) (* 2 d))
10.0ms	(/ (/ (* M D) 2) d)
6.0ms	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

323.0ms	(* (sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l))))) w0)
197.0ms	(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (/ (* M D) 2) d) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
49.0ms	(/ (/ (* M D) 2) d)
33.0ms	(/ (* M D) (* 2 d))

simplify1.0s

Counts: 132 → 132

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.8b

localize64.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (/ M 2) (/ D d))
5.5b	(* (/ M 2) (/ D d))
4.9b	(sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h)))))
2.6b	(* (sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h))))) w0)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
80×	`times-frac`
52×	`*-un-lft-identity`
45×	`associate-l`
36×	`add-cube-cbrt`
33×	`sqrt-prod`
30×	`add-cbrt-cube` `add-exp-log`
29×	`associate-r`
24×	`difference-of-squares`
16×	`cbrt-prod`
11×	`pow1`
10×	`unswap-sqr`
9×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`frac-times` `flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 177

Calls

4 calls:

Slowest

59.0ms	(* (sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h))))) w0)
37.0ms	(sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h)))))
31.0ms	(* (/ M 2) (/ D d))
22.0ms	(* (/ M 2) (/ D d))

series632.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

341.0ms	(* (sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h))))) w0)
210.0ms	(sqrt (- 1 (/ (* (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h))) (/ (* (/ M 2) (/ D d)) (/ (cbrt l) (cbrt h)))) (/ (cbrt l) (cbrt h)))))
47.0ms	(* (/ M 2) (/ D d))
34.0ms	(* (/ M 2) (/ D d))

simplify1.0s

Counts: 189 → 189

prune3.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

regimes2.2s

Accuracy

0% (1.4b remaining)

Error of 8.4b against oracle of 6.9b and baseline of 8.4b

bsearch7.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.3s	9292×	body	80	valid
593.0ms	3105×	body	80	nan