Details

sample121.0ms

Algorithm

intervals

Results

72.0ms	292×	body	80	valid
17.0ms	87×	body	80	nan

simplify1.8s

Counts: 1 → 1

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize36.0ms

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))

rewrite261.0ms

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

217.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
18.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

190.0ms	(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
128.0ms	(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
42.0ms	(/ (* M D) (* 2 d))
35.0ms	(/ (* M D) (* 2 d))

simplify2.4s

Counts: 210 → 210

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

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×	`sqrt-div` `insert-posit16` `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 → 85

Calls

4 calls:

Slowest

31.0ms	(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l))))) w0)
10.0ms	(/ (* M D) (* 2 d))
10.0ms	(/ (* M D) (* 2 d))
4.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l)))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

399.0ms	(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l))))) w0)
221.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))) (/ (cbrt h) (cbrt l)))))
52.0ms	(/ (* M D) (* 2 d))
41.0ms	(/ (* M D) (* 2 d))

simplify6.3s

Counts: 97 → 97

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.4b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

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×	`associate-/r*` `sqrt-div` `insert-posit16` `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 → 112

Calls

4 calls:

Slowest

25.0ms	(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l))))) w0)
20.0ms	(/ (* M D) (* 2 d))
20.0ms	(/ (/ (* M D) 2) d)
8.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

843.0ms	(* (sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l))))) w0)
221.0ms	(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (cbrt h) (cbrt l)) (/ (/ (* M D) 2) d))) (/ (cbrt h) (cbrt l)))))
54.0ms	(/ (* M D) (* 2 d))
50.0ms	(/ (/ (* M D) 2) d)

simplify1.1s

Counts: 124 → 124

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize70.0ms

Local error

Found 4 expressions with local error:

8.0b	(/ (* (/ 2 M) d) D)
8.0b	(/ (* (/ 2 M) d) D)
4.9b	(sqrt (- 1 (* (* (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D)) (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))) (/ (cbrt h) (cbrt l)))))
3.2b	(/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

697×	`times-frac`
292×	`add-sqr-sqrt`
291×	`*-un-lft-identity` `add-cube-cbrt`
288×	`cbrt-prod`
54×	`add-exp-log`
52×	`div-inv`
46×	`add-cbrt-cube`
42×	`associate-/l*`
28×	`cbrt-undiv` `div-exp`
13×	`associate-/r*`
8×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod` `associate-/l/`
2×	`sqrt-div` `associate-*l/`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--`

Counts

4 → 422

Calls

4 calls:

Slowest

26.0ms	(/ (* (/ 2 M) d) D)
14.0ms	(/ (* (/ 2 M) d) D)
14.0ms	(/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))
4.0ms	(sqrt (- 1 (* (* (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D)) (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))) (/ (cbrt h) (cbrt l)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

393.0ms	(/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))
196.0ms	(sqrt (- 1 (* (* (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D)) (/ (/ (cbrt h) (cbrt l)) (/ (* (/ 2 M) d) D))) (/ (cbrt h) (cbrt l)))))
62.0ms	(/ (* (/ 2 M) d) D)
32.0ms	(/ (* (/ 2 M) d) D)

simplify1.6s

Counts: 434 → 434

prune8.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

regimes1.6s

Accuracy

16.9% (1.1b remaining)

Error of 8.0b against oracle of 6.9b and baseline of 8.3b

bsearch13.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	9292×	body	80	valid
1.0s	3105×	body	80	nan