Details

sample129.0ms

Algorithm

intervals

Results

34.0ms	194×	body	80	valid
32.0ms	29×	body	2560	valid
16.0ms	17×	body	1280	valid
15.0ms	256×	pre	80	true
6.0ms	8×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify111.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize39.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (+ (* x x) (* p (* 4 p))))
0.9b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
0.0b	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

Slowest

35.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
19.0ms	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
18.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
8.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

277.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
115.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
74.0ms	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
55.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify989.0ms

Counts: 98 → 98

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize84.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (+ (* x x) (* (* p 4) p)))
16.1b	(sqrt (+ (* x x) (* (* p 4) p)))
16.1b	(sqrt (+ (* x x) (* (* p 4) p)))
3.8b	(/ (* x x) (+ (* x x) (* (* p 4) p)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 72

Calls

4 calls:

Slowest

28.0ms	(/ (* x x) (+ (* x x) (* (* p 4) p)))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
71.0ms	(/ (* x x) (+ (* x x) (* (* p 4) p)))
62.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
56.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.1s

Counts: 84 → 84

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize93.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.1b	(sqrt (+ (* x x) (* (* p 4) p)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`associate-/r/`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 73

Calls

4 calls:

Slowest

12.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
11.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
7.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
160.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
152.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
69.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.0s

Counts: 85 → 85

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize156.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.6b	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
16.1b	(sqrt (+ (* x x) (* (* p 4) p)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`associate-/r/`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 73

Calls

4 calls:

Slowest

9.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
6.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

174.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
163.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
161.0ms	(cbrt (/ (* x x) (+ (* x x) (* (* p 4) p))))
49.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.0s

Counts: 85 → 85

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.9b

regimes175.0ms

Accuracy

0% (1.2b remaining)

Error of 14.1b against oracle of 12.9b and baseline of 14.1b

bsearch12.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

834.0ms	728×	body	2560	valid
584.0ms	6062×	body	80	valid
383.0ms	613×	body	1280	valid
294.0ms	8000×	pre	80	true
134.0ms	320×	body	640	valid
37.0ms	143×	body	320	valid
33.0ms	50×	body	5120	valid
16.0ms	84×	body	160	valid