Details

sample124.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
21.0ms	241×	body	80	nan

simplify96.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

95.0ms

(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1 x) (+ 1 x))
0.0b	(atan (sqrt (/ (- 1 x) (+ 1 x))))
0.0b	(sqrt (/ (- 1 x) (+ 1 x)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
49×	`times-frac`
30×	`sqrt-prod`
26×	`add-cube-cbrt`
18×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`distribute-lft-out--`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

3 → 103

Calls

3 calls:

Slowest

34.0ms	(/ (- 1 x) (+ 1 x))
11.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

series113.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

66.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
40.0ms	(/ (- 1 x) (+ 1 x))
6.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify6.4s

Counts

166 → 112

Calls

166 calls:

Slowest

434.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
367.0ms	(* (+ 1 x) (+ (* 1 1) (+ (* x x) (* 1 x))))
275.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
260.0ms	(* (* (/ (- 1 x) (+ 1 x)) (/ (- 1 x) (+ 1 x))) (/ (- 1 x) (+ 1 x)))
231.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
0.0b	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
82×	`*-un-lft-identity`
63×	`times-frac`
62×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
16×	`difference-of-squares`
10×	`distribute-lft-out`
9×	`associate-/l*`
8×	`distribute-lft-out--`
7×	`associate-/r*`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
2×	`pow1` `associate-/r/` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--`

Counts

2 → 105

Calls

2 calls:

Slowest

21.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
8.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

series73.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

70.0ms	(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
2.0ms	(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.9s

Counts

175 → 111

Calls

175 calls:

Slowest

356.0ms	(* (* (/ (sqrt (- 1 x)) (sqrt (+ 1 x))) (/ (sqrt (- 1 x)) (sqrt (+ 1 x)))) (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
243.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
235.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
228.0ms	(/ (sqrt (- 1 x)) (sqrt (+ (pow 1 3) (pow x 3))))
156.0ms	(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes95.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

937.0ms	8000×	body	80	valid
893.0ms	8062×	body	80	nan