Details

sample169.0ms

Algorithm

intervals

Results

111.0ms	827×	body	80	nan
37.0ms	256×	body	80	valid

simplify49.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

49.0ms

(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
46×	`times-frac`
41×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
28×	`sqrt-prod`
13×	`fma-def`
10×	`difference-of-squares`
8×	`div-inv` `distribute-lft-out` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `sqrt-div`
3×	`expm1-log1p-u` `associate-/r*` `distribute-rgt-out` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `frac-add` `distribute-rgt1-in` `flip-+`

Counts

3 → 112

Calls

3 calls:

Slowest

28.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
13.0ms	(/ (sqrt (- 1 (* x x))) x)
10.0ms	(sqrt (- 1 (* x x)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

133.0ms	(/ (sqrt (- 1 (* x x))) x)
112.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
76.0ms	(sqrt (- 1 (* x x)))

simplify5.8s

Counts

114 → 121

Calls

114 calls:

Slowest

448.0ms	(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
439.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
406.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))
388.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
330.0ms	(+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (+ (sqrt -1) (* 1/8 (/ 1 (* (pow x 4) (sqrt -1))))))

prune1.0s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt x))
0.3b	(/ 1 (sqrt x))
0.1b	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))
0.0b	(sqrt (- 1 (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `times-frac`
35×	`add-cube-cbrt`
29×	`sqrt-prod`
12×	`associate-/r*` `add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-div` `1-exp` `div-inv` `inv-pow` `difference-of-squares`
1×	`rem-sqrt-square` `flip3--` `fma-udef` `flip--`

Counts

4 → 127

Calls

4 calls:

Slowest

9.0ms	(/ 1 (sqrt x))
5.0ms	(sqrt (- 1 (* x x)))
5.0ms	(/ 1 (sqrt x))
0.0ms	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))

series318.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

188.0ms	(fma (/ 1 (sqrt x)) (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) x))
61.0ms	(sqrt (- 1 (* x x)))
39.0ms	(/ 1 (sqrt x))
29.0ms	(/ 1 (sqrt x))

simplify2.6s

Counts

121 → 139

Calls

121 calls:

Slowest

351.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
282.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))
250.0ms	(- (+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1)))))
174.0ms	(- 1 (+ (* 1/2 (pow x 2)) (* 1/8 (pow x 4))))
130.0ms	(sqrt (- (* 1 1) (* (* x x) (* x x))))

prune1.4s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.4s	23734×	body	80	nan
990.0ms	8000×	body	80	valid