Details

sample154.0ms

Algorithm

intervals

Results

96.0ms	717×	body	80	nan
34.0ms	256×	body	80	valid

simplify44.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

44.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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

23.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
18.0ms	(/ (sqrt (- 1 (* x x))) x)
6.0ms	(sqrt (- 1 (* x x)))

series275.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

127.0ms	(/ (sqrt (- 1 (* x x))) x)
78.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
70.0ms	(sqrt (- 1 (* x x)))

simplify5.8s

Counts

114 → 121

Calls

114 calls:

Slowest

452.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
399.0ms	(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
334.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
334.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))
292.0ms	(+ (* 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

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`associate-l`
12×	`add-exp-log` `sqrt-prod`
11×	`times-frac`
8×	`fma-def` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r` `add-log-exp`
4×	`prod-exp` `distribute-lft-out` `difference-of-squares`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `distribute-lft-in` `sqrt-pow1` `flip3--` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `flip--`

Counts

3 → 90

Calls

3 calls:

Slowest

92.0ms	(* (/ 1 x) (+ (sqrt (- 1 (* x x))) 1))
30.0ms	(+ (sqrt (- 1 (* x x))) 1)
5.0ms	(sqrt (- 1 (* x x)))

series213.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

108.0ms	(* (/ 1 x) (+ (sqrt (- 1 (* x x))) 1))
54.0ms	(sqrt (- 1 (* x x)))
50.0ms	(+ (sqrt (- 1 (* x x))) 1)

simplify7.3s

Counts

67 → 99

Calls

67 calls:

Slowest

1.1s	(* (* (* (/ 1 x) (/ 1 x)) (/ 1 x)) (* (* (+ (sqrt (- 1 (* x x))) 1) (+ (sqrt (- 1 (* x x))) 1)) (+ (sqrt (- 1 (* x x))) 1)))
755.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
448.0ms	(+ (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (- (* 1 1) (* (sqrt (- 1 (* x x))) 1)))
428.0ms	(* x (+ (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (- (* 1 1) (* (sqrt (- 1 (* x x))) 1))))
395.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))

prune884.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.4s	23852×	body	80	nan
958.0ms	8000×	body	80	valid