Details

Time bar (total: 16.7s)

sample583.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
25.0ms257×body80nan

simplify88.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
88.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
55×add-sqr-sqrt
49×times-frac
30×sqrt-prod
25×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
4×associate-/r* add-cbrt-cube add-exp-log associate-/r/
3×pow1
2×rem-sqrt-square flip3-+ flip-+ insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
2 → 95
Calls
2 calls:
Slowest
29.0ms
(/ (- 1 x) (+ 1 x))
16.0ms
(sqrt (/ (- 1 x) (+ 1 x)))

series112.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
59.0ms
(/ (- 1 x) (+ 1 x))
52.0ms
(sqrt (/ (- 1 x) (+ 1 x)))

simplify3.4s

Counts
103 → 101
Calls
103 calls:
Slowest
456.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
259.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
200.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
199.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
125.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune916.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
30×associate-*l*
29×*-un-lft-identity
25×times-frac
16×difference-of-squares
14×add-cube-cbrt
7×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
5×flip3-- sqrt-div flip-- distribute-lft-out--
4×frac-times associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 pow-prod-down associate-*l/ prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
1×cbrt-undiv pow1/2 div-exp *-commutative sqrt-prod div-inv
Counts
2 → 78
Calls
2 calls:
Slowest
80.0ms
(* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x))
23.0ms
(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x)))

series119.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
76.0ms
(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x)))
43.0ms
(* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x))

simplify8.0s

Counts
69 → 84
Calls
69 calls:
Slowest
546.0ms
(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- (* 1 1) (* x x))))
491.0ms
(sqrt (* (- 1 x) (- (pow 1 3) (pow x 3))))
470.0ms
(* (- (* 1 1) (* x x)) (+ 1 x))
466.0ms
(* (- x) (/ (- 1 x) (- (* 1 1) (* x x))))
445.0ms
(* (- 1 x) (- (pow 1 3) (pow x 3)))

prune793.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.4s8000×body80valid
761.0ms7749×body80nan