Details

Time bar (total: 9.6s)

sample133.0ms

Algorithm
intervals
Results
42.0ms240×body160nan
39.0ms517×body80nan
32.0ms256×body80valid

simplify105.0ms

Calls
1 calls:
Slowest
105.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize24.0ms

Local error

Found 2 expressions with local error:

30.4b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
3×*-un-lft-identity add-cube-cbrt
2×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 add-log-exp
1×+-commutative rem-sqrt-square flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip--
Calls
2 calls:
Slowest
5.0ms
(sqrt (- (* x x) 1))
3.0ms
(+ x (sqrt (- (* x x) 1)))

series62.0ms

Calls
2 calls:
Slowest
37.0ms
(+ x (sqrt (- (* x x) 1)))
25.0ms
(sqrt (- (* x x) 1))

simplify1.6s

Calls
13 calls:
Slowest
283.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
222.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
200.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
143.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
140.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))

prune256.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b
(sqrt (+ x 1))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×sqrt-div
9×add-sqr-sqrt sqrt-prod
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l*
5×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+
4×frac-times
3×flip3-- pow1/2 insert-posit16 flip-- add-log-exp
2×pow-prod-down associate-*l/ associate-*r/
1×+-commutative rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
3 calls:
Slowest
13.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
4.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
1.0ms
(sqrt (+ x 1))

series120.0ms

Calls
3 calls:
Slowest
57.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
46.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
17.0ms
(sqrt (+ x 1))

simplify2.1s

Calls
43 calls:
Slowest
222.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
211.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
170.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
159.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))
146.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune603.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.9s7569×body160nan
1.3s16321×body80nan
782.0ms8000×body80valid