Details

Time bar (total: 9.1s)

sample122.0ms

Algorithm
intervals
Results
44.0ms514×body80nan
38.0ms234×body160nan
22.0ms256×body80valid

simplify127.0ms

Calls
1 calls:
Slowest
127.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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
2.0ms
(sqrt (- (* x x) 1))
2.0ms
(+ x (sqrt (- (* x x) 1)))

series133.0ms

Calls
2 calls:
Slowest
85.0ms
(+ x (sqrt (- (* x x) 1)))
48.0ms
(sqrt (- (* x x) 1))

simplify1.3s

Calls
13 calls:
Slowest
171.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
152.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
137.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
122.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))
121.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune288.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b
(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 add-cbrt-cube add-exp-log
4×frac-times flip3-+ flip3-- flip-+ flip--
3×pow1/2 insert-posit16 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))

series223.0ms

Calls
3 calls:
Slowest
104.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
71.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
48.0ms
(sqrt (- x 1))

simplify1.9s

Calls
43 calls:
Slowest
201.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
192.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
182.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))
161.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
96.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))

prune659.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s7557×body160nan
1.4s16003×body80nan
721.0ms8000×body80valid