Details

Time bar (total: 12.5s)

sample125.0ms

Algorithm
intervals
Results
41.0ms233×body160nan
40.0ms525×body80nan
24.0ms256×body80valid

simplify131.0ms

Calls
1 calls:
Slowest
131.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize27.0ms

Local error

Found 3 expressions with local error:

31.9b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))
0.0b
(- (* x x) 1)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×add-sqr-sqrt add-log-exp
6×sqrt-prod
4×pow1 add-cube-cbrt difference-of-squares
3×add-cbrt-cube add-exp-log insert-posit16
2×flip3-- sqrt-div difference-of-sqr-1 flip--
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+ distribute-lft-out
Calls
3 calls:
Slowest
21.0ms
(+ x (sqrt (- (* x x) 1)))
16.0ms
(sqrt (- (* x x) 1))
7.0ms
(- (* x x) 1)

series183.0ms

Calls
3 calls:
Slowest
72.0ms
(+ x (sqrt (- (* x x) 1)))
56.0ms
(sqrt (- (* x x) 1))
54.0ms
(- (* x x) 1)

simplify2.6s

Calls
27 calls:
Slowest
425.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
261.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
245.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
207.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
205.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))

prune482.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×sqrt-prod
15×*-un-lft-identity
14×sqrt-div
10×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
5×flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp
4×frac-times unswap-sqr
3×sqrt-pow1 flip3-- pow1/2 pow-prod-down insert-posit16 flip--
2×associate-*l/ associate-*r/ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out--
Calls
3 calls:
Slowest
30.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
10.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
8.0ms
(sqrt (+ x 1))

series220.0ms

Calls
3 calls:
Slowest
95.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
91.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
34.0ms
(sqrt (+ x 1))

simplify3.5s

Calls
61 calls:
Slowest
337.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
289.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
257.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
230.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
216.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune763.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.9s7653×body160nan
1.3s16393×body80nan
806.0ms8000×body80valid