Details

Time bar (total: 29.4s)

sample86.0ms

Algorithm
intervals
Results
28.0ms217×body160nan
27.0ms496×body80nan
17.0ms256×body80valid

simplify117.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
117.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize22.0ms

Local error

Found 2 expressions with local error:

27.7b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity sqrt-prod
5×add-sqr-sqrt
4×add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 difference-of-sqr-1 flip-+ flip-- distribute-lft-out
Counts
2 → 32
Calls
2 calls:
Slowest
11.0ms
(+ x (sqrt (- (* x x) 1)))
7.0ms
(sqrt (- (* x x) 1))

series117.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
66.0ms
(+ x (sqrt (- (* x x) 1)))
51.0ms
(sqrt (- (* x x) 1))

simplify2.4s

Counts
18 → 38
Calls
18 calls:
Slowest
472.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
294.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
214.0ms
(sqrt (- (* (* x x) (* x x)) (* 1 1)))
209.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
195.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune300.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
10×associate-*r*
7×associate-*l*
6×pow1 add-cube-cbrt
4×frac-times flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp unswap-sqr
3×flip3-- pow-prod-down flip--
2×sqrt-pow1 pow1/2 associate-*l/ associate-*r/ insert-posit16 difference-of-squares
1×+-commutative sum-log sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 56
Calls
2 calls:
Slowest
42.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
6.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series197.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
117.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
80.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify3.3s

Counts
50 → 62
Calls
50 calls:
Slowest
323.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
288.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
262.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
237.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
231.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune547.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (+ x 1)) (sqrt (sqrt (- x 1))))
0.3b
(* (* (sqrt (+ x 1)) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1))))
0.1b
(sqrt (sqrt (- x 1)))
0.1b
(sqrt (sqrt (- x 1)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-div
83×sqrt-prod
48×add-sqr-sqrt
32×frac-times
30×*-un-lft-identity
26×associate-*r*
23×flip3-- flip--
20×pow1
16×associate-*l/ add-cube-cbrt
13×sqrt-pow1
12×flip3-+ flip-+
11×add-cbrt-cube add-exp-log
10×pow-prod-down associate-*r/
9×pow1/2
8×associate-*l* difference-of-squares
6×unswap-sqr
4×rem-sqrt-square difference-of-sqr-1 prod-exp cbrt-unprod insert-posit16 distribute-lft-out-- add-log-exp
3×sqrt-unprod
2×*-commutative
1×distribute-lft-out
Counts
4 → 159
Calls
4 calls:
Slowest
86.0ms
(* (* (sqrt (+ x 1)) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1))))
33.0ms
(* (sqrt (+ x 1)) (sqrt (sqrt (- x 1))))
10.0ms
(sqrt (sqrt (- x 1)))
10.0ms
(sqrt (sqrt (- x 1)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(* (sqrt (+ x 1)) (sqrt (sqrt (- x 1))))
109.0ms
(* (* (sqrt (+ x 1)) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1))))
95.0ms
(sqrt (sqrt (- x 1)))
80.0ms
(sqrt (sqrt (- x 1)))

simplify14.9s

Counts
162 → 171
Calls
162 calls:
Slowest
476.0ms
(* (* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (sqrt (- x 1))) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1))))) (* (* (sqrt (sqrt (- x 1))) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1)))))
476.0ms
(* (* (sqrt (+ x 1)) (sqrt (sqrt (- (* x x) (* 1 1))))) (sqrt (sqrt (- x 1))))
445.0ms
(* (* (sqrt (- (* x x) (* 1 1))) (sqrt (sqrt (- (pow x 3) (pow 1 3))))) (sqrt (sqrt (- (* x x) (* 1 1)))))
414.0ms
(* (* (sqrt (- (* x x) (* 1 1))) (sqrt (sqrt (- (* x x) (* 1 1))))) (sqrt (sqrt (- (pow x 3) (pow 1 3)))))
404.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (sqrt (- x 1))) (sqrt (sqrt (- x 1)))) (sqrt (sqrt (- x 1)))))

prune2.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s16300×body80nan
1.4s7539×body160nan
857.0ms8000×body80valid