Details

Time bar (total: 17.5s)

sample146.0ms

Algorithm
intervals
Results
49.0ms255×body160nan
40.0ms509×body80nan
34.0ms256×body80valid

simplify134.0ms

Calls
1 calls:
Slowest
134.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize12.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (- (* x x) 1))
0.0b
(+ x (sqrt (- (* x x) 1)))
0.0b
(- (* x x) 1)
0.0b
(log (+ x (sqrt (- (* x x) 1))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×add-cbrt-cube sqrt-prod insert-posit16 add-log-exp
3×log-prod
2×log-div flip3-+ flip3-- sqrt-div difference-of-sqr-1 flip-+ flip--
1×+-commutative rem-sqrt-square sub-neg pow1/2 rem-log-exp log-pow
Calls
4 calls:
Slowest
9.0ms
(log (+ x (sqrt (- (* x x) 1))))
4.0ms
(- (* x x) 1)
3.0ms
(+ x (sqrt (- (* x x) 1)))
3.0ms
(sqrt (- (* x x) 1))

series153.0ms

Calls
4 calls:
Slowest
79.0ms
(log (+ x (sqrt (- (* x x) 1))))
28.0ms
(- (* x x) 1)
24.0ms
(+ x (sqrt (- (* x x) 1)))
22.0ms
(sqrt (- (* x x) 1))

simplify3.2s

Calls
26 calls:
Slowest
361.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
270.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
263.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
241.0ms
(log (+ (pow x 3) (pow (sqrt (- (* x x) 1)) 3)))
236.0ms
(log (- (* x x) (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1)))))

prune461.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

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
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 associate-*r* associate-*l* add-exp-log sqrt-prod
5×flip3-+ add-cbrt-cube flip-+
4×frac-times
3×log-prod flip3-- insert-posit16 flip-- add-log-exp
2×log-div pow1/2 pow-prod-down associate-*l/ associate-*r/
1×+-commutative sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod
Calls
3 calls:
Slowest
12.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
4.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
2.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series177.0ms

Calls
3 calls:
Slowest
84.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
50.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
42.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify3.3s

Calls
43 calls:
Slowest
576.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
340.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))
273.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
267.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
226.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune605.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-div
12×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l* add-cube-cbrt sqrt-prod
8×frac-times pow1 flip3-+ add-cbrt-cube add-exp-log flip-+
6×flip3-- flip--
4×pow1/2 pow-prod-down associate-*l/ associate-*r/ insert-posit16 add-log-exp
2×+-commutative sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
7.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
7.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
2.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
2.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series149.0ms

Calls
4 calls:
Slowest
45.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
43.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
34.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
27.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify3.6s

Calls
68 calls:
Slowest
255.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
236.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
235.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
198.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
193.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune1.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s7744×body160nan
1.2s16315×body80nan
788.0ms8000×body80valid