Details

Time bar (total: 14.2s)

sample174.0ms

Algorithm
intervals
Results
80.0ms256×body80valid
28.0ms233×body80nan

simplify50.0ms

Calls
1 calls:
Slowest
49.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(atan (sqrt (/ (- 1 x) (+ 1 x))))
0.0b
(sqrt (/ (- 1 x) (+ 1 x)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
61×add-sqr-sqrt
49×times-frac
30×sqrt-prod
28×add-cube-cbrt
20×difference-of-squares
15×sqrt-div
14×distribute-lft-out
12×associate-/l*
10×distribute-lft-out--
8×associate-/r*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r/ associate-/l/
3×insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg flip3-+ flip3-- flip-+ div-inv flip--
1×cbrt-undiv sqrt-pow1 pow1/2 div-sub div-exp
Calls
3 calls:
Slowest
134.0ms
(/ (- 1 x) (+ 1 x))
40.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series290.0ms

Calls
3 calls:
Slowest
204.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
81.0ms
(/ (- 1 x) (+ 1 x))
5.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.7s

Calls
120 calls:
Slowest
424.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
263.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
230.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
213.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
120.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1 x))
0.0b
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
0.0b
(sqrt (- 1 x))
0.0b
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
98×sqrt-prod
91×*-un-lft-identity
71×add-sqr-sqrt
63×times-frac
42×add-cube-cbrt
18×difference-of-squares
11×distribute-lft-out
9×associate-/l* distribute-lft-out--
8×sqrt-div
7×associate-/r*
6×pow1 add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp div-inv
Calls
4 calls:
Slowest
16.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
9.0ms
(sqrt (+ 1 x))
7.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))
5.0ms
(sqrt (- 1 x))

series137.0ms

Calls
4 calls:
Slowest
59.0ms
(/ (sqrt (- 1 x)) (sqrt (+ 1 x)))
38.0ms
(sqrt (- 1 x))
38.0ms
(sqrt (+ 1 x))
2.0ms
(atan (/ (sqrt (- 1 x)) (sqrt (+ 1 x))))

simplify4.3s

Calls
178 calls:
Slowest
274.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
255.0ms
(/ (* (* (sqrt (- 1 x)) (sqrt (- 1 x))) (sqrt (- 1 x))) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
215.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
185.0ms
(- 1 (+ (* 1/2 x) (* 1/8 (pow x 2))))
119.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch3.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s8247×body80nan
976.0ms8000×body80valid