Details

Time bar (total: 15.4s)

sample131.0ms

Algorithm
intervals
Results
84.0ms736×body80nan
29.0ms256×body80valid

simplify24.0ms

Calls
1 calls:
Slowest
24.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 3 expressions with local error:

0.2b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×div-inv
8×log-prod
6×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×pow1 distribute-rgt-out add-exp-log distribute-lft-out
3×log-div add-cbrt-cube sqrt-prod insert-posit16
2×flip3-+ sqrt-div frac-add distribute-rgt1-in flip-+
1×+-commutative rem-sqrt-square sum-log flip3-- pow1/2 rem-log-exp log-pow flip--
Calls
3 calls:
Slowest
5.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
4.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
1.0ms
(sqrt (- 1 (* x x)))

series408.0ms

Calls
3 calls:
Slowest
268.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
71.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
69.0ms
(sqrt (- 1 (* x x)))

simplify3.8s

Calls
37 calls:
Slowest
812.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* (/ (sqrt (- 1 (* x x))) x) (/ (sqrt (- 1 (* x x))) x))))
369.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
329.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
313.0ms
(log (+ (pow (/ 1 x) 3) (pow (/ (sqrt (- 1 (* x x))) x) 3)))
303.0ms
(- (+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1)))))

prune499.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log (/ 1 x)) (log (+ 1 (sqrt (- 1 (* x x))))))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(+ 1 (sqrt (- 1 (* x x))))
0.0b
(log (+ 1 (sqrt (- 1 (* x x)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×log-prod
9×add-sqr-sqrt pow1
8×add-cube-cbrt
5×log-div add-exp-log log-pow
4×associate-+l+ flip3-+ add-cbrt-cube flip-+ insert-posit16 distribute-lft-out add-log-exp
3×associate-+r+ sqrt-prod
2×+-commutative associate-+r- sqrt-div
1×rem-sqrt-square sum-log flip3-- pow1/2 rem-log-exp associate-+l- div-inv flip--
Calls
4 calls:
Slowest
6.0ms
(+ (log (/ 1 x)) (log (+ 1 (sqrt (- 1 (* x x))))))
2.0ms
(+ 1 (sqrt (- 1 (* x x))))
2.0ms
(log (+ 1 (sqrt (- 1 (* x x)))))
1.0ms
(sqrt (- 1 (* x x)))

series572.0ms

Calls
4 calls:
Slowest
245.0ms
(+ (log (/ 1 x)) (log (+ 1 (sqrt (- 1 (* x x))))))
197.0ms
(log (+ 1 (sqrt (- 1 (* x x)))))
72.0ms
(sqrt (- 1 (* x x)))
59.0ms
(+ 1 (sqrt (- 1 (* x x))))

simplify4.5s

Calls
39 calls:
Slowest
421.0ms
(- (+ (log (sqrt -1)) (log -1)) (+ (* 1/3 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ 1 (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
390.0ms
(- (+ (* 1/3 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ 1 (* (pow x 3) (sqrt -1)))) (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1)))))) (log (/ 1 x)))
386.0ms
(log (+ (* 1 1) (- (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (* 1 (sqrt (- 1 (* x x)))))))
371.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
359.0ms
(log (- (* 1 1) (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))))))

prune780.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.7s24268×body80nan
1.3s8000×body80valid