Details

Time bar (total: 1.7m)

sample141.0ms

Algorithm
intervals
Results
91.0ms757×body80nan
29.0ms256×body80valid

simplify43.0ms

Calls
1 calls:
Slowest
42.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 2 expressions with local error:

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
321×add-sqr-sqrt
261×*-un-lft-identity
258×associate-/l*
236×log-div
234×frac-add
204×sqrt-prod
130×difference-of-squares
117×add-cube-cbrt
108×associate-/r*
79×times-frac
36×clear-num frac-2neg
32×distribute-lft-out--
26×swap-sqr *-commutative unswap-sqr
21×log-prod
20×sqrt-div associate-/l/
16×associate-*l*
14×distribute-lft-out
10×flip3-- flip--
7×div-inv
5×add-exp-log
4×add-cbrt-cube
3×pow1 distribute-rgt-out
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv flip3-+ div-exp rem-log-exp distribute-rgt1-in log-pow flip-+
Calls
2 calls:
Slowest
73.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
34.0ms
(/ (sqrt (- 1 (* x x))) x)

series362.0ms

Calls
2 calls:
Slowest
223.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
139.0ms
(/ (sqrt (- 1 (* x x))) x)

simplify36.7s

Calls
395 calls:
Slowest
829.0ms
(log (+ (* (/ 1 (* (cbrt x) (cbrt x))) (cbrt x)) (* (cbrt x) (/ (sqrt (- 1 (* x x))) (* (cbrt x) (cbrt x))))))
620.0ms
(log (+ (* 1 (* x (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x))))))) (* (/ x 1) (sqrt (- (pow 1 3) (pow (* x x) 3))))))
427.0ms
(log (+ (* (/ 1 (* (cbrt x) (cbrt x))) (* x (sqrt (+ 1 (* x x))))) (* (cbrt x) (sqrt (- (* 1 1) (* (* x x) (* x x)))))))
422.0ms
(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
402.0ms
(log (+ (* (/ 1 (* (cbrt x) (cbrt x))) (/ x (cbrt (sqrt (- 1 (* x x)))))) (* (cbrt x) (* (cbrt (sqrt (- 1 (* x x)))) (cbrt (sqrt (- 1 (* x x))))))))

prune3.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- 1 (* x x))) (sqrt x))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))
0.2b
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
580×add-sqr-sqrt
558×sqrt-prod
494×*-un-lft-identity
362×log-div
350×associate-+r-
348×frac-add
330×associate-/l*
270×associate-/r*
255×add-cube-cbrt
228×times-frac
190×difference-of-squares
64×log-prod
54×distribute-lft-out--
45×clear-num frac-2neg
42×associate-+r+
38×swap-sqr *-commutative distribute-lft-out unswap-sqr
27×associate-*l*
26×sqrt-div associate-/l/
22×associate-+l+
15×pow1
14×add-exp-log
13×flip3-- flip--
12×associate-+l-
11×div-inv
10×add-cbrt-cube
9×log-pow pow-flip
8×fma-def add-log-exp
5×div-exp
4×expm1-log1p-u sum-log distribute-rgt-out insert-posit16 log1p-expm1-u
3×cbrt-undiv sqrt-pow1 pow1/2 inv-pow
2×rec-exp flip3-+ 1-exp flip-+
1×+-commutative sqrt-undiv distribute-rgt1-in
Calls
4 calls:
Slowest
150.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
46.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
10.0ms
(/ 1 (sqrt x))
8.0ms
(/ 1 (sqrt x))

series655.0ms

Calls
4 calls:
Slowest
451.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
102.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
54.0ms
(/ 1 (sqrt x))
48.0ms
(/ 1 (sqrt x))

simplify43.0s

Calls
795 calls:
Slowest
545.0ms
(log (+ (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (- (* (/ (sqrt (- 1 (* x x))) (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))) (* (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))))
468.0ms
(log (* (/ (sqrt x) (sqrt 1)) (/ (sqrt x) (sqrt (- 1 x)))))
305.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
289.0ms
(log (* (/ (sqrt x) (cbrt 1)) (* (sqrt x) (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x))))))))
264.0ms
(log (* (/ (sqrt x) (sqrt 1)) (* (sqrt x) (sqrt (+ (* 1 1) (+ (* (* x x) (* x x)) (* 1 (* x x))))))))

prune9.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
31×add-sqr-sqrt
25×log-prod
21×times-frac distribute-lft-out
16×add-cube-cbrt
15×log-div sqrt-prod
10×distribute-lft-out--
9×associate-/l*
5×associate-*l* add-exp-log
4×add-log-exp
3×pow1 associate-/r* fma-def log-rec
2×expm1-log1p-u clear-num flip3-+ add-cbrt-cube rem-log-exp flip-+ insert-posit16 log1p-expm1-u associate-/l/
1×+-commutative sum-log frac-2neg div-exp log-pow div-inv
Calls
2 calls:
Slowest
141.0ms
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
54.0ms
(+ 1 (sqrt (- 1 (* x x))))

series295.0ms

Calls
2 calls:
Slowest
252.0ms
(log (/ (+ 1 (sqrt (- 1 (* x x)))) x))
42.0ms
(+ 1 (sqrt (- 1 (* x x))))

simplify3.6s

Calls
61 calls:
Slowest
417.0ms
(+ (* 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))))))
279.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
275.0ms
(log (+ (pow 1 3) (pow (sqrt (- 1 (* x x))) 3)))
256.0ms
(- 1 (+ (* x (sqrt -1)) (* 1/2 (/ 1 (* x (sqrt -1))))))
186.0ms
(log (/ (* (cbrt (+ 1 (sqrt (- 1 (* x x))))) (cbrt (+ 1 (sqrt (- 1 (* x x)))))) (* (cbrt x) (cbrt x))))

prune789.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
3.2s24255×body80nan
1.1s8000×body80valid