Details

Time bar (total: 24.1s)

sample121.0ms

Algorithm
intervals
Results
78.0ms750×body80nan
27.0ms256×body80valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
50×times-frac
43×add-sqr-sqrt
31×add-cube-cbrt sqrt-prod
16×distribute-lft-out
15×log-prod
13×div-inv
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×sqrt-div insert-posit16
3×log-div associate-/r*
2×flip3-+ flip3-- frac-add distribute-rgt1-in flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp log-pow
Counts
4 → 121
Calls
4 calls:
Slowest
30.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
23.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
18.0ms
(/ (sqrt (- 1 (* x x))) x)
8.0ms
(sqrt (- 1 (* x x)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
226.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
176.0ms
(/ (sqrt (- 1 (* x x))) x)
83.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
80.0ms
(sqrt (- 1 (* x x)))

simplify7.0s

Counts
125 → 133
Calls
125 calls:
Slowest
418.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
376.0ms
(+ (* 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))))))
356.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
342.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
341.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* (/ (sqrt (- 1 (* x x))) x) (/ (sqrt (- 1 (* x x))) x))))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize49.0ms

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)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
136×times-frac
131×*-un-lft-identity
120×sqrt-prod
111×add-sqr-sqrt
88×add-cube-cbrt
48×log-prod
26×associate-+r+
22×associate-+l+ distribute-lft-out
18×associate-/r*
14×add-exp-log associate-/l* difference-of-squares
12×pow1
11×div-inv
10×add-cbrt-cube
6×pow-flip
5×div-exp
4×log-div distribute-rgt-out log-pow insert-posit16 add-log-exp
3×cbrt-undiv clear-num associate-+r- frac-2neg
2×rec-exp sqrt-pow1 flip3-+ pow1/2 sqrt-div 1-exp flip-+ inv-pow associate-/l/
1×+-commutative sqrt-undiv sum-log flip3-- frac-add distribute-rgt1-in associate-+l- flip--
Counts
4 → 238
Calls
4 calls:
Slowest
48.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
17.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
8.0ms
(/ 1 (sqrt x))
8.0ms
(/ 1 (sqrt x))

series566.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
416.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
87.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
33.0ms
(/ 1 (sqrt x))
30.0ms
(/ 1 (sqrt x))

simplify6.8s

Counts
283 → 250
Calls
283 calls:
Slowest
333.0ms
(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))))))
269.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
171.0ms
(/ (* (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (sqrt (- 1 (* x x)))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
155.0ms
(* (/ 1 (sqrt x)) (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))
116.0ms
(log (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))

prune2.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.9s24245×body80nan
1.4s8000×body80valid