Details

Time bar (total: 26.8s)

sample130.0ms

Algorithm
intervals
Results
85.0ms750×body80nan
27.0ms256×body80valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

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)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
59×times-frac
50×add-sqr-sqrt
38×add-cube-cbrt
31×sqrt-prod
16×distribute-lft-out
15×log-prod
14×div-inv
13×fma-def
10×difference-of-squares
8×associate-/l*
7×add-exp-log
6×pow1 distribute-rgt-out add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
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 → 142
Calls
4 calls:
Slowest
25.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
23.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
9.0ms
(/ (sqrt (- 1 (* x x))) x)
5.0ms
(sqrt (- 1 (* x x)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
124.0ms
(/ (sqrt (- 1 (* x x))) x)
99.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
59.0ms
(sqrt (- 1 (* x x)))

simplify7.9s

Counts
136 → 154
Calls
136 calls:
Slowest
468.0ms
(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
452.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
423.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
419.0ms
(+ (* 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))))))
395.0ms
(+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (+ (sqrt -1) (* 1/8 (/ 1 (* (pow x 4) (sqrt -1))))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize51.0ms

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)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
136×times-frac
132×*-un-lft-identity
120×sqrt-prod
112×add-sqr-sqrt
89×add-cube-cbrt
48×log-prod
26×associate-+r+
22×associate-+l+ distribute-lft-out
18×associate-/r*
15×pow1
14×add-exp-log associate-/l* difference-of-squares
11×div-inv
10×add-cbrt-cube
9×log-pow pow-flip
8×fma-def
5×div-exp
4×expm1-log1p-u log-div distribute-rgt-out insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv clear-num associate-+r- frac-2neg sqrt-pow1 pow1/2 inv-pow
2×rec-exp flip3-+ sqrt-div 1-exp flip-+ associate-/l/
1×+-commutative sqrt-undiv sum-log flip3-- frac-add distribute-rgt1-in associate-+l- flip--
Counts
4 → 254
Calls
4 calls:
Slowest
48.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
10.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
5.0ms
(/ 1 (sqrt x))
5.0ms
(/ 1 (sqrt x))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
421.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x)))))
96.0ms
(/ (sqrt (- 1 (* x x))) (sqrt x))
40.0ms
(/ 1 (sqrt x))
32.0ms
(/ 1 (sqrt x))

simplify7.6s

Counts
288 → 266
Calls
288 calls:
Slowest
564.0ms
(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))))))
356.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
190.0ms
(/ (* (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (sqrt (- 1 (* x x)))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
170.0ms
(* (/ 1 (sqrt x)) (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))
116.0ms
(sqrt (- (* 1 1) (* (* x x) (* x x))))

prune3.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.8s24245×body80nan
984.0ms8000×body80valid