Details

Time bar (total: 31.7s)

sample159.0ms

Algorithm
intervals
Results
97.0ms732×body80nan
36.0ms256×body80valid

simplify45.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
45.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
26×times-frac
21×add-sqr-sqrt
16×distribute-lft-out
15×log-prod
13×add-cube-cbrt
12×div-inv
11×sqrt-prod
6×distribute-rgt-out
5×pow1 add-log-exp
4×add-exp-log
3×log-div add-cbrt-cube insert-posit16
2×flip3-+ sqrt-div frac-add distribute-rgt1-in flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 rem-log-exp log-pow flip--
Counts
3 → 71
Calls
3 calls:
Slowest
30.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
25.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
8.0ms
(sqrt (- 1 (* x x)))

series398.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
232.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
107.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
58.0ms
(sqrt (- 1 (* x x)))

simplify4.6s

Counts
61 → 80
Calls
61 calls:
Slowest
442.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* (/ (sqrt (- 1 (* x x))) x) (/ (sqrt (- 1 (* x x))) x))))
385.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
382.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
382.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
372.0ms
(+ (* 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))))))

prune746.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(sqrt (sqrt (- 1 (* x x))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
61×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
27×*-un-lft-identity
20×pow1/2 add-cube-cbrt
17×swap-sqr
14×difference-of-squares
11×associate-*r* associate-*l*
9×flip3-- pow-prod-up flip-- unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square insert-posit16 add-log-exp
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 150
Calls
4 calls:
Slowest
51.0ms
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))
9.0ms
(sqrt (sqrt (- 1 (* x x))))
8.0ms
(sqrt (- 1 (* x x)))
8.0ms
(sqrt (- 1 (* x x)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(sqrt (sqrt (- 1 (* x x))))
69.0ms
(sqrt (- 1 (* x x)))
68.0ms
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))
61.0ms
(sqrt (- 1 (* x x)))

simplify10.3s

Counts
171 → 162
Calls
171 calls:
Slowest
780.0ms
(* (sqrt (sqrt (- (* 1 1) (* (* x x) (* x x))))) (sqrt (sqrt (- (pow 1 3) (pow (* x x) 3)))))
368.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
354.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
332.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
332.0ms
(* (sqrt (sqrt (- (pow 1 3) (pow (* x x) 3)))) (sqrt (sqrt (- (pow 1 3) (pow (* x x) 3)))))

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
16×cbrt-prod
11×associate-*r* add-cube-cbrt
10×sqrt-prod
9×log-prod
7×pow1 add-exp-log
6×cbrt-div add-cbrt-cube div-inv difference-of-squares
4×insert-posit16 add-log-exp
3×log-div distribute-rgt-out flip3-- associate-*l* flip-- unswap-sqr
2×pow1/3 sqrt-div associate-*r/ distribute-lft-out
1×flip3-+ times-frac rem-log-exp pow-prod-down frac-add distribute-rgt1-in prod-exp log-pow *-commutative cbrt-unprod flip-+
Counts
4 → 85
Calls
4 calls:
Slowest
14.0ms
(* (fabs (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x)))))
14.0ms
(log (+ (/ 1 x) (/ (* (fabs (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x))))) x)))
3.0ms
(cbrt (- 1 (* x x)))
2.0ms
(cbrt (- 1 (* x x)))

series826.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
347.0ms
(log (+ (/ 1 x) (/ (* (fabs (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x))))) x)))
205.0ms
(* (fabs (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x)))))
148.0ms
(cbrt (- 1 (* x x)))
126.0ms
(cbrt (- 1 (* x x)))

simplify6.5s

Counts
63 → 97
Calls
63 calls:
Slowest
554.0ms
(log (+ (pow (/ 1 x) 3) (pow (/ (* (fabs (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x))))) x) 3)))
441.0ms
(* (* (* (fabs (cbrt (- 1 (* x x)))) (fabs (cbrt (- 1 (* x x))))) (fabs (cbrt (- 1 (* x x))))) (* (* (sqrt (cbrt (- 1 (* x x)))) (sqrt (cbrt (- 1 (* x x))))) (sqrt (cbrt (- 1 (* x x))))))
372.0ms
(- (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2)))))
370.0ms
(- (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 4))) (* 1/3 (/ (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 x)))))) (pow x 2)))))
340.0ms
(- (+ (log (/ 1 x)) (log (+ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) 1))) (+ (* 1/72 (/ (* (pow (fabs (pow (- 1 (pow x 2)) 1/3)) 2) (pow (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x)))))) 2)) (* (pow x 4) (pow (+ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) 1) 2)))) (+ (* 5/72 (/ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) (* (pow x 4) (+ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) 1)))) (* 1/6 (/ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) (* (pow x 2) (+ (* (fabs (pow (- 1 (pow x 2)) 1/3)) (exp (* 1/6 (- (log -1) (* 2 (log (/ 1 x))))))) 1)))))))

prune1.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
3.1s23745×body80nan
919.0ms8000×body80valid