Details

Time bar (total: 46.4s)

sample93.0ms

Algorithm
intervals
Results
29.0ms273×body80nan
22.0ms67×body640valid
14.0ms33×body1280valid
11.0ms130×body80valid
4.0ms16×body320valid
1.0ms10×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize20.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×prod-diff
23×*-un-lft-identity
22×add-sqr-sqrt
19×add-cube-cbrt
17×div-inv
12×sqrt-div
10×associate-/r/
9×associate-/r*
6×pow1 flip3-+ add-exp-log sqrt-prod flip-+ add-log-exp
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u pow-flip distribute-lft-out--
3×pow1/2
2×rec-exp clear-num frac-2neg inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
4 calls:
Slowest
8.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms
(/ 1 (sqrt (+ x 1)))
1.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series196.0ms

Calls
4 calls:
Slowest
95.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
37.0ms
(/ 1 (sqrt x))
35.0ms
(sqrt (+ x 1))
29.0ms
(/ 1 (sqrt (+ x 1)))

simplify4.9s

Calls
92 calls:
Slowest
203.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
199.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
189.0ms
(fma (sqrt (/ 1 (sqrt x))) (sqrt (/ 1 (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
184.0ms
(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))
176.0ms
(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.4b

localize14.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
32×frac-sub
28×times-frac
24×div-inv
20×add-sqr-sqrt add-cube-cbrt distribute-lft-out
18×associate-/l/
17×frac-times associate-*l/ associate-*r/ un-div-inv
16×pow1
15×add-exp-log
12×pow-flip
10×associate-/r*
9×difference-of-squares
8×add-cbrt-cube
7×inv-pow
6×pow-prod-up add-log-exp
5×rec-exp pow1/2
4×expm1-log1p-u associate-*r* associate-*l* pow-prod-down prod-exp insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 cbrt-undiv sub-neg flip3-+ pow-plus fma-neg diff-log div-sub div-exp prod-diff frac-add *-commutative cbrt-unprod flip-+
Calls
4 calls:
Slowest
58.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
11.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
9.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
2.0ms
(/ 1 (sqrt x))

series271.0ms

Calls
4 calls:
Slowest
149.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
47.0ms
(/ 1 (sqrt x))
42.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
33.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify23.7s

Calls
179 calls:
Slowest
777.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
565.0ms
(/ (* (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))))) (* (cbrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (cbrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))
525.0ms
(/ (* (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))))) (sqrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
510.0ms
(/ (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (cbrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
501.0ms
(- (log (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (log (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.2b

localize9.0ms

Local error

Found 4 expressions with local error:

6.5b
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (fma x x x))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
32×div-inv
28×times-frac
21×add-sqr-sqrt add-cube-cbrt
20×distribute-lft-out
19×associate-/r*
11×add-exp-log
7×pow1
6×add-cbrt-cube
5×associate-/r/ pow-flip
4×expm1-log1p-u rec-exp clear-num frac-2neg insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×sqrt-prod inv-pow
2×flip3-+ pow1/2 sqrt-div div-exp flip-+
1×cbrt-undiv frac-add associate-/l/
Calls
4 calls:
Slowest
15.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.0ms
(/ 1 (sqrt (+ x 1)))
1.0ms
(/ 1 (sqrt x))
1.0ms
(/ 1 (fma x x x))

series215.0ms

Calls
4 calls:
Slowest
134.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
31.0ms
(/ 1 (sqrt x))
27.0ms
(/ 1 (sqrt (+ x 1)))
23.0ms
(/ 1 (fma x x x))

simplify5.4s

Calls
102 calls:
Slowest
287.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
284.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
282.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
282.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
281.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

prune881.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
0.5b
(/ x (sqrt x))
0.2b
(/ x (sqrt (+ x 1)))
0.1b
(* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
15×flip3-+ flip-+
13×associate-/r/
12×frac-times
11×*-un-lft-identity
10×associate-/r*
9×add-sqr-sqrt pow1 add-exp-log add-cube-cbrt
6×add-cbrt-cube frac-add associate-*r/
5×associate-*r* div-inv
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* sqrt-prod
2×rec-exp sqrt-div pow-prod-down prod-exp pow-flip distribute-lft-out
1×distribute-rgt-in distribute-lft-in *-commutative cbrt-unprod inv-pow
Calls
4 calls:
Slowest
11.0ms
(* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
8.0ms
(/ 1 (* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
1.0ms
(/ x (sqrt (+ x 1)))
0.0ms
(/ x (sqrt x))

series365.0ms

Calls
4 calls:
Slowest
147.0ms
(/ 1 (* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))
122.0ms
(* (+ x 1) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
50.0ms
(/ x (sqrt (+ x 1)))
47.0ms
(/ x (sqrt x))

simplify5.0s

Calls
66 calls:
Slowest
541.0ms
(* (- (* x x) (* 1 1)) (+ (pow (/ x (sqrt x)) 3) (pow (/ x (sqrt (+ x 1))) 3)))
317.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (* (sqrt x) (sqrt (+ x 1))))
307.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (* (sqrt x) (sqrt (+ x 1))))
301.0ms
(* (+ (pow x 3) (pow 1 3)) (+ (/ x (sqrt x)) (/ x (sqrt (+ x 1)))))
277.0ms
(+ (* (/ x (sqrt x)) (/ x (sqrt x))) (- (* (/ x (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (* (/ x (sqrt x)) (/ x (sqrt (+ x 1))))))

prune683.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
770.0ms1879×body640valid
516.0ms8046×body80nan
415.0ms1115×body1280valid
263.0ms4052×body80valid
107.0ms628×body320valid
58.0ms326×body160valid