Details

Time bar (total: 1.5m)

sample85.0ms

Algorithm
intervals
Results
22.0ms67×body640valid
18.0ms273×body80nan
14.0ms130×body80valid
13.0ms33×body1280valid
5.0ms16×body320valid
1.0ms10×body160valid

simplify18.0ms

Calls
1 calls:
Slowest
18.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize56.0ms

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))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
97×*-un-lft-identity times-frac
64×sqrt-prod
42×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l* add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Calls
4 calls:
Slowest
45.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
9.0ms
(sqrt (+ x 1))

series222.0ms

Calls
4 calls:
Slowest
109.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
47.0ms
(/ 1 (sqrt x))
41.0ms
(/ 1 (sqrt (+ x 1)))
25.0ms
(sqrt (+ x 1))

simplify4.1s

Calls
204 calls:
Slowest
193.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
148.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
119.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
70.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))
64.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.4b

localize42.0ms

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))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
274×*-un-lft-identity
209×add-sqr-sqrt
134×sqrt-prod
127×add-cube-cbrt
80×distribute-lft-out
50×add-exp-log
32×frac-sub
30×swap-sqr
29×pow1
28×div-inv
27×pow-flip
25×unswap-sqr
22×associate-/r* associate-*r* associate-*l*
20×add-cbrt-cube
19×div-exp
18×difference-of-squares associate-/l/
17×frac-times associate-*l/ associate-*r/ un-div-inv
16×prod-exp
9×rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-up inv-pow
7×associate-/l*
6×cbrt-undiv add-log-exp
5×pow-prod-down pow-sqr
4×cbrt-unprod insert-posit16
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg flip3-+ pow-plus diff-log div-sub frac-add *-commutative flip-+
Calls
4 calls:
Slowest
105.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
19.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
15.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
5.0ms
(/ 1 (sqrt x))

series287.0ms

Calls
4 calls:
Slowest
156.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
51.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
46.0ms
(/ 1 (sqrt x))
35.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify36.6s

Calls
476 calls:
Slowest
880.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))))
581.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
526.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
424.0ms
(/ (* (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) 1))
383.0ms
(- (log (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (log (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.2b

localize28.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
0.5b
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))

rewrite548.0ms

Algorithm
rewrite-expression-head
Rules
108×sqrt-div
98×associate-*r/
89×add-exp-log
84×frac-times
72×flip3-+ flip-+
71×pow1
68×*-un-lft-identity
56×sqrt-prod
54×prod-exp
53×add-sqr-sqrt
51×add-cbrt-cube
35×associate-/r/
32×pow-prod-down
29×associate-*l* add-cube-cbrt
28×cbrt-unprod
24×associate-*l/
22×distribute-lft-out
21×times-frac
19×swap-sqr
18×frac-add
16×sqrt-pow1 pow1/2
14×associate-*r*
12×div-exp
10×pow-prod-up
8×unswap-sqr
6×cbrt-undiv rec-exp 1-exp pow-sqr pow-flip
5×div-inv
4×insert-posit16 add-log-exp
3×*-commutative associate-/l*
2×pow2 rem-square-sqrt pow-plus sqrt-unprod
1×clear-num associate-/r* frac-2neg inv-pow
Calls
4 calls:
Slowest
293.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
217.0ms
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
23.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
8.0ms
(* (sqrt x) (sqrt x))

series297.0ms

Calls
4 calls:
Slowest
146.0ms
(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
119.0ms
(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
17.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
15.0ms
(* (sqrt x) (sqrt x))

simplify25.7s

Calls
298 calls:
Slowest
637.0ms
(* (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ (pow x 3) (pow 1 3))))))
511.0ms
(/ (* (* 1 1) 1) (* (* (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))))
471.0ms
(/ (* (* 1 1) 1) (* (* (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (* (* (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))))
418.0ms
(/ (* (* 1 1) 1) (* (* (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))))
410.0ms
(* (* (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))
0.4b
(/ (+ x 1) (sqrt x))
0.3b
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
0.0b
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
39×times-frac
35×add-sqr-sqrt
33×add-cube-cbrt
24×add-exp-log
15×sqrt-prod
11×associate-/r*
10×add-cbrt-cube
9×div-exp distribute-lft-out
7×associate-/l*
6×pow1 pow-exp add-log-exp
5×flip3-+ flip-+
4×rec-exp unpow-prod-down sqrt-div 1-exp associate-*r* frac-add prod-exp associate-*r/ insert-posit16 sqr-pow
3×pow-to-exp associate-*l*
2×cbrt-undiv clear-num frac-2neg div-inv associate-/l/
1×distribute-rgt-in +-commutative sum-log distribute-lft-in pow-prod-down *-commutative cbrt-unprod pow-flip inv-pow unswap-sqr
Calls
4 calls:
Slowest
80.0ms
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
27.0ms
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))
14.0ms
(/ (+ x 1) (sqrt x))
10.0ms
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))

series387.0ms

Calls
4 calls:
Slowest
138.0ms
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))
116.0ms
(* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x))))
88.0ms
(+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))
45.0ms
(/ (+ x 1) (sqrt x))

simplify9.2s

Calls
142 calls:
Slowest
413.0ms
(/ 1 (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) (/ 1 2)))
349.0ms
(/ (cbrt 1) (sqrt (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1)))
251.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1)) (cbrt (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))))
248.0ms
(/ (sqrt 1) (* (cbrt (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1)) (cbrt (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))))
243.0ms
(/ (cbrt 1) (pow (* x (+ (sqrt (+ x 1)) (/ (+ x 1) (sqrt x)))) 1))

prune892.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
606.0ms1115×body1280valid
502.0ms8046×body80nan
488.0ms1879×body640valid
247.0ms4052×body80valid
121.0ms628×body320valid
35.0ms326×body160valid