Details

Time bar (total: 39.3s)

sample51.0ms

Algorithm
intervals
Results
11.0ms274×body80nan
9.0ms47×body1280valid
8.0ms51×body640valid
6.0ms128×body80valid
2.0ms21×body320valid
1.0ms9×body160valid

simplify33.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize15.0ms

Local error

Found 1 expressions with local error:

2.4b
(- (sqrt (+ x 1)) (sqrt x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out
Counts
1 → 20
Calls
1 calls:
Slowest
26.0ms
(- (sqrt (+ x 1)) (sqrt x))

series95.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
95.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts
29 → 23
Calls
29 calls:
Slowest
348.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
218.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
69.0ms
(exp (- (sqrt (+ x 1)) (sqrt x)))
46.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
38.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

prune140.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
18×times-frac
16×sqrt-prod distribute-lft-out
12×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
5×add-exp-log
3×add-cbrt-cube associate-/l*
2×pow1 div-exp associate-/r/
1×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp flip-+ insert-posit16 div-inv pow-flip inv-pow add-log-exp
Counts
1 → 46
Calls
1 calls:
Slowest
46.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.7s

Counts
67 → 49
Calls
67 calls:
Slowest
371.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
197.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
142.0ms
(* (* (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
60.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
49.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune348.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
308×*-un-lft-identity
290×sqrt-prod
168×times-frac
136×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
43×swap-sqr
31×pow1
27×sqrt-pow1 associate-*r* associate-*l*
16×unswap-sqr
14×add-exp-log associate-/r/
12×associate-/r*
11×pow-flip inv-pow
10×add-cbrt-cube
9×pow1/2 pow-prod-up div-inv
7×flip3-+ flip-+
6×associate-/l*
5×sqrt-div pow-prod-down pow-sqr
4×div-exp insert-posit16 add-log-exp
3×rem-sqrt-square
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp
1×pow2 frac-times rem-square-sqrt pow-plus sqrt-unprod associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 282
Calls
4 calls:
Slowest
149.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
37.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
30.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
85.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
82.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
80.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify12.4s

Counts
408 → 294
Calls
408 calls:
Slowest
451.0ms
(* (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))) (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
446.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))))
422.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
407.0ms
(* (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
382.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
24×sqrt-prod distribute-lft-out
17×pow1
15×add-sqr-sqrt
13×pow-unpow add-cube-cbrt
10×swap-sqr
9×times-frac
7×add-exp-log
6×pow-pow flip3-+ associate-*r* associate-*l* flip-+
4×frac-times add-cbrt-cube
2×pow2 pow-plus pow-prod-down associate-*l/ pow-exp prod-exp associate-*r/ pow-sqr pow-prod-up insert-posit16 add-log-exp
1×distribute-rgt-in pow-to-exp unpow-prod-down distribute-lft-in *-commutative cbrt-unprod div-inv unswap-sqr sqr-pow
Counts
2 → 81
Calls
2 calls:
Slowest
157.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
68.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))

series287.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
211.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))
75.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))

simplify16.2s

Counts
104 → 87
Calls
104 calls:
Slowest
688.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (sqrt -1) 1))
646.0ms
(* (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
599.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (* (cbrt -1) (cbrt -1)) (* (cbrt 2) (cbrt 2))))
564.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (sqrt -1) (sqrt 2)))
496.0ms
(* (* (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2)) (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))) (pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2)))

prune827.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
515.0ms1668×body1280valid
451.0ms8167×body80nan
289.0ms1217×body640valid
272.0ms4186×body80valid
93.0ms638×body320valid
30.0ms291×body160valid