Details

Time bar (total: 48.0s)

sample50.0ms

Algorithm
intervals
Results
12.0ms274×body80nan
10.0ms47×body1280valid
9.0ms51×body640valid
6.0ms128×body80valid
3.0ms21×body320valid
1.0ms9×body160valid

simplify11.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
50×*-un-lft-identity
42×prod-diff
37×add-sqr-sqrt
29×add-cube-cbrt
8×distribute-lft-out
7×fma-neg
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip--
Counts
1 → 71
Calls
1 calls:
Slowest
60.0ms
(- (sqrt (+ x 1)) (sqrt x))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
70.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify6.7s

Counts
122 → 74
Calls
122 calls:
Slowest
408.0ms
(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))
374.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
273.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
229.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
194.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune586.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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×expm1-log1p-u cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp flip-+ insert-posit16 log1p-expm1-u div-inv pow-flip inv-pow add-log-exp
Counts
1 → 48
Calls
1 calls:
Slowest
46.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series76.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
76.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.0s

Counts
69 → 51
Calls
69 calls:
Slowest
420.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
259.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
168.0ms
(* (* (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
83.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
49.0ms
(log (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

prune417.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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))))

rewrite262.0ms

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×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u 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 → 290
Calls
4 calls:
Slowest
133.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
51.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
36.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
121.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
87.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
84.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify13.4s

Counts
416 → 302
Calls
416 calls:
Slowest
548.0ms
(* (* (* (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))))))
497.0ms
(* (* (* (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))))))
489.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
483.0ms
(* (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))))
436.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

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))

rewrite208.0ms

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 expm1-log1p-u pow-plus pow-prod-down associate-*l/ pow-exp prod-exp associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u 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 → 85
Calls
2 calls:
Slowest
155.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
51.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))

series364.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
267.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))
97.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))

simplify17.8s

Counts
108 → 91
Calls
108 calls:
Slowest
733.0ms
(* (+ (* (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)))))
597.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (sqrt -1) (sqrt 2)))
552.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (sqrt -1) (* (cbrt 2) (cbrt 2))))
546.0ms
(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ (* (cbrt -1) (cbrt -1)) (* (cbrt 2) (cbrt 2))))
529.0ms
(* (- (sqrt (+ x 1)) (sqrt x)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune742.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
481.0ms8167×body80nan
410.0ms1668×body1280valid
339.0ms1217×body640valid
231.0ms4186×body80valid
123.0ms638×body320valid
26.0ms291×body160valid