Details

Time bar (total: 33.3s)

sample66.0ms

Algorithm
intervals
Results
20.0ms298×body80nan
13.0ms46×body1280valid
10.0ms46×body640valid
8.0ms136×body80valid
3.0ms16×body320valid
1.0ms12×body160valid

simplify10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize18.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))

rewrite73.0ms

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
71.0ms
(- (sqrt (+ x 1)) (sqrt x))

series91.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
91.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify5.3s

Counts
107 → 74
Calls
107 calls:
Slowest
248.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
195.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
183.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
183.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
173.0ms
(fma (- (cbrt (sqrt x))) (* (cbrt (sqrt x)) (cbrt (sqrt x))) (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))))

prune659.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.5b

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.2b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
64×sqrt-prod
56×add-sqr-sqrt
34×pow1
32×add-cube-cbrt
26×distribute-lft-out
24×times-frac
19×swap-sqr
16×sqrt-pow1 pow1/2
13×associate-*r* associate-*l*
12×sqrt-div
10×add-cbrt-cube add-exp-log pow-prod-up
8×difference-of-squares unswap-sqr
7×flip3-+ flip-+
6×associate-/r* pow-prod-down pow-sqr add-log-exp
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u associate-/l*
2×pow2 rem-square-sqrt pow-plus flip3-- sqrt-unprod associate-*l/ prod-exp associate-*r/ associate-/r/ *-commutative cbrt-unprod flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 189
Calls
4 calls:
Slowest
71.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
52.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
39.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt x))

series194.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(* (sqrt x) (sqrt x))
27.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
23.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.3s

Counts
214 → 201
Calls
214 calls:
Slowest
708.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
430.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
314.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
231.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))
231.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
15×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×associate-/r* add-exp-log
4×add-cbrt-cube add-log-exp
3×pow1 associate-/l*
2×expm1-log1p-u flip3-+ div-exp associate-/r/ flip-+ insert-posit16 log1p-expm1-u
1×cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
2 → 72
Calls
2 calls:
Slowest
25.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series183.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
85.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify1.3s

Counts
68 → 78
Calls
68 calls:
Slowest
259.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
189.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
68.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
29.0ms
(/ (sqrt 1) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
28.0ms
(/ 1 (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune608.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

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))))

rewrite235.0ms

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
125.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
44.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
26.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
106.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
104.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
80.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify9.1s

Counts
359 → 302
Calls
359 calls:
Slowest
433.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
387.0ms
(* (* (* (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))))))
351.0ms
(* (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))))
335.0ms
(sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))
249.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
513.0ms8141×body80nan
499.0ms1722×body1280valid
336.0ms4102×body80valid
318.0ms1216×body640valid
140.0ms647×body320valid
32.0ms313×body160valid