Details

Time bar (total: 1.0m)

sample71.0ms

Algorithm
intervals
Results
23.0ms56×body1280valid
14.0ms271×body80nan
10.0ms43×body640valid
8.0ms129×body80valid
3.0ms18×body320valid
1.0ms10×body160valid

simplify10.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize14.0ms

Local error

Found 2 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
55×*-un-lft-identity
43×add-sqr-sqrt
42×prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 92
Calls
2 calls:
Slowest
71.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

series111.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
78.0ms
(- (sqrt (+ x 1)) (sqrt x))
33.0ms
(sqrt (+ x 1))

simplify5.7s

Counts
120 → 98
Calls
120 calls:
Slowest
207.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
204.0ms
(fma (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (sqrt (cbrt (+ 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))))))
191.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
185.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune892.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 29.1b

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
0.5b
(* (sqrt x) (sqrt x))
0.3b
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.0b
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite156.0ms

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
82.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
20.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
10.0ms
(* (sqrt x) (sqrt x))

series165.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
17.0ms
(* (sqrt x) (sqrt x))
16.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.6s

Counts
214 → 201
Calls
214 calls:
Slowest
721.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
503.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
317.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
254.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
238.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×sqrt-div div-exp associate-/r/ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 93
Calls
3 calls:
Slowest
53.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
35.0ms
(+ (sqrt (+ x 1)) (sqrt x))
5.0ms
(sqrt (+ x 1))

series221.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
90.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
85.0ms
(+ (sqrt (+ x 1)) (sqrt x))
46.0ms
(sqrt (+ x 1))

simplify1.6s

Counts
81 → 102
Calls
81 calls:
Slowest
255.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
147.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
141.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
80.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
56.0ms
(sqrt (- (* x x) (* 1 1)))

prune891.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
708×sqrt-prod
594×times-frac
280×distribute-lft-out
270×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
17×add-exp-log
15×pow1
14×flip3-+ flip-+
12×div-inv
11×add-cbrt-cube
8×div-exp hypot-def pow-flip
7×sqrt-pow1 pow1/2
6×pow-div
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square rec-exp clear-num frac-2neg 1-exp inv-pow
1×associate-/l/
Counts
4 → 479
Calls
4 calls:
Slowest
90.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
48.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
35.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
154.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
140.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
110.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify33.3s

Counts
767 → 491
Calls
767 calls:
Slowest
670.0ms
(/ (* (* (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (* (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
455.0ms
(/ (/ 1 (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (* (cbrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (cbrt (sqrt (+ (sqrt (+ x 1)) (sqrt x))))))
428.0ms
(/ (/ 1 (sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))) (sqrt (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
411.0ms
(/ (/ 1 (sqrt (cbrt (+ (sqrt (+ x 1)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
395.0ms
(sqrt (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))

prune4.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
658.0ms4065×body80valid
556.0ms1739×body1280valid
512.0ms8063×body80nan
305.0ms1253×body640valid
167.0ms601×body320valid
67.0ms342×body160valid