Details

Time bar (total: 26.8s)

sample65.0ms

Algorithm
intervals
Results
15.0ms131×body80valid
12.0ms52×body1280valid
12.0ms261×body80nan
8.0ms43×body640valid
2.0ms18×body320valid
1.0ms12×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (sqrt (+ x 1)) (sqrt x))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.3b
(- (sqrt (+ x 1)) (sqrt x))
0.0b
(sqrt (+ x 1))

rewrite56.0ms

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
44.0ms
(- (sqrt (+ x 1)) (sqrt x))
10.0ms
(sqrt (+ x 1))

series113.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
75.0ms
(- (sqrt (+ x 1)) (sqrt x))
37.0ms
(sqrt (+ x 1))

simplify6.0s

Counts
120 → 98
Calls
120 calls:
Slowest
230.0ms
(fma (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
206.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
192.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
181.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
174.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune779.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* (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)))

rewrite193.0ms

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
103.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
19.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))
17.0ms
(* (sqrt x) (sqrt x))

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms
(* (sqrt x) (sqrt x))
24.0ms
(* (sqrt (+ x 1)) (sqrt (+ x 1)))
20.0ms
(- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))

simplify7.7s

Counts
214 → 201
Calls
214 calls:
Slowest
746.0ms
(- (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x))))
523.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
338.0ms
(- (pow (* (sqrt (+ x 1)) (sqrt (+ x 1))) 3) (pow (* (sqrt x) (sqrt x)) 3))
251.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (+ (pow x 3) (pow 1 3))))
228.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (+ (pow x 3) (pow 1 3))))

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

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
39.0ms
(+ (sqrt (+ x 1)) (sqrt x))
28.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
5.0ms
(sqrt (+ x 1))

series207.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
108.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms
(+ (sqrt (+ x 1)) (sqrt x))
33.0ms
(sqrt (+ x 1))

simplify1.7s

Counts
81 → 102
Calls
81 calls:
Slowest
267.0ms
(/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
186.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))
158.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
65.0ms
(sqrt (+ (pow x 3) (pow 1 3)))
51.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune888.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
20×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
9×pow1 times-frac
8×sqrt-pow1 sqrt-div add-exp-log
6×add-cbrt-cube
4×expm1-log1p-u rem-sqrt-square pow1/2 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×flip3-+ div-exp flip-+ distribute-lft-out
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp fma-udef div-inv pow-flip inv-pow
Counts
4 → 95
Calls
4 calls:
Slowest
9.0ms
(sqrt (sqrt (+ x 1)))
8.0ms
(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
5.0ms
(sqrt (sqrt (+ x 1)))
0.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
150.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))
53.0ms
(sqrt (sqrt (+ x 1)))
37.0ms
(sqrt (sqrt (+ x 1)))

simplify2.8s

Counts
67 → 107
Calls
67 calls:
Slowest
377.0ms
(/ (* (* 1 1) 1) (* (* (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)) (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))) (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))))
266.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
242.0ms
(- (+ (pow (/ 1 x) -1/4) (* 1/4 (pow (/ 1 (pow x 3)) 1/4))) (* 3/32 (pow (/ 1 (pow x 7)) 1/4)))
228.0ms
(- (+ (* 1/4 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) x)) (exp (* 1/4 (- (log -1) (log (/ -1 x)))))) (* 3/32 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) (pow x 2))))
206.0ms
(- (+ (* 1/4 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) x)) (exp (* 1/4 (- (log -1) (log (/ -1 x)))))) (* 3/32 (/ (exp (* 1/4 (- (log -1) (log (/ -1 x))))) (pow x 2))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
532.0ms1686×body1280valid
523.0ms8167×body80nan
327.0ms1272×body640valid
299.0ms4082×body80valid
166.0ms653×body320valid
31.0ms307×body160valid