Details

Time bar (total: 22.9s)

sample83.0ms

Algorithm
intervals
Results
21.0ms62×body1280valid
16.0ms243×body80nan
15.0ms123×body80valid
12.0ms42×body640valid
4.0ms19×body320valid
1.0ms10×body160valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1))
2.4b
(- (sqrt (+ x 1)) (sqrt x))

rewrite59.0ms

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:
9.0ms
(sqrt (+ x 1))
47.0ms
(- (sqrt (+ x 1)) (sqrt x))

series120.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(sqrt (+ x 1))
74.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify3.6s

Counts
98 → 98
Iterations
IterNodes
43956
31441
2597
1283
0134

prune794.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite80.0ms

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:
5.0ms
(sqrt (+ x 1))
26.0ms
(+ (sqrt (+ x 1)) (sqrt x))
47.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series182.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(sqrt (+ x 1))
75.0ms
(+ (sqrt (+ x 1)) (sqrt x))
81.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.3s

Counts
102 → 102
Iterations
IterNodes
42673
31160
2569
1256
0126

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite277.0ms

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:
26.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
33.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
156.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series559.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
127.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
121.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
126.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.2s

Counts
302 → 302
Iterations
IterNodes
32173
2917
1455
0235

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
706×sqrt-prod
655×*-un-lft-identity
461×times-frac
264×distribute-lft-out
205×add-sqr-sqrt
192×add-cube-cbrt
30×associate-/l*
26×associate-/r/
15×associate-/r*
14×flip3-+ flip-+
13×div-inv
12×pow1
10×sqrt-pow1 add-exp-log
8×add-cbrt-cube
6×sqrt-div
4×expm1-log1p-u rem-sqrt-square pow1/2 hypot-def insert-posit16 log1p-expm1-u pow-flip inv-pow add-log-exp pow-div
3×div-exp
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sqrt-undiv 1-exp associate-/l/
Counts
4 → 417
Calls
4 calls:
54.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
51.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
56.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms
(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series569.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
196.0ms
(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
114.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
127.0ms
(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.9s

Counts
429 → 429
Iterations
IterNodes
32603
21065
1585
0360

prune5.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
214
114
012

end0.0ms

sample2.0s

Algorithm
intervals
Results
575.0ms7976×body80nan
492.0ms1749×body1280valid
297.0ms4070×body80valid
288.0ms1292×body640valid
92.0ms588×body320valid
63.0ms301×body160valid