Details

Time bar (total: 13.1s)

sample39.0ms

Algorithm
intervals
Results
8.0ms334×body80nan
7.0ms63×body1280valid
3.0ms32×body640valid
3.0ms130×body80valid
1.0ms17×body320valid
1.0ms14×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt 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×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
15.0ms
(sqrt (+ x 1.0))
107.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series151.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(sqrt (+ x 1.0))
109.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.4s

Counts
95 → 95
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01371993
13011432
26771124
31959950
done5000846

prune147.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt x) (sqrt (+ x 1.0)))
0.1b
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
27×sqrt-prod
21×distribute-lft-out
20×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
6×fma-def associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 84
Calls
3 calls:
7.0ms
(sqrt (+ x 1.0))
20.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
51.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series297.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(sqrt (+ x 1.0))
79.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
186.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.9s

Counts
93 → 93
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01581171
13641060
2967972
32933955
done5000954

prune263.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
0.1b
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
0.1b
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

rewrite350.0ms

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*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 461
Calls
4 calls:
43.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
55.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
127.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

series947.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
196.0ms
(sqrt (+ (sqrt x) (sqrt (+ x 1.0))))
386.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
183.0ms
(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))

simplify1.4s

Counts
473 → 473
Iterations

Useful iterations: done (1.3s)

IterNodesCost
044615335
1106012320
2232911633
done500011008

prune900.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.4b
(pow (sqrt x) 3/2)
0.5b
(* (sqrt x) (sqrt x))
3.1b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-div
47×add-sqr-sqrt sqrt-prod
37×*-un-lft-identity
36×pow1
30×flip3-+ flip-+
28×associate-*r/
23×add-cube-cbrt
19×swap-sqr
17×sqrt-pow1 pow1/2
16×frac-sub
13×associate-*r* associate-*l*
12×frac-times
10×pow-prod-up
9×add-exp-log
8×associate-*l/ add-cbrt-cube unswap-sqr
6×unpow-prod-down pow-prod-down pow-sqr distribute-lft-out add-log-exp
4×expm1-log1p-u log1p-expm1-u sub-div
3×pow-unpow pow-pow
2×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- fma-neg diff-log prod-diff pow-exp sqrt-pow2 flip-- sqr-pow
Counts
4 → 177
Calls
4 calls:
43.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms
(pow (sqrt x) 3/2)
21.0ms
(* (sqrt x) (sqrt x))
37.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
170.0ms
(pow (sqrt x) 3/2)
27.0ms
(* (sqrt x) (sqrt x))
76.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify1.6s

Counts
189 → 189
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02793250
16882107
220771869
done50011857

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes52.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.1s

Algorithm
intervals
Results
209.0ms8104×body80nan
205.0ms1713×body1280valid
128.0ms1318×body640valid
106.0ms4060×body80valid
43.0ms605×body320valid
15.0ms304×body160valid