Details

Time bar (total: 17.0s)

sample53.0ms

Algorithm
intervals
Results
13.0ms60×body1280valid
10.0ms243×body80nan
6.0ms132×body80valid
6.0ms33×body640valid
3.0ms23×body320valid
1.0ms8×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite123.0ms

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))
96.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series165.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(sqrt (+ x 1.0))
115.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.3s

Counts
95 → 95
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01371993
13011432
26771124
31959950
done5000846

prune213.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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))))

rewrite117.0ms

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:
16.0ms
(sqrt (+ x 1.0))
26.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
69.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series351.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(sqrt (+ x 1.0))
93.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
215.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.2s

Counts
93 → 93
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01581171
13641060
2967972
32933955
done5000954

prune294.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 258
Calls
4 calls:
55.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
48.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
46.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
279.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
472.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
221.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
223.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
208.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.5s

Counts
270 → 270
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03176276
16744462
221054194
done50004091

prune885.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
0.2b
(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))

rewrite812.0ms

Algorithm
rewrite-expression-head
Rules
210×*-un-lft-identity
192×sqrt-prod
150×times-frac
138×add-sqr-sqrt
84×add-cube-cbrt
68×distribute-lft-out
60×associate-*l*
37×associate-*r*
34×add-exp-log
22×add-cbrt-cube
18×sqrt-div associate-/r* unswap-sqr
15×pow1
11×div-exp
10×associate-/r/
9×prod-exp
6×cbrt-undiv frac-times associate-*r/ pow-prod-down associate-/l*
5×sqrt-pow1 flip3-+ cbrt-unprod flip-+ div-inv
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×rec-exp pow-flip pow1/2 1-exp
2×frac-2neg clear-num *-commutative
1×sqrt-unprod swap-sqr inv-pow
Counts
4 → 282
Calls
4 calls:
51.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
84.0ms
(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
257.0ms
(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
382.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
772.0ms
(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
403.0ms
(/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
175.0ms
(* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
221.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (* (/ 1 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))

simplify2.3s

Counts
294 → 294
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04207641
110296693
230955076
done50014983

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

end0.0ms

sample1.3s

Algorithm
intervals
Results
332.0ms1686×body1280valid
265.0ms7865×body80nan
233.0ms4165×body80valid
197.0ms1261×body640valid
53.0ms605×body320valid
16.0ms283×body160valid