Details

Time bar (total: 18.9s)

sample60.0ms

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

simplify8.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite89.0ms

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:
8.0ms
(sqrt (+ x 1.0))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series174.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(sqrt (+ x 1.0))
125.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.7s

Counts
95 → 95
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01371993
13011432
26771124
31959950
done5000846

prune157.0ms

Pruning

3 alts after pruning (3 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))))

rewrite93.0ms

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:
11.0ms
(sqrt (+ x 1.0))
19.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
57.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series355.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(sqrt (+ x 1.0))
120.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
193.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.1s

Counts
93 → 93
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01581171
13641060
2967972
32933955
done5000954

prune342.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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))))))

rewrite372.0ms

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:
39.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
38.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
49.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
226.0ms
(* (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:
439.0ms
(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
185.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
170.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
278.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.7s

Counts
270 → 270
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03176276
16744462
221054194
done50004091

prune926.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
884×sqrt-prod
683×*-un-lft-identity
517×times-frac
435×add-sqr-sqrt
244×distribute-lft-out
240×add-cube-cbrt
127×swap-sqr
87×associate-*r*
64×associate-*l*
31×unswap-sqr
22×add-exp-log sqrt-div add-cbrt-cube
18×pow1 associate-/r*
14×associate-/r/
12×associate-/l*
7×flip3-+ flip-+ div-inv
6×cbrt-undiv frac-times sqrt-undiv div-exp pow-prod-down associate-*l/
5×prod-exp cbrt-unprod
4×expm1-log1p-u sqrt-pow1 associate-*r/ log1p-expm1-u add-log-exp
2×frac-2neg pow1/2 sqrt-unprod clear-num *-commutative
1×pow2 pow-plus rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 533
Calls
4 calls:
82.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
74.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
396.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
478.0ms
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
560.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
499.0ms
(/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))
245.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
247.0ms
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify2.5s

Counts
545 → 545
Iterations

Useful iterations: done (2.5s)

IterNodesCost
042317531
1114714548
2340812088
done500111739

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes44.0ms

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

sample1.9s

Algorithm
intervals
Results
573.0ms1261×body640valid
366.0ms1686×body1280valid
342.0ms7865×body80nan
167.0ms4165×body80valid
53.0ms605×body320valid
16.0ms283×body160valid