Details

Time bar (total: 11.1s)

sample30.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms72×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ 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 div-inv
Counts
3 → 61
Calls
3 calls:
7.0ms
(sqrt (+ x 1.0))
29.0ms
(+ 1.0 (sqrt (+ x 1.0)))
51.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series254.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(sqrt (+ x 1.0))
49.0ms
(+ 1.0 (sqrt (+ x 1.0)))
171.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify865.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
0140917
1326848
21523785
done5000785

prune303.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
30×associate-*r*
28×times-frac
24×sqrt-prod
21×add-cube-cbrt
8×add-exp-log add-cbrt-cube distribute-lft-out
6×pow1 associate-*l* unswap-sqr
5×add-log-exp
3×flip3-+ flip-+
2×sqrt-div prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp pow-prod-down sum-log *-commutative div-inv
Counts
3 → 84
Calls
3 calls:
12.0ms
(sqrt (+ x 1.0))
30.0ms
(+ 1.0 (sqrt (+ x 1.0)))
155.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series290.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ x 1.0))
72.0ms
(+ 1.0 (sqrt (+ x 1.0)))
186.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify3.0s

Counts
93 → 93
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01731372
14601249
232901050
done50021026

prune346.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))
0.0b
(+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
0.2b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
9.0b
(+ (+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ x (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
121×add-exp-log
67×prod-exp
42×div-exp
35×pow-to-exp pow-exp
27×frac-add
22×associate-*r/
20×times-frac
18×add-cbrt-cube add-log-exp
16×associate-*r*
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×unpow-prod-down
8×associate-/l*
7×sum-log
6×pow1
5×flip3-- flip3-+ frac-sub flip-- cbrt-unprod flip-+
4×cbrt-undiv frac-times associate-*l/
3×cube-prod associate-*l* sqr-pow
2×+-commutative associate-+r+ diff-log div-inv unpow2
1×cube-mult associate-+r- sub-neg associate-+l+ frac-2neg unpow3 pow-prod-down clear-num associate-/r* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 153
Calls
4 calls:
96.0ms
(* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))
33.0ms
(+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
27.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
522.0ms
(+ (+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ x (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))

series2.2s

Counts
4 → 12
Calls
4 calls:
347.0ms
(* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))
828.0ms
(+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
248.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
755.0ms
(+ (+ (* (/ 1/4 (pow (+ (sqrt 1.0) 1.0) 3)) (/ (pow x 3) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (/ x (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))

simplify669.0ms

Counts
165 → 165
Iterations

Useful iterations: done (645.0ms)

IterNodesCost
03417718
111117064
done50006590

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample780.0ms

Algorithm
intervals
Results
397.0ms7998×body80valid
81.0ms2672×body80nan
0.0ms2×body1280valid