Average Error: 0.1 → 0.1
Time: 16.8s
Precision: 64
\[x + \frac{x - y}{2}\]
↓
\[1.5 \cdot x - 0.5 \cdot y\]
x + \frac{x - y}{2}
↓
1.5 \cdot x - 0.5 \cdot y
double f(double x, double y) {
        double r456334 = x;
        double r456335 = y;
        double r456336 = r456334 - r456335;
        double r456337 = 2.0;
        double r456338 = r456336 / r456337;
        double r456339 = r456334 + r456338;
        return r456339;
}
↓
double f(double x, double y) {
        double r456340 = 1.5;
        double r456341 = x;
        double r456342 = r456340 * r456341;
        double r456343 = 0.5;
        double r456344 = y;
        double r456345 = r456343 * r456344;
        double r456346 = r456342 - r456345;
        return r456346;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[1.5 \cdot x - 0.5 \cdot y\]

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{1.5 \cdot x - 0.5 \cdot y}\]

  3. Final simplification0.1

    \[\leadsto 1.5 \cdot x - 0.5 \cdot y\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* 1.5 x) (* 0.5 y))

  (+ x (/ (- x y) 2)))