Average Error: 0.1 → 0.1
Time: 17.8s
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 r29925003 = x;
        double r29925004 = y;
        double r29925005 = r29925003 - r29925004;
        double r29925006 = 2.0;
        double r29925007 = r29925005 / r29925006;
        double r29925008 = r29925003 + r29925007;
        return r29925008;
}
↓
double f(double x, double y) {
        double r29925009 = 1.5;
        double r29925010 = x;
        double r29925011 = r29925009 * r29925010;
        double r29925012 = 0.5;
        double r29925013 = y;
        double r29925014 = r29925012 * r29925013;
        double r29925015 = r29925011 - r29925014;
        return r29925015;
}

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 2019192 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Axis.Types:hBufferRect from Chart-1.5.3"

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

  (+ x (/ (- x y) 2.0)))