Average Error: 0.1 → 0.1
Time: 17.2s
Precision: 64
\[x + \frac{x - y}{2.0}\]
↓
\[1.5 \cdot x - 0.5 \cdot y\]
x + \frac{x - y}{2.0}
↓
1.5 \cdot x - 0.5 \cdot y
double f(double x, double y) {
        double r34661108 = x;
        double r34661109 = y;
        double r34661110 = r34661108 - r34661109;
        double r34661111 = 2.0;
        double r34661112 = r34661110 / r34661111;
        double r34661113 = r34661108 + r34661112;
        return r34661113;
}
↓
double f(double x, double y) {
        double r34661114 = 1.5;
        double r34661115 = x;
        double r34661116 = r34661114 * r34661115;
        double r34661117 = 0.5;
        double r34661118 = y;
        double r34661119 = r34661117 * r34661118;
        double r34661120 = r34661116 - r34661119;
        return r34661120;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.1

    \[x + \frac{x - y}{2.0}\]

  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 2019164 
(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)))