Average Error: 0.1 → 0.1
Time: 5.3s
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 r767366 = x;
        double r767367 = y;
        double r767368 = r767366 - r767367;
        double r767369 = 2.0;
        double r767370 = r767368 / r767369;
        double r767371 = r767366 + r767370;
        return r767371;
}
↓
double f(double x, double y) {
        double r767372 = 1.5;
        double r767373 = x;
        double r767374 = r767372 * r767373;
        double r767375 = 0.5;
        double r767376 = y;
        double r767377 = r767375 * r767376;
        double r767378 = r767374 - r767377;
        return r767378;
}

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

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

  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 2020100 
(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)))