Average Error: 0.1 → 0.1
Time: 8.7s
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 r754104 = x;
        double r754105 = y;
        double r754106 = r754104 - r754105;
        double r754107 = 2.0;
        double r754108 = r754106 / r754107;
        double r754109 = r754104 + r754108;
        return r754109;
}
↓
double f(double x, double y) {
        double r754110 = 1.5;
        double r754111 = x;
        double r754112 = r754110 * r754111;
        double r754113 = 0.5;
        double r754114 = y;
        double r754115 = r754113 * r754114;
        double r754116 = r754112 - r754115;
        return r754116;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 2020046 
(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)))