Average Error: 0.1 → 0.0
Time: 5.7s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r827554 = 4.0;
        double r827555 = x;
        double r827556 = y;
        double r827557 = r827555 - r827556;
        double r827558 = z;
        double r827559 = 0.5;
        double r827560 = r827558 * r827559;
        double r827561 = r827557 - r827560;
        double r827562 = r827554 * r827561;
        double r827563 = r827562 / r827558;
        return r827563;
}
↓
double f(double x, double y, double z) {
        double r827564 = x;
        double r827565 = y;
        double r827566 = r827564 - r827565;
        double r827567 = z;
        double r827568 = r827566 / r827567;
        double r827569 = 0.5;
        double r827570 = r827568 - r827569;
        double r827571 = 4.0;
        double r827572 = r827570 * r827571;
        return r827572;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4}\]

  3. Final simplification0.0

    \[\leadsto \left(\frac{x - y}{z} - 0.5\right) \cdot 4\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))