Average Error: 0.1 → 0.0
Time: 1.2s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r708121 = 4.0;
        double r708122 = x;
        double r708123 = y;
        double r708124 = r708122 - r708123;
        double r708125 = z;
        double r708126 = 0.5;
        double r708127 = r708125 * r708126;
        double r708128 = r708124 - r708127;
        double r708129 = r708121 * r708128;
        double r708130 = r708129 / r708125;
        return r708130;
}
↓
double f(double x, double y, double z) {
        double r708131 = 4.0;
        double r708132 = x;
        double r708133 = y;
        double r708134 = r708132 - r708133;
        double r708135 = z;
        double r708136 = r708134 / r708135;
        double r708137 = r708131 * r708136;
        double r708138 = 2.0;
        double r708139 = -r708138;
        double r708140 = r708137 + r708139;
        return r708140;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} + \left(-2\right)}\]

  4. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - y}{z} + \left(-2\right)\]

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))