Average Error: 0.1 → 0.0
Time: 5.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r930156 = 4.0;
        double r930157 = x;
        double r930158 = y;
        double r930159 = r930157 - r930158;
        double r930160 = z;
        double r930161 = 0.5;
        double r930162 = r930160 * r930161;
        double r930163 = r930159 - r930162;
        double r930164 = r930156 * r930163;
        double r930165 = r930164 / r930160;
        return r930165;
}
↓
double f(double x, double y, double z) {
        double r930166 = 4.0;
        double r930167 = x;
        double r930168 = z;
        double r930169 = r930167 / r930168;
        double r930170 = y;
        double r930171 = r930170 / r930168;
        double r930172 = r930169 - r930171;
        double r930173 = 0.5;
        double r930174 = r930172 - r930173;
        double r930175 = r930166 * r930174;
        return r930175;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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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

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} - \frac{0.5}{1}\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - \frac{0.5}{1}\right)\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))