Average Error: 0.2 → 0.0
Time: 12.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r35753331 = 4.0;
        double r35753332 = x;
        double r35753333 = y;
        double r35753334 = r35753332 - r35753333;
        double r35753335 = z;
        double r35753336 = 0.5;
        double r35753337 = r35753335 * r35753336;
        double r35753338 = r35753334 - r35753337;
        double r35753339 = r35753331 * r35753338;
        double r35753340 = r35753339 / r35753335;
        return r35753340;
}
↓
double f(double x, double y, double z) {
        double r35753341 = x;
        double r35753342 = z;
        double r35753343 = r35753341 / r35753342;
        double r35753344 = y;
        double r35753345 = r35753344 / r35753342;
        double r35753346 = r35753343 - r35753345;
        double r35753347 = 0.5;
        double r35753348 = r35753346 - r35753347;
        double r35753349 = 4.0;
        double r35753350 = r35753348 * r35753349;
        return r35753350;
}

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

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

Derivation

  1. Initial program 0.2

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(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))