Average Error: 0.2 → 0.0
Time: 39.2s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0
double f(double x, double y, double z) {
        double r13747382 = 1.0;
        double r13747383 = 4.0;
        double r13747384 = x;
        double r13747385 = y;
        double r13747386 = 0.75;
        double r13747387 = r13747385 * r13747386;
        double r13747388 = r13747384 + r13747387;
        double r13747389 = z;
        double r13747390 = r13747388 - r13747389;
        double r13747391 = r13747383 * r13747390;
        double r13747392 = r13747391 / r13747385;
        double r13747393 = r13747382 + r13747392;
        return r13747393;
}
↓
double f(double x, double y, double z) {
        double r13747394 = 0.75;
        double r13747395 = z;
        double r13747396 = x;
        double r13747397 = r13747395 - r13747396;
        double r13747398 = y;
        double r13747399 = r13747397 / r13747398;
        double r13747400 = r13747394 - r13747399;
        double r13747401 = 4.0;
        double r13747402 = r13747400 * r13747401;
        double r13747403 = 1.0;
        double r13747404 = r13747402 + r13747403;
        return r13747404;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0}\]

  3. Final simplification0.0

    \[\leadsto \left(0.75 - \frac{z - x}{y}\right) \cdot 4.0 + 1.0\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))