Average Error: 0.1 → 0.0
Time: 13.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)
double f(double x, double y, double z) {
        double r316520 = 1.0;
        double r316521 = 4.0;
        double r316522 = x;
        double r316523 = y;
        double r316524 = 0.75;
        double r316525 = r316523 * r316524;
        double r316526 = r316522 + r316525;
        double r316527 = z;
        double r316528 = r316526 - r316527;
        double r316529 = r316521 * r316528;
        double r316530 = r316529 / r316523;
        double r316531 = r316520 + r316530;
        return r316531;
}
↓
double f(double x, double y, double z) {
        double r316532 = 0.75;
        double r316533 = x;
        double r316534 = z;
        double r316535 = r316533 - r316534;
        double r316536 = y;
        double r316537 = r316535 / r316536;
        double r316538 = r316532 + r316537;
        double r316539 = 4.0;
        double r316540 = 1.0;
        double r316541 = fma(r316538, r316539, r316540);
        return r316541;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(0.75 + \frac{x - z}{y}, 4, 1\right)\]

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))