Average Error: 10.2 → 0.0
Time: 15.6s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\frac{x}{z} - y \cdot \frac{x}{z}\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\frac{x}{z} - y \cdot \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r134248193 = x;
        double r134248194 = y;
        double r134248195 = z;
        double r134248196 = r134248195 - r134248193;
        double r134248197 = r134248194 * r134248196;
        double r134248198 = r134248193 + r134248197;
        double r134248199 = r134248198 / r134248195;
        return r134248199;
}
↓
double f(double x, double y, double z) {
        double r134248200 = y;
        double r134248201 = x;
        double r134248202 = z;
        double r134248203 = r134248201 / r134248202;
        double r134248204 = r134248200 * r134248203;
        double r134248205 = r134248203 - r134248204;
        double r134248206 = r134248200 + r134248205;
        return r134248206;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.6

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

  4. Applied associate-/l*2.9

    \[\leadsto \left(y + \frac{x}{z}\right) - \color{blue}{\frac{x}{\frac{z}{y}}}\]
  5. Using strategy rm

  6. Applied associate--l+2.9

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))