Average Error: 10.2 → 0.0
Time: 15.4s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r545124 = x;
        double r545125 = y;
        double r545126 = z;
        double r545127 = r545126 - r545124;
        double r545128 = r545125 * r545127;
        double r545129 = r545124 + r545128;
        double r545130 = r545129 / r545126;
        return r545130;
}
↓
double f(double x, double y, double z) {
        double r545131 = x;
        double r545132 = z;
        double r545133 = r545131 / r545132;
        double r545134 = y;
        double r545135 = r545133 + r545134;
        double r545136 = r545133 * r545134;
        double r545137 = r545135 - r545136;
        return r545137;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified10.2

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

  3. Taylor expanded around 0 3.3

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

  5. Applied *-un-lft-identity3.3

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

  6. Applied *-un-lft-identity3.3

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

  7. Applied distribute-lft-out--3.3

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(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))