Average Error: 10.5 → 0.0
Time: 3.2s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(1 - y\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(1 - y\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r648206 = x;
        double r648207 = y;
        double r648208 = z;
        double r648209 = r648208 - r648206;
        double r648210 = r648207 * r648209;
        double r648211 = r648206 + r648210;
        double r648212 = r648211 / r648208;
        return r648212;
}
↓
double f(double x, double y, double z) {
        double r648213 = 1.0;
        double r648214 = y;
        double r648215 = r648213 - r648214;
        double r648216 = x;
        double r648217 = z;
        double r648218 = r648216 / r648217;
        double r648219 = r648215 * r648218;
        double r648220 = r648219 + r648214;
        return r648220;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.5
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.5

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, \frac{x}{z}, y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

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

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