Average Error: 10.0 → 10.0
Time: 4.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\frac{x + y \cdot \left(z - x\right)}{z}
double f(double x, double y, double z) {
        double r442331 = x;
        double r442332 = y;
        double r442333 = z;
        double r442334 = r442333 - r442331;
        double r442335 = r442332 * r442334;
        double r442336 = r442331 + r442335;
        double r442337 = r442336 / r442333;
        return r442337;
}
↓
double f(double x, double y, double z) {
        double r442338 = x;
        double r442339 = y;
        double r442340 = z;
        double r442341 = r442340 - r442338;
        double r442342 = r442339 * r442341;
        double r442343 = r442338 + r442342;
        double r442344 = r442343 / r442340;
        return r442344;
}

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

Original10.0
Target0.0
Herbie10.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.9618762888681135e-84 or 6.777650331950524e-29 < z

    1. Initial program 14.2

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

    2. Taylor expanded around 0 4.9

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

    4. Applied *-un-lft-identity4.9

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

    5. Applied times-frac0.3

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

    6. Simplified0.3

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

    if -1.9618762888681135e-84 < z < 6.777650331950524e-29

    1. Initial program 0.1

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

    3. Applied clear-num0.3

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x + y \cdot \left(z - x\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.0

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

Reproduce

herbie shell --seed 2019304 
(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))