Average Error: 11.1 → 1.3
Time: 4.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{z - t}{z - a} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{z - t}{z - a} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r556198 = x;
        double r556199 = y;
        double r556200 = z;
        double r556201 = t;
        double r556202 = r556200 - r556201;
        double r556203 = r556199 * r556202;
        double r556204 = a;
        double r556205 = r556200 - r556204;
        double r556206 = r556203 / r556205;
        double r556207 = r556198 + r556206;
        return r556207;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r556208 = z;
        double r556209 = t;
        double r556210 = r556208 - r556209;
        double r556211 = a;
        double r556212 = r556208 - r556211;
        double r556213 = r556210 / r556212;
        double r556214 = y;
        double r556215 = r556213 * r556214;
        double r556216 = x;
        double r556217 = r556215 + r556216;
        return r556217;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.1
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  2. Simplified2.9

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

  4. Applied clear-num3.2

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

  6. Applied fma-udef3.2

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

  7. Simplified3.0

    \[\leadsto \color{blue}{\frac{z - t}{\frac{z - a}{y}}} + x\]
  8. Using strategy rm

  9. Applied associate-/r/1.3

    \[\leadsto \color{blue}{\frac{z - t}{z - a} \cdot y} + x\]

  10. Final simplification1.3

    \[\leadsto \frac{z - t}{z - a} \cdot y + x\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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