Average Error: 10.9 → 1.3
Time: 45.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{z - t}{a - t} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{z - t}{a - t} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r21519665 = x;
        double r21519666 = y;
        double r21519667 = z;
        double r21519668 = t;
        double r21519669 = r21519667 - r21519668;
        double r21519670 = r21519666 * r21519669;
        double r21519671 = a;
        double r21519672 = r21519671 - r21519668;
        double r21519673 = r21519670 / r21519672;
        double r21519674 = r21519665 + r21519673;
        return r21519674;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r21519675 = z;
        double r21519676 = t;
        double r21519677 = r21519675 - r21519676;
        double r21519678 = a;
        double r21519679 = r21519678 - r21519676;
        double r21519680 = r21519677 / r21519679;
        double r21519681 = y;
        double r21519682 = r21519680 * r21519681;
        double r21519683 = x;
        double r21519684 = r21519682 + r21519683;
        return r21519684;
}

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

Original10.9
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  2. Simplified3.0

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

  4. Applied add-cube-cbrt3.5

    \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{a - t}, z - t, x\right)\]

  5. Applied associate-/l*3.5

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

  7. Applied fma-udef3.5

    \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{a - t}{\sqrt[3]{y}}} \cdot \left(z - t\right) + x}\]

  8. Simplified3.0

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

  10. Applied associate-/r/1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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