Average Error: 10.4 → 1.4
Time: 16.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r290796 = x;
        double r290797 = y;
        double r290798 = z;
        double r290799 = t;
        double r290800 = r290798 - r290799;
        double r290801 = r290797 * r290800;
        double r290802 = a;
        double r290803 = r290798 - r290802;
        double r290804 = r290801 / r290803;
        double r290805 = r290796 + r290804;
        return r290805;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r290806 = x;
        double r290807 = y;
        double r290808 = z;
        double r290809 = t;
        double r290810 = r290808 - r290809;
        double r290811 = a;
        double r290812 = r290808 - r290811;
        double r290813 = r290810 / r290812;
        double r290814 = r290807 * r290813;
        double r290815 = r290806 + r290814;
        return r290815;
}

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

Original10.4
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  2. Simplified3.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)}\]
  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. Simplified2.9

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

  9. Applied *-un-lft-identity2.9

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

  10. Applied *-un-lft-identity2.9

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

  11. Applied times-frac2.9

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

  12. Applied *-un-lft-identity2.9

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

  13. Applied times-frac2.9

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

  14. Simplified2.9

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

  15. Simplified1.4

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

  16. Final simplification1.4

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

Reproduce

herbie shell --seed 2019325 +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))))