Average Error: 1.4 → 1.3
Time: 4.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\left(z - a\right) \cdot \frac{1}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r675560 = x;
        double r675561 = y;
        double r675562 = z;
        double r675563 = t;
        double r675564 = r675562 - r675563;
        double r675565 = a;
        double r675566 = r675562 - r675565;
        double r675567 = r675564 / r675566;
        double r675568 = r675561 * r675567;
        double r675569 = r675560 + r675568;
        return r675569;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r675570 = y;
        double r675571 = z;
        double r675572 = a;
        double r675573 = r675571 - r675572;
        double r675574 = 1.0;
        double r675575 = t;
        double r675576 = r675571 - r675575;
        double r675577 = r675574 / r675576;
        double r675578 = r675573 * r675577;
        double r675579 = r675570 / r675578;
        double r675580 = x;
        double r675581 = r675579 + r675580;
        return r675581;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

    \[x + y \cdot \frac{z - t}{z - a}\]
  2. Using strategy rm

  3. Applied clear-num1.5

    \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied pow11.5

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

  6. Applied pow11.5

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

  7. Applied pow-prod-down1.5

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

  8. Simplified1.3

    \[\leadsto x + {\color{blue}{\left(\frac{y}{\frac{z - a}{z - t}}\right)}}^{1}\]
  9. Using strategy rm

  10. Applied div-inv1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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