Average Error: 1.5 → 1.4
Time: 4.7s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r699373 = x;
        double r699374 = y;
        double r699375 = z;
        double r699376 = t;
        double r699377 = r699375 - r699376;
        double r699378 = a;
        double r699379 = r699375 - r699378;
        double r699380 = r699377 / r699379;
        double r699381 = r699374 * r699380;
        double r699382 = r699373 + r699381;
        return r699382;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r699383 = y;
        double r699384 = z;
        double r699385 = a;
        double r699386 = r699384 - r699385;
        double r699387 = t;
        double r699388 = r699384 - r699387;
        double r699389 = r699386 / r699388;
        double r699390 = r699383 / r699389;
        double r699391 = x;
        double r699392 = r699390 + r699391;
        return r699392;
}

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

Original1.5
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.5

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

  2. Simplified1.5

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

  4. Applied add-cube-cbrt1.8

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

  6. Applied fma-udef1.8

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

  7. Simplified10.7

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

  9. Applied associate-/l*1.4

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

  10. Final simplification1.4

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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)))))