Average Error: 10.6 → 1.4
Time: 1.1m
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{z - t}{a - t} \cdot y\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{z - t}{a - t} \cdot y
double f(double x, double y, double z, double t, double a) {
        double r29478596 = x;
        double r29478597 = y;
        double r29478598 = z;
        double r29478599 = t;
        double r29478600 = r29478598 - r29478599;
        double r29478601 = r29478597 * r29478600;
        double r29478602 = a;
        double r29478603 = r29478602 - r29478599;
        double r29478604 = r29478601 / r29478603;
        double r29478605 = r29478596 + r29478604;
        return r29478605;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29478606 = x;
        double r29478607 = z;
        double r29478608 = t;
        double r29478609 = r29478607 - r29478608;
        double r29478610 = a;
        double r29478611 = r29478610 - r29478608;
        double r29478612 = r29478609 / r29478611;
        double r29478613 = y;
        double r29478614 = r29478612 * r29478613;
        double r29478615 = r29478606 + r29478614;
        return r29478615;
}

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

Original10.6
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied *-un-lft-identity10.6

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

  4. Applied times-frac1.4

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

  5. Simplified1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019200 
(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))))