Average Error: 2.1 → 0.2
Time: 16.6s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \left(\frac{z}{1 + \left(t - z\right)} \cdot a - \frac{y}{1 + \left(t - z\right)} \cdot a\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \left(\frac{z}{1 + \left(t - z\right)} \cdot a - \frac{y}{1 + \left(t - z\right)} \cdot a\right)
double f(double x, double y, double z, double t, double a) {
        double r546608 = x;
        double r546609 = y;
        double r546610 = z;
        double r546611 = r546609 - r546610;
        double r546612 = t;
        double r546613 = r546612 - r546610;
        double r546614 = 1.0;
        double r546615 = r546613 + r546614;
        double r546616 = a;
        double r546617 = r546615 / r546616;
        double r546618 = r546611 / r546617;
        double r546619 = r546608 - r546618;
        return r546619;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r546620 = x;
        double r546621 = z;
        double r546622 = 1.0;
        double r546623 = t;
        double r546624 = r546623 - r546621;
        double r546625 = r546622 + r546624;
        double r546626 = r546621 / r546625;
        double r546627 = a;
        double r546628 = r546626 * r546627;
        double r546629 = y;
        double r546630 = r546629 / r546625;
        double r546631 = r546630 * r546627;
        double r546632 = r546628 - r546631;
        double r546633 = r546620 + r546632;
        return r546633;
}

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

Original2.1
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  2. Simplified2.1

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

  4. Applied div-sub2.1

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

  5. Simplified1.0

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))