Average Error: 2.0 → 0.2
Time: 3.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[a \cdot \frac{z - y}{\left(t - z\right) + 1} + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
a \cdot \frac{z - y}{\left(t - z\right) + 1} + x
double f(double x, double y, double z, double t, double a) {
        double r606779 = x;
        double r606780 = y;
        double r606781 = z;
        double r606782 = r606780 - r606781;
        double r606783 = t;
        double r606784 = r606783 - r606781;
        double r606785 = 1.0;
        double r606786 = r606784 + r606785;
        double r606787 = a;
        double r606788 = r606786 / r606787;
        double r606789 = r606782 / r606788;
        double r606790 = r606779 - r606789;
        return r606790;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r606791 = a;
        double r606792 = z;
        double r606793 = y;
        double r606794 = r606792 - r606793;
        double r606795 = t;
        double r606796 = r606795 - r606792;
        double r606797 = 1.0;
        double r606798 = r606796 + r606797;
        double r606799 = r606794 / r606798;
        double r606800 = r606791 * r606799;
        double r606801 = x;
        double r606802 = r606800 + r606801;
        return r606802;
}

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

Original2.0
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

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

  2. Simplified1.8

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

  4. Applied fma-udef1.8

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

  6. Applied div-inv1.8

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

  7. Applied associate-*l*0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))