Average Error: 2.1 → 0.3
Time: 23.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \frac{a}{\frac{t + \left(1 - z\right)}{z - y}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \frac{a}{\frac{t + \left(1 - z\right)}{z - y}}
double f(double x, double y, double z, double t, double a) {
        double r20529795 = x;
        double r20529796 = y;
        double r20529797 = z;
        double r20529798 = r20529796 - r20529797;
        double r20529799 = t;
        double r20529800 = r20529799 - r20529797;
        double r20529801 = 1.0;
        double r20529802 = r20529800 + r20529801;
        double r20529803 = a;
        double r20529804 = r20529802 / r20529803;
        double r20529805 = r20529798 / r20529804;
        double r20529806 = r20529795 - r20529805;
        return r20529806;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r20529807 = x;
        double r20529808 = a;
        double r20529809 = t;
        double r20529810 = 1.0;
        double r20529811 = z;
        double r20529812 = r20529810 - r20529811;
        double r20529813 = r20529809 + r20529812;
        double r20529814 = y;
        double r20529815 = r20529811 - r20529814;
        double r20529816 = r20529813 / r20529815;
        double r20529817 = r20529808 / r20529816;
        double r20529818 = r20529807 + r20529817;
        return r20529818;
}

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
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  2. Simplified0.2

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

  4. Applied div-inv0.3

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

  6. Applied fma-udef0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))))