Average Error: 2.0 → 0.3
Time: 17.1s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + a \cdot \frac{z - y}{\left(t + 1\right) - z}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + a \cdot \frac{z - y}{\left(t + 1\right) - z}
double f(double x, double y, double z, double t, double a) {
        double r503770 = x;
        double r503771 = y;
        double r503772 = z;
        double r503773 = r503771 - r503772;
        double r503774 = t;
        double r503775 = r503774 - r503772;
        double r503776 = 1.0;
        double r503777 = r503775 + r503776;
        double r503778 = a;
        double r503779 = r503777 / r503778;
        double r503780 = r503773 / r503779;
        double r503781 = r503770 - r503780;
        return r503781;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r503782 = x;
        double r503783 = a;
        double r503784 = z;
        double r503785 = y;
        double r503786 = r503784 - r503785;
        double r503787 = t;
        double r503788 = 1.0;
        double r503789 = r503787 + r503788;
        double r503790 = r503789 - r503784;
        double r503791 = r503786 / r503790;
        double r503792 = r503783 * r503791;
        double r503793 = r503782 + r503792;
        return r503793;
}

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

Derivation

  1. Initial program 2.0

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

  2. Simplified0.3

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

  4. Applied clear-num0.4

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

  6. Applied fma-udef0.4

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

  7. Simplified1.9

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

  9. Applied div-inv1.9

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

  10. Applied associate-*l*0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 +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))))