Average Error: 2.1 → 0.3
Time: 4.3s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r685099 = x;
        double r685100 = y;
        double r685101 = z;
        double r685102 = r685100 - r685101;
        double r685103 = t;
        double r685104 = r685103 - r685101;
        double r685105 = 1.0;
        double r685106 = r685104 + r685105;
        double r685107 = a;
        double r685108 = r685106 / r685107;
        double r685109 = r685102 / r685108;
        double r685110 = r685099 - r685109;
        return r685110;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r685111 = x;
        double r685112 = y;
        double r685113 = z;
        double r685114 = r685112 - r685113;
        double r685115 = 1.0;
        double r685116 = t;
        double r685117 = r685116 - r685113;
        double r685118 = 1.0;
        double r685119 = r685117 + r685118;
        double r685120 = r685115 / r685119;
        double r685121 = r685114 * r685120;
        double r685122 = a;
        double r685123 = r685121 * r685122;
        double r685124 = r685111 - r685123;
        return r685124;
}

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. Using strategy rm

  3. Applied associate-/r/0.3

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

  5. Applied div-inv0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 
(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))))