Average Error: 2.2 → 0.3
Time: 18.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \frac{1}{\frac{\left(t + 1\right) - z}{z - y}} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \frac{1}{\frac{\left(t + 1\right) - z}{z - y}} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r483069 = x;
        double r483070 = y;
        double r483071 = z;
        double r483072 = r483070 - r483071;
        double r483073 = t;
        double r483074 = r483073 - r483071;
        double r483075 = 1.0;
        double r483076 = r483074 + r483075;
        double r483077 = a;
        double r483078 = r483076 / r483077;
        double r483079 = r483072 / r483078;
        double r483080 = r483069 - r483079;
        return r483080;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r483081 = x;
        double r483082 = 1.0;
        double r483083 = t;
        double r483084 = 1.0;
        double r483085 = r483083 + r483084;
        double r483086 = z;
        double r483087 = r483085 - r483086;
        double r483088 = y;
        double r483089 = r483086 - r483088;
        double r483090 = r483087 / r483089;
        double r483091 = r483082 / r483090;
        double r483092 = a;
        double r483093 = r483091 * r483092;
        double r483094 = r483081 + r483093;
        return r483094;
}

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

Original2.2
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.2

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

  2. Simplified2.2

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

  4. Applied associate-/r/0.2

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

  5. Simplified0.2

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

  7. Applied clear-num0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(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))))