Average Error: 2.0 → 0.3
Time: 8.4s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r607163 = x;
        double r607164 = y;
        double r607165 = z;
        double r607166 = r607164 - r607165;
        double r607167 = t;
        double r607168 = r607167 - r607165;
        double r607169 = 1.0;
        double r607170 = r607168 + r607169;
        double r607171 = a;
        double r607172 = r607170 / r607171;
        double r607173 = r607166 / r607172;
        double r607174 = r607163 - r607173;
        return r607174;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r607175 = x;
        double r607176 = y;
        double r607177 = z;
        double r607178 = r607176 - r607177;
        double r607179 = t;
        double r607180 = r607179 - r607177;
        double r607181 = 1.0;
        double r607182 = r607180 + r607181;
        double r607183 = r607178 / r607182;
        double r607184 = 1.0;
        double r607185 = a;
        double r607186 = r607184 / r607185;
        double r607187 = r607183 / r607186;
        double r607188 = r607175 - r607187;
        return r607188;
}

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

Derivation

  1. Initial program 2.0

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

  3. Applied div-inv2.0

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 1978988140 
(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))))