Average Error: 2.0 → 0.3
Time: 13.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}
double f(double x, double y, double z, double t, double a) {
        double r25727593 = x;
        double r25727594 = y;
        double r25727595 = z;
        double r25727596 = r25727594 - r25727595;
        double r25727597 = t;
        double r25727598 = r25727597 - r25727595;
        double r25727599 = 1.0;
        double r25727600 = r25727598 + r25727599;
        double r25727601 = a;
        double r25727602 = r25727600 / r25727601;
        double r25727603 = r25727596 / r25727602;
        double r25727604 = r25727593 - r25727603;
        return r25727604;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25727605 = x;
        double r25727606 = a;
        double r25727607 = y;
        double r25727608 = z;
        double r25727609 = r25727607 - r25727608;
        double r25727610 = t;
        double r25727611 = r25727610 - r25727608;
        double r25727612 = 1.0;
        double r25727613 = r25727611 + r25727612;
        double r25727614 = r25727609 / r25727613;
        double r25727615 = r25727606 * r25727614;
        double r25727616 = r25727605 - r25727615;
        return r25727616;
}

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
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.3

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1.0} \cdot a}\]

  4. Final simplification0.3

    \[\leadsto x - a \cdot \frac{y - z}{\left(t - z\right) + 1.0}\]

Reproduce

herbie shell --seed 2019165 
(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))))