Average Error: 1.8 → 0.2
Time: 10.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r647657 = x;
        double r647658 = y;
        double r647659 = z;
        double r647660 = r647658 - r647659;
        double r647661 = t;
        double r647662 = r647661 - r647659;
        double r647663 = 1.0;
        double r647664 = r647662 + r647663;
        double r647665 = a;
        double r647666 = r647664 / r647665;
        double r647667 = r647660 / r647666;
        double r647668 = r647657 - r647667;
        return r647668;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r647669 = x;
        double r647670 = y;
        double r647671 = z;
        double r647672 = r647670 - r647671;
        double r647673 = t;
        double r647674 = r647673 - r647671;
        double r647675 = 1.0;
        double r647676 = r647674 + r647675;
        double r647677 = r647672 / r647676;
        double r647678 = a;
        double r647679 = r647677 * r647678;
        double r647680 = r647669 - r647679;
        return r647680;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

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

  3. Applied *-un-lft-identity1.8

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

  4. Applied *-un-lft-identity1.8

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

  5. Applied times-frac1.8

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

  6. Applied *-un-lft-identity1.8

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

  7. Applied times-frac1.8

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

  8. Simplified1.8

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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))))