Average Error: 1.8 → 0.3
Time: 9.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{1}{\frac{\left(t - z\right) + 1}{y - z}} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{1}{\frac{\left(t - z\right) + 1}{y - z}} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r605534 = x;
        double r605535 = y;
        double r605536 = z;
        double r605537 = r605535 - r605536;
        double r605538 = t;
        double r605539 = r605538 - r605536;
        double r605540 = 1.0;
        double r605541 = r605539 + r605540;
        double r605542 = a;
        double r605543 = r605541 / r605542;
        double r605544 = r605537 / r605543;
        double r605545 = r605534 - r605544;
        return r605545;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r605546 = x;
        double r605547 = 1.0;
        double r605548 = t;
        double r605549 = z;
        double r605550 = r605548 - r605549;
        double r605551 = 1.0;
        double r605552 = r605550 + r605551;
        double r605553 = y;
        double r605554 = r605553 - r605549;
        double r605555 = r605552 / r605554;
        double r605556 = r605547 / r605555;
        double r605557 = a;
        double r605558 = r605556 * r605557;
        double r605559 = r605546 - r605558;
        return r605559;
}

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

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. Using strategy rm

  11. Applied clear-num0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 
(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))))