Average Error: 7.0 → 1.9
Time: 10.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[x + \frac{y - x}{\frac{t}{z}}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
x + \frac{y - x}{\frac{t}{z}}
double f(double x, double y, double z, double t) {
        double r339887 = x;
        double r339888 = y;
        double r339889 = r339888 - r339887;
        double r339890 = z;
        double r339891 = r339889 * r339890;
        double r339892 = t;
        double r339893 = r339891 / r339892;
        double r339894 = r339887 + r339893;
        return r339894;
}
↓
double f(double x, double y, double z, double t) {
        double r339895 = x;
        double r339896 = y;
        double r339897 = r339896 - r339895;
        double r339898 = t;
        double r339899 = z;
        double r339900 = r339898 / r339899;
        double r339901 = r339897 / r339900;
        double r339902 = r339895 + r339901;
        return r339902;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.0
Target2.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;x \lt -9.025511195533004570453352523209034680317 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.275032163700714748507147332551979944314 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 3.721695370812968e-308

    1. Initial program 7.2

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

    3. Applied associate-/l*1.5

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]

    if 3.721695370812968e-308 < z

    1. Initial program 6.8

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

    3. Applied associate-/l*2.3

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]
    4. Using strategy rm

    5. Applied clear-num2.3

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{t}{z}}{y - x}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity2.3

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

    8. Applied add-sqr-sqrt2.4

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

    9. Applied *-un-lft-identity2.4

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

    10. Applied times-frac2.4

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

    11. Applied times-frac2.5

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{1}{\sqrt{z}}}{1} \cdot \frac{\frac{t}{\sqrt{z}}}{y - x}}}\]

    12. Applied associate-/r*2.5

      \[\leadsto x + \color{blue}{\frac{\frac{1}{\frac{\frac{1}{\sqrt{z}}}{1}}}{\frac{\frac{t}{\sqrt{z}}}{y - x}}}\]

    13. Simplified2.5

      \[\leadsto x + \frac{\color{blue}{\sqrt{z}}}{\frac{\frac{t}{\sqrt{z}}}{y - x}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.9

    \[\leadsto x + \frac{y - x}{\frac{t}{z}}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.0255111955330046e-135) (- x (* (/ z t) (- x y))) (if (< x 4.2750321637007147e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))