Average Error: 6.5 → 1.3
Time: 3.4s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -6.238364551015496 \cdot 10^{+307}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -1.696373183776563 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{t}{z}} - \frac{x}{\frac{t}{z}}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -6.238364551015496 \cdot 10^{+307}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -1.696373183776563 \cdot 10^{-260}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\frac{y}{\frac{t}{z}} - \frac{x}{\frac{t}{z}}\right)\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* (- y x) z) t)) -6.238364551015496e+307)
   (+ x (* z (/ (- y x) t)))
   (if (<= (+ x (/ (* (- y x) z) t)) -1.696373183776563e-260)
     (+ x (/ (* (- y x) z) t))
     (+ x (- (/ y (/ t z)) (/ x (/ t z)))))))
double code(double x, double y, double z, double t) {
	return x + (((y - x) * z) / t);
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + (((y - x) * z) / t)) <= -6.238364551015496e+307) {
		tmp = x + (z * ((y - x) / t));
	} else if ((x + (((y - x) * z) / t)) <= -1.696373183776563e-260) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = x + ((y / (t / z)) - (x / (t / z)));
	}
	return tmp;
}

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

Original6.5
Target2.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -6.23836455101549579e307

    1. Initial program 63.3

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

    3. Applied associate-/l*_binary64_129810.5

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

    5. Applied associate-/r/_binary64_129820.2

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

    if -6.23836455101549579e307 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -1.69637318377656301e-260

    1. Initial program 0.6

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

    if -1.69637318377656301e-260 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

    1. Initial program 6.4

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

    3. Applied associate-/l*_binary64_129811.9

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

    5. Applied div-sub_binary64_130411.9

      \[\leadsto x + \color{blue}{\left(\frac{y}{\frac{t}{z}} - \frac{x}{\frac{t}{z}}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -6.238364551015496 \cdot 10^{+307}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -1.696373183776563 \cdot 10^{-260}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{t}{z}} - \frac{x}{\frac{t}{z}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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