Average Error: 6.3 → 1.8
Time: 2.8s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -5.816891157054731 \cdot 10^{-255} \lor \neg \left(x \leq 6.796788894209597 \cdot 10^{-196}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -5.816891157054731 \cdot 10^{-255} \lor \neg \left(x \leq 6.796788894209597 \cdot 10^{-196}\right):\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* (- y x) z) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.816891157054731e-255) (not (<= x 6.796788894209597e-196)))
   (+ x (/ (- y x) (/ t z)))
   (+ x (* (/ (- y x) (* (cbrt t) (cbrt t))) (/ z (cbrt t))))))
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 <= -5.816891157054731e-255) || !(x <= 6.796788894209597e-196)) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + (((y - x) / (cbrt(t) * cbrt(t))) * (z / cbrt(t)));
	}
	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

Original6.3
Target1.9
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.81689115705473114e-255 or 6.7967888942095968e-196 < x

    1. Initial program 6.4

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

    3. Applied associate-/l*_binary641.3

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

    if -5.81689115705473114e-255 < x < 6.7967888942095968e-196

    1. Initial program 5.9

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

    3. Applied add-cube-cbrt_binary646.7

      \[\leadsto x + \frac{\left(y - x\right) \cdot z}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\]

    4. Applied times-frac_binary644.8

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.816891157054731 \cdot 10^{-255} \lor \neg \left(x \leq 6.796788894209597 \cdot 10^{-196}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020233 
(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)))