Average Error: 6.4 → 1.8
Time: 12.1min
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 2.0118681967895242 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{elif}\;t \le 5.82668425736250235 \cdot 10^{-51}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le 2.0118681967895242 \cdot 10^{-307}:\\
\;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\

\mathbf{elif}\;t \le 5.82668425736250235 \cdot 10^{-51}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (((double) (y - x)) * z)) / t)));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((t <= 2.011868196789524e-307)) {
		VAR = ((double) (x + (1.0 / ((t / z) / ((double) (y - x))))));
	} else {
		double VAR_1;
		if ((t <= 5.826684257362502e-51)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - x)) * z)) * (1.0 / t)))));
		} else {
			VAR_1 = ((double) (x + ((((double) (y - x)) / t) / (1.0 / z))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original6.4
Target1.9
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < 2.0118681967895242e-307

    1. Initial program 6.5

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

    3. Applied associate-/l*2.1

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

    5. Applied clear-num2.1

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

    if 2.0118681967895242e-307 < t < 5.82668425736250235e-51

    1. Initial program 2.2

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

    3. Applied div-inv2.3

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

    if 5.82668425736250235e-51 < t

    1. Initial program 8.2

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

    3. Applied associate-/l*1.3

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

    5. Applied div-inv1.3

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

    6. Applied associate-/r*1.1

      \[\leadsto x + \color{blue}{\frac{\frac{y - x}{t}}{\frac{1}{z}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 2.0118681967895242 \cdot 10^{-307}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{t}{z}}{y - x}}\\ \mathbf{elif}\;t \le 5.82668425736250235 \cdot 10^{-51}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{t}}{\frac{1}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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)))