Average Error: 3.7 → 0.6
Time: 3.9s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1.2187058822034261 \cdot 10^{+68}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{3 \cdot \frac{z \cdot y}{t}}\\ \mathbf{elif}\;z \cdot 3 \leq 4.524571068069238 \cdot 10^{-86}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;z \cdot 3 \leq -1.2187058822034261 \cdot 10^{+68}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{3 \cdot \frac{z \cdot y}{t}}\\

\mathbf{elif}\;z \cdot 3 \leq 4.524571068069238 \cdot 10^{-86}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - (y / ((double) (z * 3.0))))) + (t / ((double) (((double) (z * 3.0)) * y)))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (z * 3.0)) <= -1.2187058822034261e+68)) {
		VAR = ((double) (((double) (x - (y / ((double) (z * 3.0))))) + (1.0 / ((double) (3.0 * (((double) (z * y)) / t))))));
	} else {
		double VAR_1;
		if ((((double) (z * 3.0)) <= 4.524571068069238e-86)) {
			VAR_1 = ((double) (((double) (x - (y / ((double) (z * 3.0))))) + ((double) ((1.0 / ((double) (z * 3.0))) * (t / y)))));
		} else {
			VAR_1 = ((double) (((double) (x - ((y / z) / 3.0))) + (t / ((double) (((double) (z * 3.0)) * y)))));
		}
		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

Original3.7
Target1.7
Herbie0.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if (* z 3.0) < -1.218705882203426e68

    1. Initial program Error: 0.5 bits

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied clear-numError: 0.5 bits

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{\frac{\left(z \cdot 3\right) \cdot y}{t}}}\]

    4. SimplifiedError: 0.5 bits

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{\color{blue}{\frac{z \cdot y}{t} \cdot 3}}\]

    if -1.218705882203426e68 < (* z 3.0) < 4.5245710680692381e-86

    1. Initial program Error: 10.2 bits

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied *-un-lft-identityError: 10.2 bits

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{1 \cdot t}}{\left(z \cdot 3\right) \cdot y}\]

    4. Applied times-fracError: 0.7 bits

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{z \cdot 3} \cdot \frac{t}{y}}\]

    if 4.5245710680692381e-86 < (* z 3.0)

    1. Initial program Error: 0.7 bits

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*Error: 0.7 bits

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

  4. Final simplificationError: 0.6 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1.2187058822034261 \cdot 10^{+68}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{3 \cdot \frac{z \cdot y}{t}}\\ \mathbf{elif}\;z \cdot 3 \leq 4.524571068069238 \cdot 10^{-86}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))