Average Error: 3.7 → 1.1
Time: 4.6s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.11239943139134638 \cdot 10^{-76}:\\ \;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;t \le 2.5459723469470038 \cdot 10^{-216}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.11239943139134638 \cdot 10^{-76}:\\
\;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\

\mathbf{elif}\;t \le 2.5459723469470038 \cdot 10^{-216}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (t / ((double) (((double) (z * 3.0)) * y))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((t <= -1.1123994313913464e-76)) {
		VAR = ((double) (((double) (x - ((double) (y * ((double) (1.0 / ((double) (z * 3.0)))))))) + ((double) (t / ((double) (((double) (z * 3.0)) * y))))));
	} else {
		double VAR_1;
		if ((t <= 2.5459723469470038e-216)) {
			VAR_1 = ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (((double) (1.0 / ((double) (z * 3.0)))) * ((double) (t / y))))));
		} else {
			VAR_1 = ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (((double) (t / z)) / ((double) (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
Target1.8
Herbie1.1
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.1123994313913464e-76

    1. Initial program 0.8

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

    3. Applied div-inv0.8

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

    if -1.1123994313913464e-76 < t < 2.5459723469470038e-216

    1. Initial program 7.0

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

    3. Applied *-un-lft-identity7.0

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

    4. Applied times-frac0.2

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

    if 2.5459723469470038e-216 < t

    1. Initial program 3.1

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

    3. Applied associate-*l*3.1

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

    5. Applied associate-/r*2.0

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.11239943139134638 \cdot 10^{-76}:\\ \;\;\;\;\left(x - y \cdot \frac{1}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;t \le 2.5459723469470038 \cdot 10^{-216}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z \cdot 3} \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(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))))