Average Error: 9.8 → 0.5
Time: 3.4s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} = -inf.0:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 5.89657563244339658 \cdot 10^{300}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{3}}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} = -inf.0:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 5.89657563244339658 \cdot 10^{300}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{3}}}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z)) <= -inf.0)) {
		VAR = ((double) (x / ((double) (z / ((double) (((double) (y - z)) + 1.0))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z)) <= 5.896575632443397e+300)) {
			VAR_1 = ((double) (((double) (((double) (((double) (x * y)) / z)) + ((double) (1.0 * ((double) (x / z)))))) - x));
		} else {
			VAR_1 = ((double) (x / ((double) cbrt(((double) pow(((double) (z / ((double) (((double) (y - z)) + 1.0)))), 3.0))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.8
Target0.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -inf.0

    1. Initial program 64.0

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

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

    if -inf.0 < (/ (* x (+ (- y z) 1.0)) z) < 5.896575632443397e+300

    1. Initial program 0.1

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

    2. Taylor expanded around 0 0.1

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

    if 5.896575632443397e+300 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 60.8

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.8

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied add-cbrt-cube58.5

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

    6. Applied add-cbrt-cube59.6

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

    7. Applied cbrt-undiv59.7

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

    8. Simplified5.1

      \[\leadsto \frac{x}{\sqrt[3]{\color{blue}{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{3}}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} = -inf.0:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 5.89657563244339658 \cdot 10^{300}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{z}{\left(y - z\right) + 1}\right)}^{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))