Average Error: 7.3 → 0.3
Time: 4.4s
Precision: binary64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -0.00022260243656131037:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{elif}\;z \leq 2.998544093326645 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -0.00022260243656131037:\\
\;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\

\mathbf{elif}\;z \leq 2.998544093326645 \cdot 10^{+19}:\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

\mathbf{else}:\\
\;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= z -0.00022260243656131037)
   (* (* (cosh x) y) (/ (/ 1.0 x) z))
   (if (<= z 2.998544093326645e+19)
     (/ (/ (* (cosh x) y) z) x)
     (* (cosh x) (/ y (* z x))))))
double code(double x, double y, double z) {
	return (cosh(x) * (y / x)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.00022260243656131037) {
		tmp = (cosh(x) * y) * ((1.0 / x) / z);
	} else if (z <= 2.998544093326645e+19) {
		tmp = ((cosh(x) * y) / z) / x;
	} else {
		tmp = cosh(x) * (y / (z * x));
	}
	return tmp;
}

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

Original7.3
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y < 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.22602436561310371e-4

    1. Initial program 10.9

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied div-inv_binary64_1321711.0

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

    4. Applied associate-*r*_binary64_1316211.0

      \[\leadsto \frac{\color{blue}{\left(\cosh x \cdot y\right) \cdot \frac{1}{x}}}{z}\]
    5. Using strategy rm

    6. Applied *-un-lft-identity_binary64_1322011.0

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

    7. Applied times-frac_binary64_132260.4

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{1} \cdot \frac{\frac{1}{x}}{z}}\]

    8. Simplified0.4

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

    if -2.22602436561310371e-4 < z < 29985440933266448000

    1. Initial program 0.3

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied div-inv_binary64_132170.4

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

    5. Applied associate-*r/_binary64_131640.5

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{x}} \cdot \frac{1}{z}\]

    6. Applied associate-*l/_binary64_131650.4

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

    7. Simplified0.3

      \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{z}}}{x}\]

    if 29985440933266448000 < z

    1. Initial program 11.6

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied div-inv_binary64_1321711.7

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

    5. Applied associate-*l*_binary64_1316311.7

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

    6. Simplified0.3

      \[\leadsto \cosh x \cdot \color{blue}{\frac{y}{x \cdot z}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00022260243656131037:\\ \;\;\;\;\left(\cosh x \cdot y\right) \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{elif}\;z \leq 2.998544093326645 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020281 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.0385305359351529e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))