\[ \begin{array}{c}[a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \end{array} \]

\[\frac{a1 \cdot a2}{b1 \cdot b2} \]

↓

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -1.117539720539455 \cdot 10^{-304}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}\\ \mathbf{elif}\;t_0 \leq 9.809131235010281 \cdot 10^{+288}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

↓

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a1 b1) (/ a2 b2))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -1.117539720539455e-304)
       t_0
       (if (<= t_0 0.0)
         (* (/ a1 (* (cbrt b1) (cbrt b1))) (/ (/ a2 (cbrt b1)) b2))
         (if (<= t_0 9.809131235010281e+288) t_0 t_1))))))

double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

↓

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -1.117539720539455e-304) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / (cbrt(b1) * cbrt(b1))) * ((a2 / cbrt(b1)) / b2);
	} else if (t_0 <= 9.809131235010281e+288) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

↓

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a1 / b1) * (a2 / b2);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -1.117539720539455e-304) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = (a1 / (Math.cbrt(b1) * Math.cbrt(b1))) * ((a2 / Math.cbrt(b1)) / b2);
	} else if (t_0 <= 9.809131235010281e+288) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

↓

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a1 / b1) * Float64(a2 / b2))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -1.117539720539455e-304)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(Float64(a1 / Float64(cbrt(b1) * cbrt(b1))) * Float64(Float64(a2 / cbrt(b1)) / b2));
	elseif (t_0 <= 9.809131235010281e+288)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

↓

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a1 / b1), $MachinePrecision] * N[(a2 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -1.117539720539455e-304], t$95$0, If[LessEqual[t$95$0, 0.0], N[(N[(a1 / N[(N[Power[b1, 1/3], $MachinePrecision] * N[Power[b1, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a2 / N[Power[b1, 1/3], $MachinePrecision]), $MachinePrecision] / b2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 9.809131235010281e+288], t$95$0, t$95$1]]]]]]

\frac{a1 \cdot a2}{b1 \cdot b2}

↓

\begin{array}{l}
t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\
t_1 := \frac{a1}{b1} \cdot \frac{a2}{b2}\\
\mathbf{if}\;t_0 \leq -\infty:\\
\;\;\;\;t_1\\

\mathbf{elif}\;t_0 \leq -1.117539720539455 \cdot 10^{-304}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;t_0 \leq 0:\\
\;\;\;\;\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}\\

\mathbf{elif}\;t_0 \leq 9.809131235010281 \cdot 10^{+288}:\\
\;\;\;\;t_0\\

\mathbf{else}:\\
\;\;\;\;t_1\\


\end{array}

Original	11.2
Target	11.2
Herbie	2.2

Derivation

Split input into 3 regimes
if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or 9.80913123501028139e288 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))
1. Initial program 61.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
2. Applied times-frac_binary649.0
  \[\leadsto \color{blue}{\frac{a1}{b1} \cdot \frac{a2}{b2}} \]
if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.11753972053945503e-304 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 9.80913123501028139e288
1. Initial program 0.8
  \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
2. Applied associate-/r*_binary648.4
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}} \]
3. Applied *-un-lft-identity_binary648.4
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}} \]
4. Applied div-inv_binary648.4
  \[\leadsto \frac{\color{blue}{\left(a1 \cdot a2\right) \cdot \frac{1}{b1}}}{1 \cdot b2} \]
5. Applied times-frac_binary641.2
  \[\leadsto \color{blue}{\frac{a1 \cdot a2}{1} \cdot \frac{\frac{1}{b1}}{b2}} \]
6. Applied associate-*l/_binary641.2
  \[\leadsto \color{blue}{\frac{\left(a1 \cdot a2\right) \cdot \frac{\frac{1}{b1}}{b2}}{1}} \]
7. Simplified0.8
  \[\leadsto \frac{\color{blue}{\frac{a1 \cdot a2}{b2 \cdot b1}}}{1} \]
if -1.11753972053945503e-304 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0
1. Initial program 13.4
  \[\frac{a1 \cdot a2}{b1 \cdot b2} \]
2. Applied associate-/r*_binary646.1
  \[\leadsto \color{blue}{\frac{\frac{a1 \cdot a2}{b1}}{b2}} \]
3. Applied *-un-lft-identity_binary646.1
  \[\leadsto \frac{\frac{a1 \cdot a2}{b1}}{\color{blue}{1 \cdot b2}} \]
4. Applied add-cube-cbrt_binary646.2
  \[\leadsto \frac{\frac{a1 \cdot a2}{\color{blue}{\left(\sqrt[3]{b1} \cdot \sqrt[3]{b1}\right) \cdot \sqrt[3]{b1}}}}{1 \cdot b2} \]
5. Applied times-frac_binary643.4
  \[\leadsto \frac{\color{blue}{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}} \cdot \frac{a2}{\sqrt[3]{b1}}}}{1 \cdot b2} \]
6. Applied times-frac_binary642.4
  \[\leadsto \color{blue}{\frac{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}}{1} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}} \]
7. Simplified2.4
  \[\leadsto \color{blue}{\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}}} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2} \]
Recombined 3 regimes into one program.
Final simplification2.2
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -1.117539720539455 \cdot 10^{-304}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 0:\\ \;\;\;\;\frac{a1}{\sqrt[3]{b1} \cdot \sqrt[3]{b1}} \cdot \frac{\frac{a2}{\sqrt[3]{b1}}}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 9.809131235010281 \cdot 10^{+288}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{b1} \cdot \frac{a2}{b2}\\ \end{array} \]

Error

Try it out

Target

Derivation

`if (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < -inf.0 or 9.80913123501028139e288 < (/.f64 (.f64 a1 a2) (.f64 b1 b2))`

`if -inf.0 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < -1.11753972053945503e-304 or 0.0 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < 9.80913123501028139e288`

`if -1.11753972053945503e-304 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < 0.0`

Reproduce

In
Out

Error

Try it out

Target

Derivation

if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or 9.80913123501028139e288 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -1.11753972053945503e-304 or 0.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 9.80913123501028139e288

if -1.11753972053945503e-304 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 0.0

Reproduce

`if (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < -inf.0 or 9.80913123501028139e288 < (/.f64 (.f64 a1 a2) (.f64 b1 b2))`

`if -inf.0 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < -1.11753972053945503e-304 or 0.0 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < 9.80913123501028139e288`

`if -1.11753972053945503e-304 < (/.f64 (.f64 a1 a2) (.f64 b1 b2)) < 0.0`