Average Error: 5.8 → 1.0
Time: 2.3s
Precision: binary64
Cost: 2000
\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]
\[\frac{x \cdot y}{z} \]
↓
\[\begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t_0 \leq -4 \cdot 10^{-247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\ \end{array} \]
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z)))
   (if (<= t_0 (- INFINITY))
     (/ y (/ z x))
     (if (<= t_0 -4e-247)
       t_0
       (if (<= t_0 5e-284)
         (/ x (/ z y))
         (if (<= t_0 5e+301) t_0 (* y (* x (/ 1.0 z)))))))))
double code(double x, double y, double z) {
	return (x * y) / z;
}
↓
double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y / (z / x);
	} else if (t_0 <= -4e-247) {
		tmp = t_0;
	} else if (t_0 <= 5e-284) {
		tmp = x / (z / y);
	} else if (t_0 <= 5e+301) {
		tmp = t_0;
	} else {
		tmp = y * (x * (1.0 / z));
	}
	return tmp;
}

public static double code(double x, double y, double z) {
	return (x * y) / z;
}
↓
public static double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (z / x);
	} else if (t_0 <= -4e-247) {
		tmp = t_0;
	} else if (t_0 <= 5e-284) {
		tmp = x / (z / y);
	} else if (t_0 <= 5e+301) {
		tmp = t_0;
	} else {
		tmp = y * (x * (1.0 / z));
	}
	return tmp;
}

def code(x, y, z):
	return (x * y) / z
↓
def code(x, y, z):
	t_0 = (x * y) / z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y / (z / x)
	elif t_0 <= -4e-247:
		tmp = t_0
	elif t_0 <= 5e-284:
		tmp = x / (z / y)
	elif t_0 <= 5e+301:
		tmp = t_0
	else:
		tmp = y * (x * (1.0 / z))
	return tmp

function code(x, y, z)
	return Float64(Float64(x * y) / z)
end
↓
function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y / Float64(z / x));
	elseif (t_0 <= -4e-247)
		tmp = t_0;
	elseif (t_0 <= 5e-284)
		tmp = Float64(x / Float64(z / y));
	elseif (t_0 <= 5e+301)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x * Float64(1.0 / z)));
	end
	return tmp
end

function tmp = code(x, y, z)
	tmp = (x * y) / z;
end
↓
function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = y / (z / x);
	elseif (t_0 <= -4e-247)
		tmp = t_0;
	elseif (t_0 <= 5e-284)
		tmp = x / (z / y);
	elseif (t_0 <= 5e+301)
		tmp = t_0;
	else
		tmp = y * (x * (1.0 / z));
	end
	tmp_2 = tmp;
end

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]
↓
code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -4e-247], t$95$0, If[LessEqual[t$95$0, 5e-284], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+301], t$95$0, N[(y * N[(x * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

\frac{x \cdot y}{z}
↓
\begin{array}{l}
t_0 := \frac{x \cdot y}{z}\\
\mathbf{if}\;t_0 \leq -\infty:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\mathbf{elif}\;t_0 \leq -4 \cdot 10^{-247}:\\
\;\;\;\;t_0\\

\mathbf{elif}\;t_0 \leq 5 \cdot 10^{-284}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;t_0 \leq 5 \cdot 10^{+301}:\\
\;\;\;\;t_0\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target6.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]

Derivation

  1. Split input into 4 regimes

  2. if (/.f64 (*.f64 x y) z) < -inf.0

    1. Initial program 64.0

      \[\frac{x \cdot y}{z} \]

    2. Simplified0.3

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

    3. Taylor expanded in x around 0 64.0

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

    4. Simplified0.2

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

    5. Applied egg-rr0.3

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

    if -inf.0 < (/.f64 (*.f64 x y) z) < -4.0000000000000001e-247 or 4.99999999999999973e-284 < (/.f64 (*.f64 x y) z) < 5.0000000000000004e301

    1. Initial program 0.5

      \[\frac{x \cdot y}{z} \]

    if -4.0000000000000001e-247 < (/.f64 (*.f64 x y) z) < 4.99999999999999973e-284

    1. Initial program 8.9

      \[\frac{x \cdot y}{z} \]

    2. Simplified1.9

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

    3. Applied egg-rr2.0

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

    if 5.0000000000000004e301 < (/.f64 (*.f64 x y) z)

    1. Initial program 58.5

      \[\frac{x \cdot y}{z} \]

    2. Applied egg-rr3.3

      \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{1}{z}\right)} \]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq -4 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error1.0
Cost1872
\[\begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ t_1 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -4 \cdot 10^{-247}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error6.1
Cost584
\[\begin{array}{l} t_0 := \frac{x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq 10^{+153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+218}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error6.4
Cost320
\[\frac{y}{\frac{z}{x}} \]

Error

Reproduce

herbie shell --seed 2022217 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))