Average Error: 15.1 → 2.1

Time: 3.7s

Precision: binary64

Cost: 1101

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{-231} \lor \neg \left(\frac{y}{z} \leq 2 \cdot 10^{-290}\right) \land \frac{y}{z} \leq 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

(FPCore (x y z t) :precision binary64 (* x (/ (* (/ y z) t) t)))

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -1e-231)
         (and (not (<= (/ y z) 2e-290)) (<= (/ y z) 1e+152)))
   (/ x (/ z y))
   (* y (/ x z))))

double code(double x, double y, double z, double t) {
	return x * (((y / z) * t) / t);
}

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -1e-231) || (!((y / z) <= 2e-290) && ((y / z) <= 1e+152))) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * (((y / z) * t) / t)
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y / z) <= (-1d-231)) .or. (.not. ((y / z) <= 2d-290)) .and. ((y / z) <= 1d+152)) then
        tmp = x / (z / y)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

public static double code(double x, double y, double z, double t) {
	return x * (((y / z) * t) / t);
}

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -1e-231) || (!((y / z) <= 2e-290) && ((y / z) <= 1e+152))) {
		tmp = x / (z / y);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

def code(x, y, z, t):
	return x * (((y / z) * t) / t)

↓

def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -1e-231) or (not ((y / z) <= 2e-290) and ((y / z) <= 1e+152)):
		tmp = x / (z / y)
	else:
		tmp = y * (x / z)
	return tmp

function code(x, y, z, t)
	return Float64(x * Float64(Float64(Float64(y / z) * t) / t))
end

↓

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y / z) <= -1e-231) || (!(Float64(y / z) <= 2e-290) && (Float64(y / z) <= 1e+152)))
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

function tmp = code(x, y, z, t)
	tmp = x * (((y / z) * t) / t);
end

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y / z) <= -1e-231) || (~(((y / z) <= 2e-290)) && ((y / z) <= 1e+152)))
		tmp = x / (z / y);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

code[x_, y_, z_, t_] := N[(x * N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y / z), $MachinePrecision], -1e-231], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], 2e-290]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 1e+152]]], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

x \cdot \frac{\frac{y}{z} \cdot t}{t}

↓

\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{-231} \lor \neg \left(\frac{y}{z} \leq 2 \cdot 10^{-290}\right) \land \frac{y}{z} \leq 10^{+152}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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


\end{array}

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	15.1
Target	1.6
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Derivation

Split input into 2 regimes

`if (/.f64 y z) < -9.9999999999999999e-232 or 2.0000000000000001e-290 < (/.f64 y z) < 1e152`

Initial program 11.5
\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

Simplified2.8

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

Proof

[Start]11.5	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
associate-/l* [=>]2.8	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
*-inverses [=>]2.8	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
/-rgt-identity [=>]2.8	\[ x \cdot \color{blue}{\frac{y}{z}} \]

Applied egg-rr2.6
\[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

`if -9.9999999999999999e-232 < (/.f64 y z) < 2.0000000000000001e-290 or 1e152 < (/.f64 y z)`

Initial program 23.9
\[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]

Simplified0.9

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

Proof

[Start]23.9	\[ x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
associate-/l* [=>]16.0	\[ x \cdot \color{blue}{\frac{\frac{y}{z}}{\frac{t}{t}}} \]
*-inverses [=>]16.0	\[ x \cdot \frac{\frac{y}{z}}{\color{blue}{1}} \]
/-rgt-identity [=>]16.0	\[ x \cdot \color{blue}{\frac{y}{z}} \]
associate-*r/ [=>]1.0	\[ \color{blue}{\frac{x \cdot y}{z}} \]
associate-*l/ [<=]0.9	\[ \color{blue}{\frac{x}{z} \cdot y} \]
*-commutative [<=]0.9	\[ \color{blue}{y \cdot \frac{x}{z}} \]

Recombined 2 regimes into one program.
Final simplification2.1
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{-231} \lor \neg \left(\frac{y}{z} \leq 2 \cdot 10^{-290}\right) \land \frac{y}{z} \leq 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	2.3
Cost	1101

\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{-231} \lor \neg \left(\frac{y}{z} \leq 0\right) \land \frac{y}{z} \leq 10^{+152}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2
Error	6.7
Cost	320

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

Reproduce

herbie shell --seed 2022356 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))