Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B

Percentage Accurate: 81.7% → 92.8%

Time: 5.8s

Alternatives: 4

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ x \cdot \frac{\frac{y}{z} \cdot t}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{\frac{y}{z} \cdot t}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := {\left(\sqrt[3]{z}\right)}^{2}\\ \mathbf{if}\;z \leq 2.45 \cdot 10^{-231}:\\ \;\;\;\;\frac{\frac{\frac{x}{\frac{t_1}{y}}}{\sqrt[3]{t_1}}}{\sqrt[3]{\sqrt[3]{z}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (pow (cbrt z) 2.0)))
   (if (<= z 2.45e-231)
     (/ (/ (/ x (/ t_1 y)) (cbrt t_1)) (cbrt (cbrt z)))
     (* x (/ y z)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double t_1 = pow(cbrt(z), 2.0);
	double tmp;
	if (z <= 2.45e-231) {
		tmp = ((x / (t_1 / y)) / cbrt(t_1)) / cbrt(cbrt(z));
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.pow(Math.cbrt(z), 2.0);
	double tmp;
	if (z <= 2.45e-231) {
		tmp = ((x / (t_1 / y)) / Math.cbrt(t_1)) / Math.cbrt(Math.cbrt(z));
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	t_1 = cbrt(z) ^ 2.0
	tmp = 0.0
	if (z <= 2.45e-231)
		tmp = Float64(Float64(Float64(x / Float64(t_1 / y)) / cbrt(t_1)) / cbrt(cbrt(z)));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Power[N[Power[z, 1/3], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[z, 2.45e-231], N[(N[(N[(x / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[Power[t$95$1, 1/3], $MachinePrecision]), $MachinePrecision] / N[Power[N[Power[z, 1/3], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 2.45000000000000002e-231

   1. Initial program 84.2%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 92.6%

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

      2. associate-*r/ 92.6%

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

      3. *-commutative 92.6%

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

      4. *-inverses 92.6%

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

      5. /-rgt-identity 92.6%

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

      6. *-commutative 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-*r/ 92.8%

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

      2. add-cube-cbrt 91.7%

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

      3. associate-/r* 91.7%

         \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}} \]

      4. add-cube-cbrt 91.6%

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

      5. cbrt-prod 91.5%

         \[\leadsto \frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\color{blue}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}}} \]

      6. associate-/r* 91.6%

         \[\leadsto \color{blue}{\frac{\frac{\frac{x \cdot y}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}}} \]

      7. associate-/l* 94.8%

         \[\leadsto \frac{\frac{\color{blue}{\frac{x}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{y}}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}} \]

      8. pow2 94.8%

         \[\leadsto \frac{\frac{\frac{x}{\frac{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}{y}}}{\sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{\sqrt[3]{z}}} \]

      9. pow2 94.8%

         \[\leadsto \frac{\frac{\frac{x}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{y}}}{\sqrt[3]{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}}}{\sqrt[3]{\sqrt[3]{z}}} \]

   5. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{y}}}{\sqrt[3]{{\left(\sqrt[3]{z}\right)}^{2}}}}{\sqrt[3]{\sqrt[3]{z}}}} \]

   if 2.45000000000000002e-231 < z

   1. Initial program 83.0%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.2%

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

      2. associate-*r/ 96.2%

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

      3. *-commutative 96.2%

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

      4. *-inverses 96.2%

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

      5. /-rgt-identity 96.2%

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

      6. *-commutative 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.45 \cdot 10^{-231}:\\ \;\;\;\;\frac{\frac{\frac{x}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{y}}}{\sqrt[3]{{\left(\sqrt[3]{z}\right)}^{2}}}}{\sqrt[3]{\sqrt[3]{z}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 2: 93.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{y}}{\frac{1}{x} \cdot \frac{z}{\sqrt{y}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 6e-246) (* x (/ y z)) (/ (sqrt y) (* (/ 1.0 x) (/ z (sqrt y))))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e-246) {
		tmp = x * (y / z);
	} else {
		tmp = sqrt(y) / ((1.0 / x) * (z / sqrt(y)));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this 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 <= 6d-246) then
        tmp = x * (y / z)
    else
        tmp = sqrt(y) / ((1.0d0 / x) * (z / sqrt(y)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6e-246) {
		tmp = x * (y / z);
	} else {
		tmp = Math.sqrt(y) / ((1.0 / x) * (z / Math.sqrt(y)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if y <= 6e-246:
		tmp = x * (y / z)
	else:
		tmp = math.sqrt(y) / ((1.0 / x) * (z / math.sqrt(y)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6e-246)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(sqrt(y) / Float64(Float64(1.0 / x) * Float64(z / sqrt(y))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6e-246)
		tmp = x * (y / z);
	else
		tmp = sqrt(y) / ((1.0 / x) * (z / sqrt(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 6e-246], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[y], $MachinePrecision] / N[(N[(1.0 / x), $MachinePrecision] * N[(z / N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6e-246

   1. Initial program 82.4%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.1%

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

      2. associate-*r/ 94.1%

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

      3. *-commutative 94.1%

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

      4. *-inverses 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   if 6e-246 < y

   1. Initial program 85.2%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.1%

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

      2. associate-*r/ 94.1%

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

      3. *-commutative 94.1%

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

      4. *-inverses 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. *-commutative 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. clear-num 94.0%

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

      2. un-div-inv 94.2%

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

   5. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   6. Step-by-step derivation

      1. associate-/l* 94.2%

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

      2. div-inv 94.1%

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

      3. *-commutative 94.1%

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

   7. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(x \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*l/ 94.2%

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

      2. *-un-lft-identity 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-/l* 94.3%

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

      5. div-inv 94.2%

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

      6. associate-/r* 94.1%

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

      7. add-sqr-sqrt 93.7%

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

      8. associate-/l* 93.8%

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

      9. associate-/l/ 95.3%

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

   9. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\frac{\sqrt{y}}{\frac{1}{x} \cdot \frac{z}{\sqrt{y}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{y}}{\frac{1}{x} \cdot \frac{z}{\sqrt{y}}}\\ \end{array} \]

Alternative 3: 93.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{y}}{\frac{\frac{z}{\sqrt{y}}}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.65e-250) (* x (/ y z)) (/ (sqrt y) (/ (/ z (sqrt y)) x))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.65e-250) {
		tmp = x * (y / z);
	} else {
		tmp = sqrt(y) / ((z / sqrt(y)) / x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this 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 <= 1.65d-250) then
        tmp = x * (y / z)
    else
        tmp = sqrt(y) / ((z / sqrt(y)) / x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.65e-250) {
		tmp = x * (y / z);
	} else {
		tmp = Math.sqrt(y) / ((z / Math.sqrt(y)) / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if y <= 1.65e-250:
		tmp = x * (y / z)
	else:
		tmp = math.sqrt(y) / ((z / math.sqrt(y)) / x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.65e-250)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(sqrt(y) / Float64(Float64(z / sqrt(y)) / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.65e-250)
		tmp = x * (y / z);
	else
		tmp = sqrt(y) / ((z / sqrt(y)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 1.65e-250], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[y], $MachinePrecision] / N[(N[(z / N[Sqrt[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.65e-250

   1. Initial program 82.3%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.1%

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

      2. associate-*r/ 94.1%

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

      3. *-commutative 94.1%

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

      4. *-inverses 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   if 1.65e-250 < y

   1. Initial program 85.3%

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.1%

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

      2. associate-*r/ 94.1%

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

      3. *-commutative 94.1%

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

      4. *-inverses 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. *-commutative 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. clear-num 94.0%

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

      2. un-div-inv 94.2%

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

   5. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]
   6. Step-by-step derivation

      1. associate-/l* 94.3%

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

      2. div-inv 94.1%

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

      3. *-commutative 94.1%

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

   7. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(x \cdot y\right)} \]
   8. Step-by-step derivation

      1. associate-*l/ 94.3%

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

      2. *-un-lft-identity 94.3%

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

      3. *-commutative 94.3%

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

      4. associate-/l* 94.3%

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

      5. div-inv 94.2%

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

      6. associate-/r* 94.1%

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

      7. add-sqr-sqrt 93.8%

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

      8. associate-/l* 93.8%

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

      9. associate-/l/ 95.3%

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

   9. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\frac{\sqrt{y}}{\frac{1}{x} \cdot \frac{z}{\sqrt{y}}}} \]
   10. Step-by-step derivation

       1. associate-*l/ 95.4%

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

       2. *-un-lft-identity 95.4%

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

   11. Applied egg-rr 95.4%

       \[\leadsto \frac{\sqrt{y}}{\color{blue}{\frac{\frac{z}{\sqrt{y}}}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{y}}{\frac{\frac{z}{\sqrt{y}}}{x}}\\ \end{array} \]

Alternative 4: 92.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \cdot \frac{y}{z} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* x (/ y z)))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this 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
    code = x * (y / z)
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	return x * (y / z)

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	return Float64(x * Float64(y / z))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t)
	tmp = x * (y / z);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

   \[x \cdot \frac{\frac{y}{z} \cdot t}{t} \]
2. Step-by-step derivation

   1. associate-/l* 94.1%

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

   2. associate-*r/ 94.1%

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

   3. *-commutative 94.1%

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

   4. *-inverses 94.1%

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

   5. /-rgt-identity 94.1%

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

   6. *-commutative 94.1%

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

3. Simplified 94.1%

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

4. Final simplification 94.1%

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

Developer target: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := \frac{\frac{y}{z} \cdot t}{t}\\ t_3 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;t_2 < -1.20672205123045 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 < -5.907522236933906 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 5.658954423153415 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 < 2.0087180502407133 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (/ (* (/ y z) t) t)) (t_3 (/ y (/ z x))))
   (if (< t_2 -1.20672205123045e+245)
     t_3
     (if (< t_2 -5.907522236933906e-275)
       t_1
       (if (< t_2 5.658954423153415e-65)
         t_3
         (if (< t_2 2.0087180502407133e+217) t_1 (/ (* y x) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = ((y / z) * t) / t;
	double t_3 = y / (z / x);
	double tmp;
	if (t_2 < -1.20672205123045e+245) {
		tmp = t_3;
	} else if (t_2 < -5.907522236933906e-275) {
		tmp = t_1;
	} else if (t_2 < 5.658954423153415e-65) {
		tmp = t_3;
	} else if (t_2 < 2.0087180502407133e+217) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Fortran

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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = ((y / z) * t) / t
    t_3 = y / (z / x)
    if (t_2 < (-1.20672205123045d+245)) then
        tmp = t_3
    else if (t_2 < (-5.907522236933906d-275)) then
        tmp = t_1
    else if (t_2 < 5.658954423153415d-65) then
        tmp = t_3
    else if (t_2 < 2.0087180502407133d+217) then
        tmp = t_1
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = ((y / z) * t) / t;
	double t_3 = y / (z / x);
	double tmp;
	if (t_2 < -1.20672205123045e+245) {
		tmp = t_3;
	} else if (t_2 < -5.907522236933906e-275) {
		tmp = t_1;
	} else if (t_2 < 5.658954423153415e-65) {
		tmp = t_3;
	} else if (t_2 < 2.0087180502407133e+217) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	t_2 = ((y / z) * t) / t
	t_3 = y / (z / x)
	tmp = 0
	if t_2 < -1.20672205123045e+245:
		tmp = t_3
	elif t_2 < -5.907522236933906e-275:
		tmp = t_1
	elif t_2 < 5.658954423153415e-65:
		tmp = t_3
	elif t_2 < 2.0087180502407133e+217:
		tmp = t_1
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(Float64(Float64(y / z) * t) / t)
	t_3 = Float64(y / Float64(z / x))
	tmp = 0.0
	if (t_2 < -1.20672205123045e+245)
		tmp = t_3;
	elseif (t_2 < -5.907522236933906e-275)
		tmp = t_1;
	elseif (t_2 < 5.658954423153415e-65)
		tmp = t_3;
	elseif (t_2 < 2.0087180502407133e+217)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	t_2 = ((y / z) * t) / t;
	t_3 = y / (z / x);
	tmp = 0.0;
	if (t_2 < -1.20672205123045e+245)
		tmp = t_3;
	elseif (t_2 < -5.907522236933906e-275)
		tmp = t_1;
	elseif (t_2 < 5.658954423153415e-65)
		tmp = t_3;
	elseif (t_2 < 2.0087180502407133e+217)
		tmp = t_1;
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y / z), $MachinePrecision] * t), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.20672205123045e+245], t$95$3, If[Less[t$95$2, -5.907522236933906e-275], t$95$1, If[Less[t$95$2, 5.658954423153415e-65], t$95$3, If[Less[t$95$2, 2.0087180502407133e+217], t$95$1, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]]]

Reproduce

herbie shell --seed 2023301 
(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)))