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

Percentage Accurate: 81.4% → 97.3%

Time: 2.8s

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: 81.4% 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: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-156}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) -2e+223)
   (* y (/ x z))
   (if (<= (/ y z) -2e-179)
     (/ x (/ z y))
     (if (<= (/ y z) 1e-156) (/ (* y x) z) (* (/ y z) x)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -2e+223) {
		tmp = y * (x / z);
	} else if ((y / z) <= -2e-179) {
		tmp = x / (z / y);
	} else if ((y / z) <= 1e-156) {
		tmp = (y * x) / z;
	} else {
		tmp = (y / z) * 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 / z) <= (-2d+223)) then
        tmp = y * (x / z)
    else if ((y / z) <= (-2d-179)) then
        tmp = x / (z / y)
    else if ((y / z) <= 1d-156) then
        tmp = (y * x) / z
    else
        tmp = (y / z) * 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 / z) <= -2e+223) {
		tmp = y * (x / z);
	} else if ((y / z) <= -2e-179) {
		tmp = x / (z / y);
	} else if ((y / z) <= 1e-156) {
		tmp = (y * x) / z;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -2e+223:
		tmp = y * (x / z)
	elif (y / z) <= -2e-179:
		tmp = x / (z / y)
	elif (y / z) <= 1e-156:
		tmp = (y * x) / z
	else:
		tmp = (y / z) * x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y / z) <= -2e+223)
		tmp = Float64(y * Float64(x / z));
	elseif (Float64(y / z) <= -2e-179)
		tmp = Float64(x / Float64(z / y));
	elseif (Float64(y / z) <= 1e-156)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(Float64(y / z) * 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 / z) <= -2e+223)
		tmp = y * (x / z);
	elseif ((y / z) <= -2e-179)
		tmp = x / (z / y);
	elseif ((y / z) <= 1e-156)
		tmp = (y * x) / z;
	else
		tmp = (y / z) * 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[N[(y / z), $MachinePrecision], -2e+223], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], -2e-179], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 1e-156], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 y z) < -2.00000000000000009e223

   1. Initial program 56.7%

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

      1. associate-/l* 69.7%

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

      2. associate-*r/ 69.7%

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

      3. *-commutative 69.7%

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

      4. *-inverses 69.7%

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

      5. /-rgt-identity 69.7%

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

      6. associate-*l/ 99.9%

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

      7. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   if -2.00000000000000009e223 < (/.f64 y z) < -2e-179

   1. Initial program 91.7%

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

      1. associate-/l* 99.6%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. *-inverses 99.6%

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

      5. /-rgt-identity 99.6%

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

      6. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 86.8%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   if -2e-179 < (/.f64 y z) < 1.00000000000000004e-156

   1. Initial program 71.3%

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

      1. associate-/l* 81.2%

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

      2. associate-*r/ 81.2%

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

      3. *-commutative 81.2%

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

      4. *-inverses 81.2%

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

      5. /-rgt-identity 81.2%

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

      6. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in x around 0 98.5%

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

   if 1.00000000000000004e-156 < (/.f64 y z)

   1. Initial program 85.9%

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

      1. associate-/l* 97.7%

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

      2. associate-*r/ 97.7%

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

      3. *-commutative 97.7%

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

      4. *-inverses 97.7%

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

      5. /-rgt-identity 97.7%

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

      6. *-commutative 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-156}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 2: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+221} \lor \neg \left(\frac{y}{z} \leq -5 \cdot 10^{-168}\right) \land \frac{y}{z} \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -1e+221)
         (and (not (<= (/ y z) -5e-168)) (<= (/ y z) 0.0)))
   (* y (/ x z))
   (* (/ y z) x)))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -1e+221) || (!((y / z) <= -5e-168) && ((y / z) <= 0.0))) {
		tmp = y * (x / z);
	} else {
		tmp = (y / z) * 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 / z) <= (-1d+221)) .or. (.not. ((y / z) <= (-5d-168))) .and. ((y / z) <= 0.0d0)) then
        tmp = y * (x / z)
    else
        tmp = (y / z) * 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 / z) <= -1e+221) || (!((y / z) <= -5e-168) && ((y / z) <= 0.0))) {
		tmp = y * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -1e+221) or (not ((y / z) <= -5e-168) and ((y / z) <= 0.0)):
		tmp = y * (x / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y / z) <= -1e+221) || (!(Float64(y / z) <= -5e-168) && (Float64(y / z) <= 0.0)))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * 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 / z) <= -1e+221) || (~(((y / z) <= -5e-168)) && ((y / z) <= 0.0)))
		tmp = y * (x / z);
	else
		tmp = (y / z) * 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[Or[LessEqual[N[(y / z), $MachinePrecision], -1e+221], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -5e-168]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 0.0]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -1e221 or -5.00000000000000001e-168 < (/.f64 y z) < -0.0

   1. Initial program 65.9%

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

      1. associate-/l* 74.5%

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

      2. associate-*r/ 74.5%

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

      3. *-commutative 74.5%

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

      4. *-inverses 74.5%

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

      5. /-rgt-identity 74.5%

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

      6. associate-*l/ 98.6%

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

      7. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   if -1e221 < (/.f64 y z) < -5.00000000000000001e-168 or -0.0 < (/.f64 y z)

   1. Initial program 87.5%

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

      1. associate-/l* 98.5%

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

      2. associate-*r/ 98.5%

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

      3. *-commutative 98.5%

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

      4. *-inverses 98.5%

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

      5. /-rgt-identity 98.5%

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

      6. *-commutative 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+221} \lor \neg \left(\frac{y}{z} \leq -5 \cdot 10^{-168}\right) \land \frac{y}{z} \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 3: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 0:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= (/ y z) -2e+223)
     t_1
     (if (<= (/ y z) -5e-168)
       (/ x (/ z y))
       (if (<= (/ y z) 0.0) t_1 (* (/ y z) x))))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if ((y / z) <= -2e+223) {
		tmp = t_1;
	} else if ((y / z) <= -5e-168) {
		tmp = x / (z / y);
	} else if ((y / z) <= 0.0) {
		tmp = t_1;
	} else {
		tmp = (y / z) * 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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / z)
    if ((y / z) <= (-2d+223)) then
        tmp = t_1
    else if ((y / z) <= (-5d-168)) then
        tmp = x / (z / y)
    else if ((y / z) <= 0.0d0) then
        tmp = t_1
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if ((y / z) <= -2e+223) {
		tmp = t_1;
	} else if ((y / z) <= -5e-168) {
		tmp = x / (z / y);
	} else if ((y / z) <= 0.0) {
		tmp = t_1;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if (y / z) <= -2e+223:
		tmp = t_1
	elif (y / z) <= -5e-168:
		tmp = x / (z / y)
	elif (y / z) <= 0.0:
		tmp = t_1
	else:
		tmp = (y / z) * x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (Float64(y / z) <= -2e+223)
		tmp = t_1;
	elseif (Float64(y / z) <= -5e-168)
		tmp = Float64(x / Float64(z / y));
	elseif (Float64(y / z) <= 0.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if ((y / z) <= -2e+223)
		tmp = t_1;
	elseif ((y / z) <= -5e-168)
		tmp = x / (z / y);
	elseif ((y / z) <= 0.0)
		tmp = t_1;
	else
		tmp = (y / z) * 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_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y / z), $MachinePrecision], -2e+223], t$95$1, If[LessEqual[N[(y / z), $MachinePrecision], -5e-168], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 0.0], t$95$1, N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -2.00000000000000009e223 or -5.00000000000000001e-168 < (/.f64 y z) < -0.0

   1. Initial program 65.5%

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

      1. associate-/l* 74.2%

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

      2. associate-*r/ 74.2%

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

      3. *-commutative 74.2%

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

      4. *-inverses 74.2%

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

      5. /-rgt-identity 74.2%

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

      6. associate-*l/ 98.6%

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

      7. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   if -2.00000000000000009e223 < (/.f64 y z) < -5.00000000000000001e-168

   1. Initial program 91.5%

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

      1. associate-/l* 99.6%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. *-inverses 99.6%

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

      5. /-rgt-identity 99.6%

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

      6. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 87.7%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   if -0.0 < (/.f64 y z)

   1. Initial program 85.0%

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

      1. associate-/l* 97.8%

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

      2. associate-*r/ 97.8%

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

      3. *-commutative 97.8%

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

      4. *-inverses 97.8%

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

      5. /-rgt-identity 97.8%

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

      6. *-commutative 97.8%

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

   3. Simplified 97.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 4: 92.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 = (y / z) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. associate-/l* 91.2%

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

   2. associate-*r/ 91.2%

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

   3. *-commutative 91.2%

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

   4. *-inverses 91.2%

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

   5. /-rgt-identity 91.2%

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

   6. *-commutative 91.2%

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

3. Simplified 91.2%

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

4. Final simplification 91.2%

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

Developer target: 98.2% 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 2023271 
(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)))