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

Percentage Accurate: 81.4% → 98.9%

Time: 3.5s

Alternatives: 5

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: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-150} \lor \neg \left(\frac{y}{z} \leq 0\right) \land \frac{y}{z} \leq 4 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

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) -5e+166)
   (* y (/ x z))
   (if (or (<= (/ y z) -5e-150)
           (and (not (<= (/ y z) 0.0)) (<= (/ y z) 4e+168)))
     (/ x (/ z y))
     (/ y (/ z x)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -5e+166) {
		tmp = y * (x / z);
	} else if (((y / z) <= -5e-150) || (!((y / z) <= 0.0) && ((y / z) <= 4e+168))) {
		tmp = x / (z / y);
	} 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) <= (-5d+166)) then
        tmp = y * (x / z)
    else if (((y / z) <= (-5d-150)) .or. (.not. ((y / z) <= 0.0d0)) .and. ((y / z) <= 4d+168)) then
        tmp = x / (z / y)
    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) <= -5e+166) {
		tmp = y * (x / z);
	} else if (((y / z) <= -5e-150) || (!((y / z) <= 0.0) && ((y / z) <= 4e+168))) {
		tmp = x / (z / y);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -5e+166:
		tmp = y * (x / z)
	elif ((y / z) <= -5e-150) or (not ((y / z) <= 0.0) and ((y / z) <= 4e+168)):
		tmp = x / (z / y)
	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) <= -5e+166)
		tmp = Float64(y * Float64(x / z));
	elseif ((Float64(y / z) <= -5e-150) || (!(Float64(y / z) <= 0.0) && (Float64(y / z) <= 4e+168)))
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(y / Float64(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) <= -5e+166)
		tmp = y * (x / z);
	elseif (((y / z) <= -5e-150) || (~(((y / z) <= 0.0)) && ((y / z) <= 4e+168)))
		tmp = x / (z / y);
	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], -5e+166], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], -5e-150], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], 0.0]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 4e+168]]], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -5.0000000000000002e166

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-/l* 90.9%

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

      3. *-inverses 90.9%

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

      4. /-rgt-identity 90.9%

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

      5. associate-*l/ 96.7%

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

      6. 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 -5.0000000000000002e166 < (/.f64 y z) < -4.9999999999999999e-150 or -0.0 < (/.f64 y z) < 3.9999999999999997e168

   1. Initial program 86.6%

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

      1. associate-/l* 99.6%

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

      2. *-inverses 99.6%

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

      3. /-rgt-identity 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -4.9999999999999999e-150 < (/.f64 y z) < -0.0 or 3.9999999999999997e168 < (/.f64 y z)

   1. Initial program 77.5%

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

      1. associate-/l* 84.2%

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

      2. *-inverses 84.2%

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

      3. /-rgt-identity 84.2%

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

   3. Simplified 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*l/ 99.3%

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

      3. associate-/l* 99.3%

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

   5. Applied egg-rr 99.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-150} \lor \neg \left(\frac{y}{z} \leq 0\right) \land \frac{y}{z} \leq 4 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 2: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+152} \lor \neg \left(\frac{y}{z} \leq -5 \cdot 10^{-286} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-293}\right) \land \frac{y}{z} \leq 5 \cdot 10^{+137}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -2e+152)
         (not
          (or (<= (/ y z) -5e-286)
              (and (not (<= (/ y z) 5e-293)) (<= (/ y z) 5e+137)))))
   (* y (/ x z))
   (* x (/ y z))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -2e+152) || !(((y / z) <= -5e-286) || (!((y / z) <= 5e-293) && ((y / z) <= 5e+137)))) {
		tmp = y * (x / z);
	} else {
		tmp = x * (y / z);
	}
	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+152)) .or. (.not. ((y / z) <= (-5d-286)) .or. (.not. ((y / z) <= 5d-293)) .and. ((y / z) <= 5d+137))) then
        tmp = y * (x / z)
    else
        tmp = x * (y / z)
    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+152) || !(((y / z) <= -5e-286) || (!((y / z) <= 5e-293) && ((y / z) <= 5e+137)))) {
		tmp = y * (x / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -2e+152) or not (((y / z) <= -5e-286) or (not ((y / z) <= 5e-293) and ((y / z) <= 5e+137))):
		tmp = y * (x / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y / z) <= -2e+152) || !((Float64(y / z) <= -5e-286) || (!(Float64(y / z) <= 5e-293) && (Float64(y / z) <= 5e+137))))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(y / z));
	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+152) || ~((((y / z) <= -5e-286) || (~(((y / z) <= 5e-293)) && ((y / z) <= 5e+137)))))
		tmp = y * (x / z);
	else
		tmp = x * (y / z);
	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], -2e+152], N[Not[Or[LessEqual[N[(y / z), $MachinePrecision], -5e-286], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], 5e-293]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e+137]]]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -2.0000000000000001e152 or -5.00000000000000037e-286 < (/.f64 y z) < 5.0000000000000003e-293 or 5.0000000000000002e137 < (/.f64 y z)

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-/l* 84.9%

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

      3. *-inverses 84.9%

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

      4. /-rgt-identity 84.9%

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

      5. associate-*l/ 98.9%

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

      6. associate-*r/ 99.0%

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

   3. Simplified 99.0%

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

   if -2.0000000000000001e152 < (/.f64 y z) < -5.00000000000000037e-286 or 5.0000000000000003e-293 < (/.f64 y z) < 5.0000000000000002e137

   1. Initial program 87.7%

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

      1. associate-/l* 99.6%

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

      2. *-inverses 99.6%

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

      3. /-rgt-identity 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+152} \lor \neg \left(\frac{y}{z} \leq -5 \cdot 10^{-286} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-293}\right) \land \frac{y}{z} \leq 5 \cdot 10^{+137}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 0 \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= (/ y z) -2e+152)
     t_1
     (if (<= (/ y z) -5e-286)
       (* x (/ y z))
       (if (or (<= (/ y z) 0.0) (not (<= (/ y z) 5e+262)))
         t_1
         (/ x (/ z y)))))))

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+152) {
		tmp = t_1;
	} else if ((y / z) <= -5e-286) {
		tmp = x * (y / z);
	} else if (((y / z) <= 0.0) || !((y / z) <= 5e+262)) {
		tmp = t_1;
	} else {
		tmp = x / (z / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / z)
    if ((y / z) <= (-2d+152)) then
        tmp = t_1
    else if ((y / z) <= (-5d-286)) then
        tmp = x * (y / z)
    else if (((y / z) <= 0.0d0) .or. (.not. ((y / z) <= 5d+262))) then
        tmp = t_1
    else
        tmp = x / (z / y)
    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+152) {
		tmp = t_1;
	} else if ((y / z) <= -5e-286) {
		tmp = x * (y / z);
	} else if (((y / z) <= 0.0) || !((y / z) <= 5e+262)) {
		tmp = t_1;
	} else {
		tmp = x / (z / y);
	}
	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+152:
		tmp = t_1
	elif (y / z) <= -5e-286:
		tmp = x * (y / z)
	elif ((y / z) <= 0.0) or not ((y / z) <= 5e+262):
		tmp = t_1
	else:
		tmp = x / (z / y)
	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+152)
		tmp = t_1;
	elseif (Float64(y / z) <= -5e-286)
		tmp = Float64(x * Float64(y / z));
	elseif ((Float64(y / z) <= 0.0) || !(Float64(y / z) <= 5e+262))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z / y));
	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+152)
		tmp = t_1;
	elseif ((y / z) <= -5e-286)
		tmp = x * (y / z);
	elseif (((y / z) <= 0.0) || ~(((y / z) <= 5e+262)))
		tmp = t_1;
	else
		tmp = x / (z / 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_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y / z), $MachinePrecision], -2e+152], t$95$1, If[LessEqual[N[(y / z), $MachinePrecision], -5e-286], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], 0.0], N[Not[LessEqual[N[(y / z), $MachinePrecision], 5e+262]], $MachinePrecision]], t$95$1, N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -2.0000000000000001e152 or -5.00000000000000037e-286 < (/.f64 y z) < -0.0 or 5.00000000000000008e262 < (/.f64 y z)

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 80.9%

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

      3. *-inverses 80.9%

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

      4. /-rgt-identity 80.9%

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

      5. associate-*l/ 98.7%

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

      6. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -2.0000000000000001e152 < (/.f64 y z) < -5.00000000000000037e-286

   1. Initial program 89.3%

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

      1. associate-/l* 99.7%

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

      2. *-inverses 99.7%

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

      3. /-rgt-identity 99.7%

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

   3. Simplified 99.7%

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

   if -0.0 < (/.f64 y z) < 5.00000000000000008e262

   1. Initial program 85.7%

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

      1. associate-/l* 99.5%

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

      2. *-inverses 99.5%

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

      3. /-rgt-identity 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 0 \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{+262}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 92.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 3e-93) (/ x (/ z y)) (/ (* x y) z)))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3e-93) {
		tmp = x / (z / y);
	} else {
		tmp = (x * y) / z;
	}
	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 (t <= 3d-93) then
        tmp = x / (z / y)
    else
        tmp = (x * y) / z
    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 (t <= 3e-93) {
		tmp = x / (z / y);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if t <= 3e-93:
		tmp = x / (z / y)
	else:
		tmp = (x * y) / z
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3e-93)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3e-93)
		tmp = x / (z / y);
	else
		tmp = (x * y) / z;
	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[t, 3e-93], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 3.0000000000000001e-93

   1. Initial program 81.9%

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

      1. associate-/l* 92.1%

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

      2. *-inverses 92.1%

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

      3. /-rgt-identity 92.1%

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

   3. Simplified 92.1%

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

      1. clear-num 91.9%

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

      2. un-div-inv 92.2%

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

   5. Applied egg-rr 92.2%

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

   if 3.0000000000000001e-93 < t

   1. Initial program 85.3%

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

      1. associate-/l* 94.8%

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

      2. *-inverses 94.8%

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

      3. /-rgt-identity 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 96.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 5: 92.5% 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 83.0%

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

   1. associate-/l* 93.0%

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

   2. *-inverses 93.0%

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

   3. /-rgt-identity 93.0%

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

3. Simplified 93.0%

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

4. Final simplification 93.0%

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

Developer target: 98.0% 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 2023229 
(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)))