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

Percentage Accurate: 81.0% → 97.9%

Time: 3.8s

Alternatives: 5

Speedup: 1.8×

• Unsound rule application detected in e-graph. Results may not be sound.

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: 81.0% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -4 \cdot 10^{-222}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269} \lor \neg \left(\frac{y}{z} \leq 10^{+234}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) -4e-222)
   (* (/ y z) x)
   (if (or (<= (/ y z) 1e-269) (not (<= (/ y z) 1e+234)))
     (/ (* y x) z)
     (/ x (/ z y)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -4e-222) {
		tmp = (y / z) * x;
	} else if (((y / z) <= 1e-269) || !((y / z) <= 1e+234)) {
		tmp = (y * x) / z;
	} 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) :: tmp
    if ((y / z) <= (-4d-222)) then
        tmp = (y / z) * x
    else if (((y / z) <= 1d-269) .or. (.not. ((y / z) <= 1d+234))) then
        tmp = (y * x) / z
    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 tmp;
	if ((y / z) <= -4e-222) {
		tmp = (y / z) * x;
	} else if (((y / z) <= 1e-269) || !((y / z) <= 1e+234)) {
		tmp = (y * x) / z;
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -4e-222:
		tmp = (y / z) * x
	elif ((y / z) <= 1e-269) or not ((y / z) <= 1e+234):
		tmp = (y * x) / z
	else:
		tmp = x / (z / y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y / z) <= -4e-222)
		tmp = Float64(Float64(y / z) * x);
	elseif ((Float64(y / z) <= 1e-269) || !(Float64(y / z) <= 1e+234))
		tmp = Float64(Float64(y * x) / z);
	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)
	tmp = 0.0;
	if ((y / z) <= -4e-222)
		tmp = (y / z) * x;
	elseif (((y / z) <= 1e-269) || ~(((y / z) <= 1e+234)))
		tmp = (y * x) / z;
	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_] := If[LessEqual[N[(y / z), $MachinePrecision], -4e-222], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], 1e-269], N[Not[LessEqual[N[(y / z), $MachinePrecision], 1e+234]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -4.00000000000000019e-222

   1. Initial program 84.9%

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

      1. associate-/l* 95.9%

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

      2. *-inverses 95.9%

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

      3. /-rgt-identity 95.9%

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

   3. Simplified 95.9%

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

   if -4.00000000000000019e-222 < (/.f64 y z) < 9.9999999999999996e-270 or 1.00000000000000002e234 < (/.f64 y z)

   1. Initial program 61.2%

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

      1. associate-/l* 71.4%

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

      2. *-inverses 71.4%

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

      3. /-rgt-identity 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in x around 0 100.0%

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

   if 9.9999999999999996e-270 < (/.f64 y z) < 1.00000000000000002e234

   1. Initial program 89.8%

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

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -4 \cdot 10^{-222}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269} \lor \neg \left(\frac{y}{z} \leq 10^{+234}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 2: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255} \lor \neg \left(\frac{y}{z} \leq 0\right) \land \frac{y}{z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

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) -5e-255) (and (not (<= (/ y z) 0.0)) (<= (/ y z) 5e+304)))
   (* (/ y z) x)
   (* y (/ x z))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -5e-255) || (!((y / z) <= 0.0) && ((y / z) <= 5e+304))) {
		tmp = (y / z) * x;
	} else {
		tmp = y * (x / 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) <= (-5d-255)) .or. (.not. ((y / z) <= 0.0d0)) .and. ((y / z) <= 5d+304)) then
        tmp = (y / z) * x
    else
        tmp = y * (x / 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) <= -5e-255) || (!((y / z) <= 0.0) && ((y / z) <= 5e+304))) {
		tmp = (y / z) * x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -5e-255) or (not ((y / z) <= 0.0) and ((y / z) <= 5e+304)):
		tmp = (y / z) * x
	else:
		tmp = y * (x / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y / z) <= -5e-255) || (!(Float64(y / z) <= 0.0) && (Float64(y / z) <= 5e+304)))
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(y * Float64(x / 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) <= -5e-255) || (~(((y / z) <= 0.0)) && ((y / z) <= 5e+304)))
		tmp = (y / z) * x;
	else
		tmp = y * (x / 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], -5e-255], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], 0.0]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e+304]]], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -4.9999999999999996e-255 or 0.0 < (/.f64 y z) < 4.9999999999999997e304

   1. Initial program 85.1%

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

      1. associate-/l* 97.8%

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

      2. *-inverses 97.8%

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

      3. /-rgt-identity 97.8%

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

   3. Simplified 97.8%

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

   if -4.9999999999999996e-255 < (/.f64 y z) < 0.0 or 4.9999999999999997e304 < (/.f64 y z)

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-/l* 64.7%

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

      3. *-inverses 64.7%

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

      4. /-rgt-identity 64.7%

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

      5. associate-*l/ 99.9%

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

      6. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255} \lor \neg \left(\frac{y}{z} \leq 0\right) \land \frac{y}{z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) -5e-255)
   (* (/ y z) x)
   (if (or (<= (/ y z) 1e-269) (not (<= (/ y z) 5e+304)))
     (* y (/ x z))
     (/ x (/ z y)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -5e-255) {
		tmp = (y / z) * x;
	} else if (((y / z) <= 1e-269) || !((y / z) <= 5e+304)) {
		tmp = y * (x / z);
	} 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) :: tmp
    if ((y / z) <= (-5d-255)) then
        tmp = (y / z) * x
    else if (((y / z) <= 1d-269) .or. (.not. ((y / z) <= 5d+304))) then
        tmp = y * (x / z)
    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 tmp;
	if ((y / z) <= -5e-255) {
		tmp = (y / z) * x;
	} else if (((y / z) <= 1e-269) || !((y / z) <= 5e+304)) {
		tmp = y * (x / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -5e-255:
		tmp = (y / z) * x
	elif ((y / z) <= 1e-269) or not ((y / z) <= 5e+304):
		tmp = y * (x / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y / z) <= -5e-255)
		tmp = Float64(Float64(y / z) * x);
	elseif ((Float64(y / z) <= 1e-269) || !(Float64(y / z) <= 5e+304))
		tmp = Float64(y * Float64(x / z));
	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)
	tmp = 0.0;
	if ((y / z) <= -5e-255)
		tmp = (y / z) * x;
	elseif (((y / z) <= 1e-269) || ~(((y / z) <= 5e+304)))
		tmp = y * (x / z);
	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_] := If[LessEqual[N[(y / z), $MachinePrecision], -5e-255], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], 1e-269], N[Not[LessEqual[N[(y / z), $MachinePrecision], 5e+304]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -4.9999999999999996e-255

   1. Initial program 83.5%

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

      1. associate-/l* 96.0%

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

      2. *-inverses 96.0%

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

      3. /-rgt-identity 96.0%

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

   3. Simplified 96.0%

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

   if -4.9999999999999996e-255 < (/.f64 y z) < 9.9999999999999996e-270 or 4.9999999999999997e304 < (/.f64 y z)

   1. Initial program 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-/l* 66.9%

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

      3. *-inverses 66.9%

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

      4. /-rgt-identity 66.9%

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

      5. associate-*l/ 100.0%

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

      6. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   if 9.9999999999999996e-270 < (/.f64 y z) < 4.9999999999999997e304

   1. Initial program 87.4%

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

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 4 \cdot 10^{+281}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

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-255)
   (* (/ y z) x)
   (if (<= (/ y z) 1e-269)
     (* y (/ x z))
     (if (<= (/ y z) 4e+281) (/ 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-255) {
		tmp = (y / z) * x;
	} else if ((y / z) <= 1e-269) {
		tmp = y * (x / z);
	} else if ((y / z) <= 4e+281) {
		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-255)) then
        tmp = (y / z) * x
    else if ((y / z) <= 1d-269) then
        tmp = y * (x / z)
    else if ((y / z) <= 4d+281) 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-255) {
		tmp = (y / z) * x;
	} else if ((y / z) <= 1e-269) {
		tmp = y * (x / z);
	} else if ((y / z) <= 4e+281) {
		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-255:
		tmp = (y / z) * x
	elif (y / z) <= 1e-269:
		tmp = y * (x / z)
	elif (y / z) <= 4e+281:
		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-255)
		tmp = Float64(Float64(y / z) * x);
	elseif (Float64(y / z) <= 1e-269)
		tmp = Float64(y * Float64(x / z));
	elseif (Float64(y / z) <= 4e+281)
		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-255)
		tmp = (y / z) * x;
	elseif ((y / z) <= 1e-269)
		tmp = y * (x / z);
	elseif ((y / z) <= 4e+281)
		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-255], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 1e-269], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y / z), $MachinePrecision], 4e+281], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 y z) < -4.9999999999999996e-255

   1. Initial program 83.5%

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

      1. associate-/l* 96.0%

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

      2. *-inverses 96.0%

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

      3. /-rgt-identity 96.0%

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

   3. Simplified 96.0%

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

   if -4.9999999999999996e-255 < (/.f64 y z) < 9.9999999999999996e-270

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-/l* 68.9%

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

      3. *-inverses 68.9%

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

      4. /-rgt-identity 68.9%

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

      5. associate-*l/ 100.0%

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

      6. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   if 9.9999999999999996e-270 < (/.f64 y z) < 4.0000000000000001e281

   1. Initial program 87.3%

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

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

   if 4.0000000000000001e281 < (/.f64 y z)

   1. Initial program 64.3%

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

      1. associate-/l* 64.3%

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

      2. *-inverses 64.3%

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

      3. /-rgt-identity 64.3%

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

   3. Simplified 64.3%

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

      1. *-commutative 64.3%

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

      2. associate-*l/ 99.9%

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

      3. associate-/l* 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{-255}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \leq 10^{-269}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq 4 \cdot 10^{+281}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 5: 92.4% 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 79.8%

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

   1. associate-/l* 90.2%

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

   2. *-inverses 90.2%

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

   3. /-rgt-identity 90.2%

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

3. Simplified 90.2%

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

4. Final simplification 90.2%

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

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 2023178 
(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)))