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

Percentage Accurate: 81.1% → 97.7%

Time: 3.7s

Alternatives: 6

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: 81.1% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-296} \lor \neg \left(\frac{y}{z} \leq 10^{-259}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (/ y z) -5e+123)
   (/ (* y x) z)
   (if (or (<= (/ y z) -5e-296) (not (<= (/ y z) 1e-259)))
     (/ x (/ z y))
     (* (* y x) (/ 1.0 z)))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y / z) <= -5e+123) {
		tmp = (y * x) / z;
	} else if (((y / z) <= -5e-296) || !((y / z) <= 1e-259)) {
		tmp = x / (z / y);
	} else {
		tmp = (y * x) * (1.0 / 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+123)) then
        tmp = (y * x) / z
    else if (((y / z) <= (-5d-296)) .or. (.not. ((y / z) <= 1d-259))) then
        tmp = x / (z / y)
    else
        tmp = (y * x) * (1.0d0 / 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+123) {
		tmp = (y * x) / z;
	} else if (((y / z) <= -5e-296) || !((y / z) <= 1e-259)) {
		tmp = x / (z / y);
	} else {
		tmp = (y * x) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if (y / z) <= -5e+123:
		tmp = (y * x) / z
	elif ((y / z) <= -5e-296) or not ((y / z) <= 1e-259):
		tmp = x / (z / y)
	else:
		tmp = (y * x) * (1.0 / z)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y / z) <= -5e+123)
		tmp = Float64(Float64(y * x) / z);
	elseif ((Float64(y / z) <= -5e-296) || !(Float64(y / z) <= 1e-259))
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(Float64(y * x) * Float64(1.0 / 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+123)
		tmp = (y * x) / z;
	elseif (((y / z) <= -5e-296) || ~(((y / z) <= 1e-259)))
		tmp = x / (z / y);
	else
		tmp = (y * x) * (1.0 / 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[N[(y / z), $MachinePrecision], -5e+123], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], -5e-296], N[Not[LessEqual[N[(y / z), $MachinePrecision], 1e-259]], $MachinePrecision]], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 y z) < -4.99999999999999974e123

   1. Initial program 83.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   if -4.99999999999999974e123 < (/.f64 y z) < -5.0000000000000003e-296 or 1.0000000000000001e-259 < (/.f64 y z)

   1. Initial program 87.6%

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

      1. clear-num 87.4%

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

      2. un-div-inv 87.5%

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

      3. *-commutative 87.5%

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

      4. associate-/r* 98.6%

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

      5. *-inverses 98.6%

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

      6. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

   if -5.0000000000000003e-296 < (/.f64 y z) < 1.0000000000000001e-259

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. div-inv 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(y \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -5 \cdot 10^{-296} \lor \neg \left(\frac{y}{z} \leq 10^{-259}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty \lor \neg \left(\frac{y}{z} \leq -1 \cdot 10^{-140}\right) \land \frac{y}{z} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

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) (- INFINITY))
         (and (not (<= (/ y z) -1e-140)) (<= (/ y z) 2e-310)))
   (* 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) <= -((double) INFINITY)) || (!((y / z) <= -1e-140) && ((y / z) <= 2e-310))) {
		tmp = y * (x / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -Double.POSITIVE_INFINITY) || (!((y / z) <= -1e-140) && ((y / z) <= 2e-310))) {
		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) <= -math.inf) or (not ((y / z) <= -1e-140) and ((y / z) <= 2e-310)):
		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) <= Float64(-Inf)) || (!(Float64(y / z) <= -1e-140) && (Float64(y / z) <= 2e-310)))
		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) <= -Inf) || (~(((y / z) <= -1e-140)) && ((y / z) <= 2e-310)))
		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], (-Infinity)], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -1e-140]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 2e-310]]], 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) < -inf.0 or -9.9999999999999998e-141 < (/.f64 y z) < 1.999999999999994e-310

   1. Initial program 78.8%

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

   2. Taylor expanded in x around 0 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l/ 99.5%

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

   4. Applied egg-rr 99.5%

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

   if -inf.0 < (/.f64 y z) < -9.9999999999999998e-141 or 1.999999999999994e-310 < (/.f64 y z)

   1. Initial program 87.9%

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

   2. Taylor expanded in x around 0 90.7%

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

      1. associate-*l/ 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -\infty \lor \neg \left(\frac{y}{z} \leq -1 \cdot 10^{-140}\right) \land \frac{y}{z} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 3: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+298} \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-278}\right) \land \frac{y}{z} \leq 2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -1e+298)
         (and (not (<= (/ y z) -2e-278)) (<= (/ y z) 2e-176)))
   (* 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) <= -1e+298) || (!((y / z) <= -2e-278) && ((y / z) <= 2e-176))) {
		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) <= (-1d+298)) .or. (.not. ((y / z) <= (-2d-278))) .and. ((y / z) <= 2d-176)) 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) <= -1e+298) || (!((y / z) <= -2e-278) && ((y / z) <= 2e-176))) {
		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) <= -1e+298) or (not ((y / z) <= -2e-278) and ((y / z) <= 2e-176)):
		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) <= -1e+298) || (!(Float64(y / z) <= -2e-278) && (Float64(y / z) <= 2e-176)))
		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) <= -1e+298) || (~(((y / z) <= -2e-278)) && ((y / z) <= 2e-176)))
		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[Or[LessEqual[N[(y / z), $MachinePrecision], -1e+298], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -2e-278]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 2e-176]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -9.9999999999999996e297 or -1.99999999999999988e-278 < (/.f64 y z) < 2e-176

   1. Initial program 75.4%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -9.9999999999999996e297 < (/.f64 y z) < -1.99999999999999988e-278 or 2e-176 < (/.f64 y z)

   1. Initial program 88.3%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.2%

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

      3. *-commutative 88.2%

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

      4. associate-/r* 98.7%

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

      5. *-inverses 98.7%

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

      6. clear-num 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+298} \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-278}\right) \land \frac{y}{z} \leq 2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 4: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+298} \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-278}\right) \land \frac{y}{z} \leq 5 \cdot 10^{-193}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ y z) -1e+298)
         (and (not (<= (/ y z) -2e-278)) (<= (/ y z) 5e-193)))
   (/ y (/ z x))
   (/ x (/ z y))))

C

assert(x < y);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) <= -1e+298) || (!((y / z) <= -2e-278) && ((y / z) <= 5e-193))) {
		tmp = y / (z / x);
	} 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) <= (-1d+298)) .or. (.not. ((y / z) <= (-2d-278))) .and. ((y / z) <= 5d-193)) then
        tmp = y / (z / x)
    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) <= -1e+298) || (!((y / z) <= -2e-278) && ((y / z) <= 5e-193))) {
		tmp = y / (z / x);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t):
	tmp = 0
	if ((y / z) <= -1e+298) or (not ((y / z) <= -2e-278) and ((y / z) <= 5e-193)):
		tmp = y / (z / x)
	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) <= -1e+298) || (!(Float64(y / z) <= -2e-278) && (Float64(y / z) <= 5e-193)))
		tmp = Float64(y / Float64(z / x));
	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) <= -1e+298) || (~(((y / z) <= -2e-278)) && ((y / z) <= 5e-193)))
		tmp = y / (z / x);
	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[Or[LessEqual[N[(y / z), $MachinePrecision], -1e+298], And[N[Not[LessEqual[N[(y / z), $MachinePrecision], -2e-278]], $MachinePrecision], LessEqual[N[(y / z), $MachinePrecision], 5e-193]]], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y z) < -9.9999999999999996e297 or -1.99999999999999988e-278 < (/.f64 y z) < 5.0000000000000005e-193

   1. Initial program 75.0%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate-*l/ 81.5%

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

   4. Simplified 81.5%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -9.9999999999999996e297 < (/.f64 y z) < -1.99999999999999988e-278 or 5.0000000000000005e-193 < (/.f64 y z)

   1. Initial program 88.4%

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

      1. clear-num 88.2%

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

      2. un-div-inv 88.3%

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

      3. *-commutative 88.3%

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

      4. associate-/r* 98.7%

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

      5. *-inverses 98.7%

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

      6. clear-num 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -1 \cdot 10^{+298} \lor \neg \left(\frac{y}{z} \leq -2 \cdot 10^{-278}\right) \land \frac{y}{z} \leq 5 \cdot 10^{-193}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-193}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

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+123)
   (/ (* y x) z)
   (if (or (<= (/ y z) -2e-278) (not (<= (/ y z) 5e-193)))
     (/ 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+123) {
		tmp = (y * x) / z;
	} else if (((y / z) <= -2e-278) || !((y / z) <= 5e-193)) {
		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+123)) then
        tmp = (y * x) / z
    else if (((y / z) <= (-2d-278)) .or. (.not. ((y / z) <= 5d-193))) 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+123) {
		tmp = (y * x) / z;
	} else if (((y / z) <= -2e-278) || !((y / z) <= 5e-193)) {
		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+123:
		tmp = (y * x) / z
	elif ((y / z) <= -2e-278) or not ((y / z) <= 5e-193):
		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+123)
		tmp = Float64(Float64(y * x) / z);
	elseif ((Float64(y / z) <= -2e-278) || !(Float64(y / z) <= 5e-193))
		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+123)
		tmp = (y * x) / z;
	elseif (((y / z) <= -2e-278) || ~(((y / z) <= 5e-193)))
		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+123], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[N[(y / z), $MachinePrecision], -2e-278], N[Not[LessEqual[N[(y / z), $MachinePrecision], 5e-193]], $MachinePrecision]], 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) < -4.99999999999999974e123

   1. Initial program 83.7%

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

   2. Taylor expanded in x around 0 99.9%

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

   if -4.99999999999999974e123 < (/.f64 y z) < -1.99999999999999988e-278 or 5.0000000000000005e-193 < (/.f64 y z)

   1. Initial program 87.7%

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

      1. clear-num 87.6%

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

      2. un-div-inv 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-/r* 98.6%

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

      5. *-inverses 98.6%

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

      6. clear-num 98.7%

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

   3. Applied egg-rr 98.7%

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

   if -1.99999999999999988e-278 < (/.f64 y z) < 5.0000000000000005e-193

   1. Initial program 76.7%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate-*l/ 83.4%

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

   4. Simplified 83.4%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \leq -5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{y}{z} \leq 5 \cdot 10^{-193}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 6: 92.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

2. Taylor expanded in x around 0 92.9%

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

   1. *-commutative 92.9%

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

   2. associate-*l/ 89.8%

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

4. Applied egg-rr 89.8%

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

5. Final simplification 89.8%

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

Developer target: 97.8% 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 2023187 
(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)))