Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.8% → 96.7%

Time: 9.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+127}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x (- y z)) (- t z)) -5e+127)
   (* (- y z) (/ x (- t z)))
   (/ x (/ (- t z) (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * (y - z)) / (t - z)) <= -5e+127) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / ((t - z) / (y - 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) :: tmp
    if (((x * (y - z)) / (t - z)) <= (-5d+127)) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x / ((t - z) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * (y - z)) / (t - z)) <= -5e+127) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / ((t - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * (y - z)) / (t - z)) <= -5e+127:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x / ((t - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y - z)) / Float64(t - z)) <= -5e+127)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * (y - z)) / (t - z)) <= -5e+127)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x / ((t - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], -5e+127], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.0000000000000004e127

   1. Initial program 72.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   if -5.0000000000000004e127 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 90.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+127}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \end{array} \]

Alternative 2: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-256}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -5.5e+31)
     t_1
     (if (<= z -2.65e-256)
       (* (- y z) (/ x t))
       (if (<= z 8.5e-26)
         (* x (/ y (- t z)))
         (if (<= z 4.9e+20) (* x (/ (- y z) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -5.5e+31) {
		tmp = t_1;
	} else if (z <= -2.65e-256) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.5e-26) {
		tmp = x * (y / (t - z));
	} else if (z <= 4.9e+20) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = x * ((z - y) / z)
    if (z <= (-5.5d+31)) then
        tmp = t_1
    else if (z <= (-2.65d-256)) then
        tmp = (y - z) * (x / t)
    else if (z <= 8.5d-26) then
        tmp = x * (y / (t - z))
    else if (z <= 4.9d+20) then
        tmp = x * ((y - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -5.5e+31) {
		tmp = t_1;
	} else if (z <= -2.65e-256) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.5e-26) {
		tmp = x * (y / (t - z));
	} else if (z <= 4.9e+20) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -5.5e+31:
		tmp = t_1
	elif z <= -2.65e-256:
		tmp = (y - z) * (x / t)
	elif z <= 8.5e-26:
		tmp = x * (y / (t - z))
	elif z <= 4.9e+20:
		tmp = x * ((y - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -5.5e+31)
		tmp = t_1;
	elseif (z <= -2.65e-256)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 8.5e-26)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 4.9e+20)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -5.5e+31)
		tmp = t_1;
	elseif (z <= -2.65e-256)
		tmp = (y - z) * (x / t);
	elseif (z <= 8.5e-26)
		tmp = x * (y / (t - z));
	elseif (z <= 4.9e+20)
		tmp = x * ((y - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+31], t$95$1, If[LessEqual[z, -2.65e-256], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-26], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+20], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.50000000000000002e31 or 4.9e20 < z

   1. Initial program 79.1%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 58.7%

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

      3. distribute-neg-frac 58.7%

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

      4. neg-sub0 58.7%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 58.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-lft-identity 68.1%

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

      3. times-frac 83.7%

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

      4. /-rgt-identity 83.7%

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

   9. Simplified 83.7%

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

   if -5.50000000000000002e31 < z < -2.65000000000000012e-256

   1. Initial program 93.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around inf 78.2%

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

   if -2.65000000000000012e-256 < z < 8.50000000000000004e-26

   1. Initial program 94.9%

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

      1. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 80.3%

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

   if 8.50000000000000004e-26 < z < 4.9e20

   1. Initial program 93.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 93.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-256}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (* x (/ (- z y) z))))
   (if (<= z -4.9e+33)
     t_2
     (if (<= z -1.25e-151)
       t_1
       (if (<= z 3.5e-29) (/ y (/ (- t z) x)) (if (<= z 2.1e+20) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * ((z - y) / z);
	double tmp;
	if (z <= -4.9e+33) {
		tmp = t_2;
	} else if (z <= -1.25e-151) {
		tmp = t_1;
	} else if (z <= 3.5e-29) {
		tmp = y / ((t - z) / x);
	} else if (z <= 2.1e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x * ((z - y) / z)
    if (z <= (-4.9d+33)) then
        tmp = t_2
    else if (z <= (-1.25d-151)) then
        tmp = t_1
    else if (z <= 3.5d-29) then
        tmp = y / ((t - z) / x)
    else if (z <= 2.1d+20) then
        tmp = t_1
    else
        tmp = t_2
    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) / t);
	double t_2 = x * ((z - y) / z);
	double tmp;
	if (z <= -4.9e+33) {
		tmp = t_2;
	} else if (z <= -1.25e-151) {
		tmp = t_1;
	} else if (z <= 3.5e-29) {
		tmp = y / ((t - z) / x);
	} else if (z <= 2.1e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x * ((z - y) / z)
	tmp = 0
	if z <= -4.9e+33:
		tmp = t_2
	elif z <= -1.25e-151:
		tmp = t_1
	elif z <= 3.5e-29:
		tmp = y / ((t - z) / x)
	elif z <= 2.1e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -4.9e+33)
		tmp = t_2;
	elseif (z <= -1.25e-151)
		tmp = t_1;
	elseif (z <= 3.5e-29)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	elseif (z <= 2.1e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -4.9e+33)
		tmp = t_2;
	elseif (z <= -1.25e-151)
		tmp = t_1;
	elseif (z <= 3.5e-29)
		tmp = y / ((t - z) / x);
	elseif (z <= 2.1e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+33], t$95$2, If[LessEqual[z, -1.25e-151], t$95$1, If[LessEqual[z, 3.5e-29], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+20], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.90000000000000014e33 or 2.1e20 < z

   1. Initial program 79.1%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 58.7%

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

      3. distribute-neg-frac 58.7%

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

      4. neg-sub0 58.7%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 58.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-lft-identity 68.1%

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

      3. times-frac 83.7%

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

      4. /-rgt-identity 83.7%

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

   9. Simplified 83.7%

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

   if -4.90000000000000014e33 < z < -1.25000000000000001e-151 or 3.4999999999999997e-29 < z < 2.1e20

   1. Initial program 90.7%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 84.8%

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

   if -1.25000000000000001e-151 < z < 3.4999999999999997e-29

   1. Initial program 95.8%

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

      1. associate-*r/ 90.6%

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

   3. Simplified 90.6%

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

      1. associate-*r/ 95.8%

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

      2. clear-num 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in y around inf 82.4%

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

      1. associate-/l* 82.4%

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

   8. Simplified 82.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 4: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (* x (/ (- z y) z))))
   (if (<= z -1.65e+34)
     t_2
     (if (<= z 7e-249)
       t_1
       (if (<= z 8.4e-29) (/ (* x y) (- t z)) (if (<= z 7.5e+22) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.65e+34) {
		tmp = t_2;
	} else if (z <= 7e-249) {
		tmp = t_1;
	} else if (z <= 8.4e-29) {
		tmp = (x * y) / (t - z);
	} else if (z <= 7.5e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x * ((z - y) / z)
    if (z <= (-1.65d+34)) then
        tmp = t_2
    else if (z <= 7d-249) then
        tmp = t_1
    else if (z <= 8.4d-29) then
        tmp = (x * y) / (t - z)
    else if (z <= 7.5d+22) then
        tmp = t_1
    else
        tmp = t_2
    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) / t);
	double t_2 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.65e+34) {
		tmp = t_2;
	} else if (z <= 7e-249) {
		tmp = t_1;
	} else if (z <= 8.4e-29) {
		tmp = (x * y) / (t - z);
	} else if (z <= 7.5e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x * ((z - y) / z)
	tmp = 0
	if z <= -1.65e+34:
		tmp = t_2
	elif z <= 7e-249:
		tmp = t_1
	elif z <= 8.4e-29:
		tmp = (x * y) / (t - z)
	elif z <= 7.5e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.65e+34)
		tmp = t_2;
	elseif (z <= 7e-249)
		tmp = t_1;
	elseif (z <= 8.4e-29)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 7.5e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.65e+34)
		tmp = t_2;
	elseif (z <= 7e-249)
		tmp = t_1;
	elseif (z <= 8.4e-29)
		tmp = (x * y) / (t - z);
	elseif (z <= 7.5e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+34], t$95$2, If[LessEqual[z, 7e-249], t$95$1, If[LessEqual[z, 8.4e-29], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999994e34 or 7.5000000000000002e22 < z

   1. Initial program 79.1%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 58.7%

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

      3. distribute-neg-frac 58.7%

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

      4. neg-sub0 58.7%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 58.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-lft-identity 68.1%

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

      3. times-frac 83.7%

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

      4. /-rgt-identity 83.7%

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

   9. Simplified 83.7%

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

   if -1.64999999999999994e34 < z < 7.00000000000000025e-249 or 8.39999999999999958e-29 < z < 7.5000000000000002e22

   1. Initial program 90.6%

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

      1. associate-*r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around inf 83.7%

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

   if 7.00000000000000025e-249 < z < 8.39999999999999958e-29

   1. Initial program 99.7%

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

      1. associate-*r/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around inf 85.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 5: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+31} \lor \neg \left(z \leq 1.15 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+31) (not (<= z 1.15e+25)))
   (* x (/ (- z y) z))
   (* x (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+31) || !(z <= 1.15e+25)) {
		tmp = x * ((z - y) / z);
	} else {
		tmp = x * ((y - z) / t);
	}
	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) :: tmp
    if ((z <= (-8d+31)) .or. (.not. (z <= 1.15d+25))) then
        tmp = x * ((z - y) / z)
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+31) || !(z <= 1.15e+25)) {
		tmp = x * ((z - y) / z);
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+31) or not (z <= 1.15e+25):
		tmp = x * ((z - y) / z)
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+31) || !(z <= 1.15e+25))
		tmp = Float64(x * Float64(Float64(z - y) / z));
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+31) || ~((z <= 1.15e+25)))
		tmp = x * ((z - y) / z);
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+31], N[Not[LessEqual[z, 1.15e+25]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999997e31 or 1.1499999999999999e25 < z

   1. Initial program 79.1%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 58.7%

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

      3. distribute-neg-frac 58.7%

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

      4. neg-sub0 58.7%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 58.7%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. *-lft-identity 68.1%

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

      3. times-frac 83.7%

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

      4. /-rgt-identity 83.7%

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

   9. Simplified 83.7%

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

   if -7.9999999999999997e31 < z < 1.1499999999999999e25

   1. Initial program 94.0%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 76.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+31} \lor \neg \left(z \leq 1.15 \cdot 10^{+25}\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+16} \lor \neg \left(t \leq 5.6 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+16) (not (<= t 5.6e+29)))
   (* x (/ (- y z) t))
   (- x (/ (* x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+16) || !(t <= 5.6e+29)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - ((x * y) / 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) :: tmp
    if ((t <= (-2.3d+16)) .or. (.not. (t <= 5.6d+29))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+16) || !(t <= 5.6e+29)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e+16) or not (t <= 5.6e+29):
		tmp = x * ((y - z) / t)
	else:
		tmp = x - ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e+16) || !(t <= 5.6e+29))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e+16) || ~((t <= 5.6e+29)))
		tmp = x * ((y - z) / t);
	else
		tmp = x - ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e+16], N[Not[LessEqual[t, 5.6e+29]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3e16 or 5.5999999999999999e29 < t

   1. Initial program 81.3%

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

      1. associate-*r/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 79.1%

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

   if -2.3e16 < t < 5.5999999999999999e29

   1. Initial program 92.2%

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

      1. associate-*r/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/l* 62.3%

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

      3. distribute-neg-frac 62.3%

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

      4. neg-sub0 62.3%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 62.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in y around 0 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. unsub-neg 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+16} \lor \neg \left(t \leq 5.6 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \end{array} \]

Alternative 7: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+74) x (if (<= z 2.5e+28) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+74) {
		tmp = x;
	} else if (z <= 2.5e+28) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	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) :: tmp
    if (z <= (-4.8d+74)) then
        tmp = x
    else if (z <= 2.5d+28) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+74) {
		tmp = x;
	} else if (z <= 2.5e+28) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+74:
		tmp = x
	elif z <= 2.5e+28:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+74)
		tmp = x;
	elseif (z <= 2.5e+28)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+74)
		tmp = x;
	elseif (z <= 2.5e+28)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+74], x, If[LessEqual[z, 2.5e+28], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000017e74 or 2.49999999999999979e28 < z

   1. Initial program 77.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.3%

      \[\leadsto \color{blue}{x} \]

   if -4.80000000000000017e74 < z < 2.49999999999999979e28

   1. Initial program 94.2%

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

      1. associate-*r/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 74.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+44) x (if (<= z 2.4e+24) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+44) {
		tmp = x;
	} else if (z <= 2.4e+24) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	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) :: tmp
    if (z <= (-3.6d+44)) then
        tmp = x
    else if (z <= 2.4d+24) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+44) {
		tmp = x;
	} else if (z <= 2.4e+24) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+44:
		tmp = x
	elif z <= 2.4e+24:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+44)
		tmp = x;
	elseif (z <= 2.4e+24)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e+44)
		tmp = x;
	elseif (z <= 2.4e+24)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+44], x, If[LessEqual[z, 2.4e+24], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e44 or 2.4000000000000001e24 < z

   1. Initial program 78.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{x} \]

   if -3.6e44 < z < 2.4000000000000001e24

   1. Initial program 94.0%

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

      1. associate-*r/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 61.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+45) x (if (<= z 9e+22) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+45) {
		tmp = x;
	} else if (z <= 9e+22) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	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) :: tmp
    if (z <= (-1.85d+45)) then
        tmp = x
    else if (z <= 9d+22) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+45) {
		tmp = x;
	} else if (z <= 9e+22) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+45:
		tmp = x
	elif z <= 9e+22:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+45)
		tmp = x;
	elseif (z <= 9e+22)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85e+45)
		tmp = x;
	elseif (z <= 9e+22)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+45], x, If[LessEqual[z, 9e+22], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999989e45 or 8.9999999999999996e22 < z

   1. Initial program 78.9%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 65.2%

      \[\leadsto \color{blue}{x} \]

   if -1.84999999999999989e45 < z < 8.9999999999999996e22

   1. Initial program 94.0%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 61.7%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. associate-*r/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 11: 34.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 87.4%

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

   1. associate-*r/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in z around inf 33.1%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 33.1%

   \[\leadsto x \]

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023208 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))