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

Percentage Accurate: 84.0% → 97.0%

Time: 11.0s

Alternatives: 13

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: 84.0% 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: 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]

Derivation

1. Initial program 81.8%

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

   1. associate-/l* 96.7%

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

3. Simplified 96.7%

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

4. Final simplification 96.7%

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

Alternative 2: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y t))))
   (if (<= z -4.7e-29)
     x
     (if (<= z -4e-190)
       (* y (/ x t))
       (if (<= z 1.6e-280)
         (/ (* x y) t)
         (if (<= z 1.02e-91)
           t_1
           (if (<= z 7e-10) (* (/ x z) (- y)) (if (<= z 2.5e+49) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double tmp;
	if (z <= -4.7e-29) {
		tmp = x;
	} else if (z <= -4e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.6e-280) {
		tmp = (x * y) / t;
	} else if (z <= 1.02e-91) {
		tmp = t_1;
	} else if (z <= 7e-10) {
		tmp = (x / z) * -y;
	} else if (z <= 2.5e+49) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / t)
    if (z <= (-4.7d-29)) then
        tmp = x
    else if (z <= (-4d-190)) then
        tmp = y * (x / t)
    else if (z <= 1.6d-280) then
        tmp = (x * y) / t
    else if (z <= 1.02d-91) then
        tmp = t_1
    else if (z <= 7d-10) then
        tmp = (x / z) * -y
    else if (z <= 2.5d+49) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double tmp;
	if (z <= -4.7e-29) {
		tmp = x;
	} else if (z <= -4e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.6e-280) {
		tmp = (x * y) / t;
	} else if (z <= 1.02e-91) {
		tmp = t_1;
	} else if (z <= 7e-10) {
		tmp = (x / z) * -y;
	} else if (z <= 2.5e+49) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / t)
	tmp = 0
	if z <= -4.7e-29:
		tmp = x
	elif z <= -4e-190:
		tmp = y * (x / t)
	elif z <= 1.6e-280:
		tmp = (x * y) / t
	elif z <= 1.02e-91:
		tmp = t_1
	elif z <= 7e-10:
		tmp = (x / z) * -y
	elif z <= 2.5e+49:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / t))
	tmp = 0.0
	if (z <= -4.7e-29)
		tmp = x;
	elseif (z <= -4e-190)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 1.6e-280)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 1.02e-91)
		tmp = t_1;
	elseif (z <= 7e-10)
		tmp = Float64(Float64(x / z) * Float64(-y));
	elseif (z <= 2.5e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / t);
	tmp = 0.0;
	if (z <= -4.7e-29)
		tmp = x;
	elseif (z <= -4e-190)
		tmp = y * (x / t);
	elseif (z <= 1.6e-280)
		tmp = (x * y) / t;
	elseif (z <= 1.02e-91)
		tmp = t_1;
	elseif (z <= 7e-10)
		tmp = (x / z) * -y;
	elseif (z <= 2.5e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e-29], x, If[LessEqual[z, -4e-190], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-280], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.02e-91], t$95$1, If[LessEqual[z, 7e-10], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 2.5e+49], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.6999999999999998e-29 or 2.5000000000000002e49 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 59.4%

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

   if -4.6999999999999998e-29 < z < -4.0000000000000001e-190

   1. Initial program 83.7%

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

      1. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 42.5%

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

      1. associate-/l* 51.4%

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

   6. Simplified 51.4%

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

      1. associate-/r/ 52.7%

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

   8. Applied egg-rr 52.7%

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

   if -4.0000000000000001e-190 < z < 1.6e-280

   1. Initial program 99.2%

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

      1. associate-*r/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around 0 92.2%

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

   if 1.6e-280 < z < 1.01999999999999994e-91 or 6.99999999999999961e-10 < z < 2.5000000000000002e49

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 69.7%

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

   if 1.01999999999999994e-91 < z < 6.99999999999999961e-10

   1. Initial program 91.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 58.5%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in t around 0 52.5%

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

      1. associate-*r/ 52.5%

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

      2. neg-mul-1 52.5%

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

   9. Simplified 52.5%

      \[\leadsto y \cdot \color{blue}{\frac{-x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y t))))
   (if (<= z -4.7e-29)
     x
     (if (<= z -7.2e-190)
       (* y (/ x t))
       (if (<= z 1.85e-280)
         (/ (* x y) t)
         (if (<= z 7.5e-91)
           t_1
           (if (<= z 5.5e-10)
             (* x (/ (- y) z))
             (if (<= z 3.5e+49) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double tmp;
	if (z <= -4.7e-29) {
		tmp = x;
	} else if (z <= -7.2e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.85e-280) {
		tmp = (x * y) / t;
	} else if (z <= 7.5e-91) {
		tmp = t_1;
	} else if (z <= 5.5e-10) {
		tmp = x * (-y / z);
	} else if (z <= 3.5e+49) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / t)
    if (z <= (-4.7d-29)) then
        tmp = x
    else if (z <= (-7.2d-190)) then
        tmp = y * (x / t)
    else if (z <= 1.85d-280) then
        tmp = (x * y) / t
    else if (z <= 7.5d-91) then
        tmp = t_1
    else if (z <= 5.5d-10) then
        tmp = x * (-y / z)
    else if (z <= 3.5d+49) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double tmp;
	if (z <= -4.7e-29) {
		tmp = x;
	} else if (z <= -7.2e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.85e-280) {
		tmp = (x * y) / t;
	} else if (z <= 7.5e-91) {
		tmp = t_1;
	} else if (z <= 5.5e-10) {
		tmp = x * (-y / z);
	} else if (z <= 3.5e+49) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / t)
	tmp = 0
	if z <= -4.7e-29:
		tmp = x
	elif z <= -7.2e-190:
		tmp = y * (x / t)
	elif z <= 1.85e-280:
		tmp = (x * y) / t
	elif z <= 7.5e-91:
		tmp = t_1
	elif z <= 5.5e-10:
		tmp = x * (-y / z)
	elif z <= 3.5e+49:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / t))
	tmp = 0.0
	if (z <= -4.7e-29)
		tmp = x;
	elseif (z <= -7.2e-190)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 1.85e-280)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 7.5e-91)
		tmp = t_1;
	elseif (z <= 5.5e-10)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 3.5e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / t);
	tmp = 0.0;
	if (z <= -4.7e-29)
		tmp = x;
	elseif (z <= -7.2e-190)
		tmp = y * (x / t);
	elseif (z <= 1.85e-280)
		tmp = (x * y) / t;
	elseif (z <= 7.5e-91)
		tmp = t_1;
	elseif (z <= 5.5e-10)
		tmp = x * (-y / z);
	elseif (z <= 3.5e+49)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e-29], x, If[LessEqual[z, -7.2e-190], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-280], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 7.5e-91], t$95$1, If[LessEqual[z, 5.5e-10], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+49], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.6999999999999998e-29 or 3.49999999999999975e49 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 59.4%

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

   if -4.6999999999999998e-29 < z < -7.20000000000000014e-190

   1. Initial program 83.7%

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

      1. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 42.5%

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

      1. associate-/l* 51.4%

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

   6. Simplified 51.4%

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

      1. associate-/r/ 52.7%

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

   8. Applied egg-rr 52.7%

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

   if -7.20000000000000014e-190 < z < 1.8499999999999999e-280

   1. Initial program 99.2%

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

      1. associate-*r/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around 0 92.2%

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

   if 1.8499999999999999e-280 < z < 7.50000000000000051e-91 or 5.4999999999999996e-10 < z < 3.49999999999999975e49

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 69.7%

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

   if 7.50000000000000051e-91 < z < 5.4999999999999996e-10

   1. Initial program 91.5%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 66.2%

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

   5. Taylor expanded in t around 0 58.1%

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

      1. associate-*r/ 58.1%

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

      2. neg-mul-1 58.1%

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

      3. distribute-rgt-neg-in 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in x around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. associate-*r/ 58.1%

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

      3. *-commutative 58.1%

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

      4. distribute-rgt-neg-in 58.1%

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

   10. Simplified 58.1%

       \[\leadsto \color{blue}{\frac{y}{z} \cdot \left(-x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-28} \lor \neg \left(y \leq 1360\right) \land \left(y \leq 1.22 \cdot 10^{+44} \lor \neg \left(y \leq 6.5 \cdot 10^{+97}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.55e-28)
         (and (not (<= y 1360.0)) (or (<= y 1.22e+44) (not (<= y 6.5e+97)))))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.55e-28) || (!(y <= 1360.0) && ((y <= 1.22e+44) || !(y <= 6.5e+97)))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (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 ((y <= (-2.55d-28)) .or. (.not. (y <= 1360.0d0)) .and. (y <= 1.22d+44) .or. (.not. (y <= 6.5d+97))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.55e-28) || (!(y <= 1360.0) && ((y <= 1.22e+44) || !(y <= 6.5e+97)))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.55e-28) or (not (y <= 1360.0) and ((y <= 1.22e+44) or not (y <= 6.5e+97))):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.55e-28) || (!(y <= 1360.0) && ((y <= 1.22e+44) || !(y <= 6.5e+97))))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.55e-28) || (~((y <= 1360.0)) && ((y <= 1.22e+44) || ~((y <= 6.5e+97)))))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.55e-28], And[N[Not[LessEqual[y, 1360.0]], $MachinePrecision], Or[LessEqual[y, 1.22e+44], N[Not[LessEqual[y, 6.5e+97]], $MachinePrecision]]]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55000000000000004e-28 or 1360 < y < 1.22e44 or 6.4999999999999999e97 < y

   1. Initial program 81.6%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around inf 75.0%

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

   if -2.55000000000000004e-28 < y < 1360 or 1.22e44 < y < 6.4999999999999999e97

   1. Initial program 82.0%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 83.0%

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

      1. neg-mul-1 83.0%

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

      2. distribute-neg-frac 83.0%

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

   6. Simplified 83.0%

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

      1. frac-2neg 83.0%

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

      2. div-inv 82.9%

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

      3. remove-double-neg 82.9%

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

      4. sub-neg 82.9%

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

      5. distribute-neg-in 82.9%

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

      6. remove-double-neg 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. associate-*r/ 83.0%

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

      2. *-rgt-identity 83.0%

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

      3. +-commutative 83.0%

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

      4. unsub-neg 83.0%

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

   10. Simplified 83.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-28} \lor \neg \left(y \leq 1360\right) \land \left(y \leq 1.22 \cdot 10^{+44} \lor \neg \left(y \leq 6.5 \cdot 10^{+97}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 5: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-120} \lor \neg \left(z \leq 4.2 \cdot 10^{-91}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.6e-35)
     t_1
     (if (<= z -6.6e-70)
       (/ x (/ t y))
       (if (or (<= z -2.15e-120) (not (<= z 4.2e-91))) t_1 (/ (* x y) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.6e-35) {
		tmp = t_1;
	} else if (z <= -6.6e-70) {
		tmp = x / (t / y);
	} else if ((z <= -2.15e-120) || !(z <= 4.2e-91)) {
		tmp = t_1;
	} else {
		tmp = (x * y) / 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-2.6d-35)) then
        tmp = t_1
    else if (z <= (-6.6d-70)) then
        tmp = x / (t / y)
    else if ((z <= (-2.15d-120)) .or. (.not. (z <= 4.2d-91))) then
        tmp = t_1
    else
        tmp = (x * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.6e-35) {
		tmp = t_1;
	} else if (z <= -6.6e-70) {
		tmp = x / (t / y);
	} else if ((z <= -2.15e-120) || !(z <= 4.2e-91)) {
		tmp = t_1;
	} else {
		tmp = (x * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.6e-35:
		tmp = t_1
	elif z <= -6.6e-70:
		tmp = x / (t / y)
	elif (z <= -2.15e-120) or not (z <= 4.2e-91):
		tmp = t_1
	else:
		tmp = (x * y) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.6e-35)
		tmp = t_1;
	elseif (z <= -6.6e-70)
		tmp = Float64(x / Float64(t / y));
	elseif ((z <= -2.15e-120) || !(z <= 4.2e-91))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.6e-35)
		tmp = t_1;
	elseif (z <= -6.6e-70)
		tmp = x / (t / y);
	elseif ((z <= -2.15e-120) || ~((z <= 4.2e-91)))
		tmp = t_1;
	else
		tmp = (x * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-35], t$95$1, If[LessEqual[z, -6.6e-70], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.15e-120], N[Not[LessEqual[z, 4.2e-91]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000005e-35 or -6.60000000000000033e-70 < z < -2.14999999999999991e-120 or 4.1999999999999998e-91 < z

   1. Initial program 75.3%

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

      1. associate-*r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      2. div-sub 73.7%

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

      3. sub-neg 73.7%

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

      4. *-inverses 73.7%

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

      5. metadata-eval 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in x around 0 73.7%

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

   if -2.60000000000000005e-35 < z < -6.60000000000000033e-70

   1. Initial program 84.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around 0 53.3%

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

      1. associate-/l* 70.0%

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

   6. Simplified 70.0%

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

   if -2.14999999999999991e-120 < z < 4.1999999999999998e-91

   1. Initial program 94.0%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 74.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-120} \lor \neg \left(z \leq 4.2 \cdot 10^{-91}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \end{array} \]

Alternative 6: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4500:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+45} \lor \neg \left(y \leq 2.4 \cdot 10^{+98}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -2.75e-27)
     t_1
     (if (<= y 4500.0)
       (/ x (- 1.0 (/ t z)))
       (if (or (<= y 2.5e+45) (not (<= y 2.4e+98)))
         t_1
         (* x (/ z (- z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2.75e-27) {
		tmp = t_1;
	} else if (y <= 4500.0) {
		tmp = x / (1.0 - (t / z));
	} else if ((y <= 2.5e+45) || !(y <= 2.4e+98)) {
		tmp = t_1;
	} else {
		tmp = x * (z / (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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-2.75d-27)) then
        tmp = t_1
    else if (y <= 4500.0d0) then
        tmp = x / (1.0d0 - (t / z))
    else if ((y <= 2.5d+45) .or. (.not. (y <= 2.4d+98))) then
        tmp = t_1
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2.75e-27) {
		tmp = t_1;
	} else if (y <= 4500.0) {
		tmp = x / (1.0 - (t / z));
	} else if ((y <= 2.5e+45) || !(y <= 2.4e+98)) {
		tmp = t_1;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -2.75e-27:
		tmp = t_1
	elif y <= 4500.0:
		tmp = x / (1.0 - (t / z))
	elif (y <= 2.5e+45) or not (y <= 2.4e+98):
		tmp = t_1
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -2.75e-27)
		tmp = t_1;
	elseif (y <= 4500.0)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif ((y <= 2.5e+45) || !(y <= 2.4e+98))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -2.75e-27)
		tmp = t_1;
	elseif (y <= 4500.0)
		tmp = x / (1.0 - (t / z));
	elseif ((y <= 2.5e+45) || ~((y <= 2.4e+98)))
		tmp = t_1;
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e-27], t$95$1, If[LessEqual[y, 4500.0], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.5e+45], N[Not[LessEqual[y, 2.4e+98]], $MachinePrecision]], t$95$1, N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7500000000000001e-27 or 4500 < y < 2.5e45 or 2.3999999999999999e98 < y

   1. Initial program 81.6%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around inf 75.0%

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

   if -2.7500000000000001e-27 < y < 4500

   1. Initial program 82.4%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 67.9%

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

      2. associate-/l* 83.6%

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

      3. distribute-neg-frac 83.6%

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

      4. div-sub 83.6%

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

      5. sub-neg 83.6%

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

      6. *-inverses 83.6%

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

      7. metadata-eval 83.6%

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

   6. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{-x}{\frac{t}{z} + -1}} \]
   7. Step-by-step derivation

      1. frac-2neg 83.6%

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

      2. div-inv 83.5%

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

      3. remove-double-neg 83.5%

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

      4. +-commutative 83.5%

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

      5. distribute-neg-in 83.5%

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

      6. metadata-eval 83.5%

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

   8. Applied egg-rr 83.5%

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

      1. associate-*r/ 83.6%

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

      2. *-rgt-identity 83.6%

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

      3. unsub-neg 83.6%

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

   10. Simplified 83.6%

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

   if 2.5e45 < y < 2.3999999999999999e98

   1. Initial program 79.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around 0 79.0%

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

      1. neg-mul-1 79.0%

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

      2. distribute-neg-frac 79.0%

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

   6. Simplified 79.0%

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

      1. frac-2neg 79.0%

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

      2. div-inv 78.9%

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

      3. remove-double-neg 78.9%

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

      4. sub-neg 78.9%

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

      5. distribute-neg-in 78.9%

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

      6. remove-double-neg 78.9%

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

   8. Applied egg-rr 78.9%

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

      1. associate-*r/ 79.0%

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

      2. *-rgt-identity 79.0%

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

      3. +-commutative 79.0%

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

      4. unsub-neg 79.0%

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

   10. Simplified 79.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 4500:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+45} \lor \neg \left(y \leq 2.4 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 7: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 2200:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq 2.82 \cdot 10^{+45} \lor \neg \left(y \leq 3.8 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.08e-26)
   (/ x (/ (- t z) y))
   (if (<= y 2200.0)
     (/ x (- 1.0 (/ t z)))
     (if (or (<= y 2.82e+45) (not (<= y 3.8e+99)))
       (* x (/ y (- t z)))
       (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.08e-26) {
		tmp = x / ((t - z) / y);
	} else if (y <= 2200.0) {
		tmp = x / (1.0 - (t / z));
	} else if ((y <= 2.82e+45) || !(y <= 3.8e+99)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (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 (y <= (-1.08d-26)) then
        tmp = x / ((t - z) / y)
    else if (y <= 2200.0d0) then
        tmp = x / (1.0d0 - (t / z))
    else if ((y <= 2.82d+45) .or. (.not. (y <= 3.8d+99))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.08e-26) {
		tmp = x / ((t - z) / y);
	} else if (y <= 2200.0) {
		tmp = x / (1.0 - (t / z));
	} else if ((y <= 2.82e+45) || !(y <= 3.8e+99)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.08e-26:
		tmp = x / ((t - z) / y)
	elif y <= 2200.0:
		tmp = x / (1.0 - (t / z))
	elif (y <= 2.82e+45) or not (y <= 3.8e+99):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.08e-26)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= 2200.0)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif ((y <= 2.82e+45) || !(y <= 3.8e+99))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.08e-26)
		tmp = x / ((t - z) / y);
	elseif (y <= 2200.0)
		tmp = x / (1.0 - (t / z));
	elseif ((y <= 2.82e+45) || ~((y <= 3.8e+99)))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.08e-26], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2200.0], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.82e+45], N[Not[LessEqual[y, 3.8e+99]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.07999999999999996e-26

   1. Initial program 81.1%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around inf 70.2%

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

   if -1.07999999999999996e-26 < y < 2200

   1. Initial program 82.4%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   5. Step-by-step derivation

      1. mul-1-neg 67.9%

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

      2. associate-/l* 83.6%

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

      3. distribute-neg-frac 83.6%

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

      4. div-sub 83.6%

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

      5. sub-neg 83.6%

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

      6. *-inverses 83.6%

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

      7. metadata-eval 83.6%

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

   6. Simplified 83.6%

      \[\leadsto \color{blue}{\frac{-x}{\frac{t}{z} + -1}} \]
   7. Step-by-step derivation

      1. frac-2neg 83.6%

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

      2. div-inv 83.5%

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

      3. remove-double-neg 83.5%

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

      4. +-commutative 83.5%

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

      5. distribute-neg-in 83.5%

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

      6. metadata-eval 83.5%

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

   8. Applied egg-rr 83.5%

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

      1. associate-*r/ 83.6%

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

      2. *-rgt-identity 83.6%

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

      3. unsub-neg 83.6%

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

   10. Simplified 83.6%

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

   if 2200 < y < 2.81999999999999995e45 or 3.8e99 < y

   1. Initial program 82.3%

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

      1. associate-*r/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in y around inf 82.4%

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

   if 2.81999999999999995e45 < y < 3.8e99

   1. Initial program 79.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around 0 79.0%

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

      1. neg-mul-1 79.0%

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

      2. distribute-neg-frac 79.0%

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

   6. Simplified 79.0%

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

      1. frac-2neg 79.0%

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

      2. div-inv 78.9%

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

      3. remove-double-neg 78.9%

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

      4. sub-neg 78.9%

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

      5. distribute-neg-in 78.9%

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

      6. remove-double-neg 78.9%

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

   8. Applied egg-rr 78.9%

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

      1. associate-*r/ 79.0%

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

      2. *-rgt-identity 79.0%

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

      3. +-commutative 79.0%

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

      4. unsub-neg 79.0%

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

   10. Simplified 79.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 2200:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;y \leq 2.82 \cdot 10^{+45} \lor \neg \left(y \leq 3.8 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 8: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e-29)
   x
   (if (<= z -3.2e-190)
     (* y (/ x t))
     (if (<= z 1.66e-280) (/ (* x y) t) (if (<= z 3e+49) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e-29) {
		tmp = x;
	} else if (z <= -3.2e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.66e-280) {
		tmp = (x * y) / t;
	} else if (z <= 3e+49) {
		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 <= (-2.4d-29)) then
        tmp = x
    else if (z <= (-3.2d-190)) then
        tmp = y * (x / t)
    else if (z <= 1.66d-280) then
        tmp = (x * y) / t
    else if (z <= 3d+49) 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 <= -2.4e-29) {
		tmp = x;
	} else if (z <= -3.2e-190) {
		tmp = y * (x / t);
	} else if (z <= 1.66e-280) {
		tmp = (x * y) / t;
	} else if (z <= 3e+49) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e-29:
		tmp = x
	elif z <= -3.2e-190:
		tmp = y * (x / t)
	elif z <= 1.66e-280:
		tmp = (x * y) / t
	elif z <= 3e+49:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e-29)
		tmp = x;
	elseif (z <= -3.2e-190)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 1.66e-280)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3e+49)
		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 <= -2.4e-29)
		tmp = x;
	elseif (z <= -3.2e-190)
		tmp = y * (x / t);
	elseif (z <= 1.66e-280)
		tmp = (x * y) / t;
	elseif (z <= 3e+49)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e-29], x, If[LessEqual[z, -3.2e-190], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.66e-280], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3e+49], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.39999999999999992e-29 or 3.0000000000000002e49 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 59.4%

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

   if -2.39999999999999992e-29 < z < -3.2000000000000001e-190

   1. Initial program 83.7%

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

      1. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 42.5%

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

      1. associate-/l* 51.4%

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

   6. Simplified 51.4%

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

      1. associate-/r/ 52.7%

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

   8. Applied egg-rr 52.7%

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

   if -3.2000000000000001e-190 < z < 1.6599999999999999e-280

   1. Initial program 99.2%

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

      1. associate-*r/ 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in z around 0 92.2%

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

   if 1.6599999999999999e-280 < z < 3.0000000000000002e49

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 58.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-190}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4600000000000 \lor \neg \left(z \leq 8.2 \cdot 10^{-91}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4600000000000.0) (not (<= z 8.2e-91)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4600000000000.0) || !(z <= 8.2e-91)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - 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 ((z <= (-4600000000000.0d0)) .or. (.not. (z <= 8.2d-91))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4600000000000.0) || !(z <= 8.2e-91)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4600000000000.0) or not (z <= 8.2e-91):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4600000000000.0) || !(z <= 8.2e-91))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4600000000000.0) || ~((z <= 8.2e-91)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4600000000000.0], N[Not[LessEqual[z, 8.2e-91]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e12 or 8.20000000000000048e-91 < z

   1. Initial program 73.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. div-sub 75.8%

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

      3. sub-neg 75.8%

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

      4. *-inverses 75.8%

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

      5. metadata-eval 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in x around 0 75.8%

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

   if -4.6e12 < z < 8.20000000000000048e-91

   1. Initial program 91.7%

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

      1. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 75.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4600000000000 \lor \neg \left(z \leq 8.2 \cdot 10^{-91}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 10: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.12e-29) x (if (<= z 4.5e+49) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e-29) {
		tmp = x;
	} else if (z <= 4.5e+49) {
		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 <= (-1.12d-29)) then
        tmp = x
    else if (z <= 4.5d+49) 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 <= -1.12e-29) {
		tmp = x;
	} else if (z <= 4.5e+49) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.12e-29:
		tmp = x
	elif z <= 4.5e+49:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.12e-29)
		tmp = x;
	elseif (z <= 4.5e+49)
		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 <= -1.12e-29)
		tmp = x;
	elseif (z <= 4.5e+49)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.12e-29], x, If[LessEqual[z, 4.5e+49], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999995e-29 or 4.49999999999999982e49 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 59.4%

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

   if -1.11999999999999995e-29 < z < 4.49999999999999982e49

   1. Initial program 90.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around 0 60.7%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-29) x (if (<= z 2.5e+49) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-29) {
		tmp = x;
	} else if (z <= 2.5e+49) {
		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 <= (-3.7d-29)) then
        tmp = x
    else if (z <= 2.5d+49) 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 <= -3.7e-29) {
		tmp = x;
	} else if (z <= 2.5e+49) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e-29:
		tmp = x
	elif z <= 2.5e+49:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-29)
		tmp = x;
	elseif (z <= 2.5e+49)
		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 <= -3.7e-29)
		tmp = x;
	elseif (z <= 2.5e+49)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-29], x, If[LessEqual[z, 2.5e+49], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999997e-29 or 2.5000000000000002e49 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 59.4%

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

   if -3.6999999999999997e-29 < z < 2.5000000000000002e49

   1. Initial program 90.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around 0 58.0%

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

      1. associate-/l* 60.7%

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

   6. Simplified 60.7%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 97.1% 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 81.8%

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

   1. associate-*r/ 96.7%

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

3. Simplified 96.7%

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

4. Final simplification 96.7%

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

Alternative 13: 35.3% 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 81.8%

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

   1. associate-*r/ 96.7%

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

3. Simplified 96.7%

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

4. Taylor expanded in z around inf 36.8%

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

5. Final simplification 36.8%

   \[\leadsto x \]

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 2023308 
(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)))