Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.3% → 98.2%

Time: 9.7s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((z - t) / (z - a)) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

   1. clear-num 99.0%

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

   2. associate-/r/ 99.1%

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

   3. clear-num 99.2%

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

5. Applied egg-rr 99.2%

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

6. Final simplification 99.2%

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

Alternative 2: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{z - a}\\ t_2 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- z a))))) (t_2 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -1.85e+58)
     t_2
     (if (<= z -2.2e-43)
       t_1
       (if (<= z 3.8e-15) (+ x (/ t (/ a y))) (if (<= z 9.5e+165) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -1.85e+58) {
		tmp = t_2;
	} else if (z <= -2.2e-43) {
		tmp = t_1;
	} else if (z <= 3.8e-15) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.5e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / (z - a)))
    t_2 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-1.85d+58)) then
        tmp = t_2
    else if (z <= (-2.2d-43)) then
        tmp = t_1
    else if (z <= 3.8d-15) then
        tmp = x + (t / (a / y))
    else if (z <= 9.5d+165) 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 a) {
	double t_1 = x + (z * (y / (z - a)));
	double t_2 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -1.85e+58) {
		tmp = t_2;
	} else if (z <= -2.2e-43) {
		tmp = t_1;
	} else if (z <= 3.8e-15) {
		tmp = x + (t / (a / y));
	} else if (z <= 9.5e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (z - a)))
	t_2 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -1.85e+58:
		tmp = t_2
	elif z <= -2.2e-43:
		tmp = t_1
	elif z <= 3.8e-15:
		tmp = x + (t / (a / y))
	elif z <= 9.5e+165:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(z - a))))
	t_2 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -1.85e+58)
		tmp = t_2;
	elseif (z <= -2.2e-43)
		tmp = t_1;
	elseif (z <= 3.8e-15)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 9.5e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (z - a)));
	t_2 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -1.85e+58)
		tmp = t_2;
	elseif (z <= -2.2e-43)
		tmp = t_1;
	elseif (z <= 3.8e-15)
		tmp = x + (t / (a / y));
	elseif (z <= 9.5e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+58], t$95$2, If[LessEqual[z, -2.2e-43], t$95$1, If[LessEqual[z, 3.8e-15], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+165], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001e58 or 9.50000000000000017e165 < z

   1. Initial program 79.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around 0 93.7%

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

      1. div-sub 93.7%

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

      2. *-inverses 93.7%

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

   8. Simplified 93.7%

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

   if -1.8500000000000001e58 < z < -2.19999999999999997e-43 or 3.8000000000000002e-15 < z < 9.50000000000000017e165

   1. Initial program 88.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-*l/ 86.4%

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

      3. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   if -2.19999999999999997e-43 < z < 3.8000000000000002e-15

   1. Initial program 95.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+165}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-37} \lor \neg \left(z \leq 0.00128\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+180)
   (+ x y)
   (if (<= z -4.8e-10)
     (- x (* t (/ y z)))
     (if (or (<= z -7.3e-37) (not (<= z 0.00128)))
       (+ x y)
       (+ x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+180) {
		tmp = x + y;
	} else if (z <= -4.8e-10) {
		tmp = x - (t * (y / z));
	} else if ((z <= -7.3e-37) || !(z <= 0.00128)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+180)) then
        tmp = x + y
    else if (z <= (-4.8d-10)) then
        tmp = x - (t * (y / z))
    else if ((z <= (-7.3d-37)) .or. (.not. (z <= 0.00128d0))) then
        tmp = x + y
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+180) {
		tmp = x + y;
	} else if (z <= -4.8e-10) {
		tmp = x - (t * (y / z));
	} else if ((z <= -7.3e-37) || !(z <= 0.00128)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+180:
		tmp = x + y
	elif z <= -4.8e-10:
		tmp = x - (t * (y / z))
	elif (z <= -7.3e-37) or not (z <= 0.00128):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+180)
		tmp = Float64(x + y);
	elseif (z <= -4.8e-10)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif ((z <= -7.3e-37) || !(z <= 0.00128))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+180)
		tmp = x + y;
	elseif (z <= -4.8e-10)
		tmp = x - (t * (y / z));
	elseif ((z <= -7.3e-37) || ~((z <= 0.00128)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+180], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.8e-10], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.3e-37], N[Not[LessEqual[z, 0.00128]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e180 or -4.8e-10 < z < -7.2999999999999997e-37 or 0.0012800000000000001 < z

   1. Initial program 78.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. +-commutative 83.5%

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

   6. Simplified 83.5%

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

   if -1.1e180 < z < -4.8e-10

   1. Initial program 90.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. mul-1-neg 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

   7. Simplified 71.5%

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

      1. div-inv 71.5%

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

      2. add-sqr-sqrt 33.0%

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

      3. sqrt-unprod 61.1%

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

      4. sqr-neg 61.1%

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

      5. sqrt-unprod 26.3%

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

      6. add-sqr-sqrt 51.1%

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

      7. distribute-rgt-neg-in 51.1%

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

      8. cancel-sign-sub-inv 51.1%

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

      9. associate-*l* 53.1%

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

      10. add-sqr-sqrt 28.3%

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

      11. sqrt-unprod 61.1%

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

      12. sqr-neg 61.1%

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

      13. sqrt-unprod 33.0%

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

      14. add-sqr-sqrt 73.5%

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

      15. div-inv 73.5%

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

   9. Applied egg-rr 73.5%

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

   if -7.2999999999999997e-37 < z < 0.0012800000000000001

   1. Initial program 95.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-10}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-37} \lor \neg \left(z \leq 0.00128\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 0.0185\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+180)
   (+ x y)
   (if (<= z -1.8e-14)
     (- x (* y (/ t z)))
     (if (or (<= z -7.2e-37) (not (<= z 0.0185)))
       (+ x y)
       (+ x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+180) {
		tmp = x + y;
	} else if (z <= -1.8e-14) {
		tmp = x - (y * (t / z));
	} else if ((z <= -7.2e-37) || !(z <= 0.0185)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+180)) then
        tmp = x + y
    else if (z <= (-1.8d-14)) then
        tmp = x - (y * (t / z))
    else if ((z <= (-7.2d-37)) .or. (.not. (z <= 0.0185d0))) then
        tmp = x + y
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+180) {
		tmp = x + y;
	} else if (z <= -1.8e-14) {
		tmp = x - (y * (t / z));
	} else if ((z <= -7.2e-37) || !(z <= 0.0185)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+180:
		tmp = x + y
	elif z <= -1.8e-14:
		tmp = x - (y * (t / z))
	elif (z <= -7.2e-37) or not (z <= 0.0185):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+180)
		tmp = Float64(x + y);
	elseif (z <= -1.8e-14)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif ((z <= -7.2e-37) || !(z <= 0.0185))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+180)
		tmp = x + y;
	elseif (z <= -1.8e-14)
		tmp = x - (y * (t / z));
	elseif ((z <= -7.2e-37) || ~((z <= 0.0185)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+180], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.8e-14], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -7.2e-37], N[Not[LessEqual[z, 0.0185]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e180 or -1.7999999999999999e-14 < z < -7.20000000000000014e-37 or 0.0184999999999999991 < z

   1. Initial program 78.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. +-commutative 83.5%

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

   6. Simplified 83.5%

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

   if -1.1e180 < z < -1.7999999999999999e-14

   1. Initial program 90.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. mul-1-neg 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

   7. Simplified 71.5%

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

      1. div-inv 71.5%

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

      2. add-sqr-sqrt 33.0%

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

      3. sqrt-unprod 61.1%

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

      4. sqr-neg 61.1%

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

      5. sqrt-unprod 26.3%

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

      6. add-sqr-sqrt 51.1%

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

      7. distribute-rgt-neg-in 51.1%

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

      8. cancel-sign-sub-inv 51.1%

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

      9. associate-*l* 53.1%

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

      10. add-sqr-sqrt 28.3%

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

      11. sqrt-unprod 61.1%

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

      12. sqr-neg 61.1%

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

      13. sqrt-unprod 33.0%

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

      14. add-sqr-sqrt 73.5%

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

      15. div-inv 73.5%

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

   9. Applied egg-rr 73.5%

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

   10. Taylor expanded in t around 0 71.5%

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

       1. associate-*r/ 73.5%

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

       2. remove-double-neg 73.5%

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

       3. *-commutative 73.5%

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

       4. distribute-rgt-neg-out 73.5%

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

       5. associate-*l/ 71.5%

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

       6. associate-*r/ 73.5%

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

       7. distribute-rgt-neg-in 73.5%

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

       8. distribute-frac-neg 73.5%

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

       9. remove-double-neg 73.5%

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

   12. Simplified 73.5%

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

   if -7.20000000000000014e-37 < z < 0.0184999999999999991

   1. Initial program 95.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 0.0185\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-38} \lor \neg \left(z \leq 0.00118\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+180)
   (+ x y)
   (if (<= z -3.8e-7)
     (- x (/ t (/ z y)))
     (if (or (<= z -1.75e-38) (not (<= z 0.00118)))
       (+ x y)
       (+ x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+180) {
		tmp = x + y;
	} else if (z <= -3.8e-7) {
		tmp = x - (t / (z / y));
	} else if ((z <= -1.75e-38) || !(z <= 0.00118)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+180)) then
        tmp = x + y
    else if (z <= (-3.8d-7)) then
        tmp = x - (t / (z / y))
    else if ((z <= (-1.75d-38)) .or. (.not. (z <= 0.00118d0))) then
        tmp = x + y
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+180) {
		tmp = x + y;
	} else if (z <= -3.8e-7) {
		tmp = x - (t / (z / y));
	} else if ((z <= -1.75e-38) || !(z <= 0.00118)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+180:
		tmp = x + y
	elif z <= -3.8e-7:
		tmp = x - (t / (z / y))
	elif (z <= -1.75e-38) or not (z <= 0.00118):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+180)
		tmp = Float64(x + y);
	elseif (z <= -3.8e-7)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif ((z <= -1.75e-38) || !(z <= 0.00118))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+180)
		tmp = x + y;
	elseif (z <= -3.8e-7)
		tmp = x - (t / (z / y));
	elseif ((z <= -1.75e-38) || ~((z <= 0.00118)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+180], N[(x + y), $MachinePrecision], If[LessEqual[z, -3.8e-7], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.75e-38], N[Not[LessEqual[z, 0.00118]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000004e180 or -3.80000000000000015e-7 < z < -1.7500000000000001e-38 or 0.0011800000000000001 < z

   1. Initial program 78.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. +-commutative 83.5%

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

   6. Simplified 83.5%

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

   if -1.45000000000000004e180 < z < -3.80000000000000015e-7

   1. Initial program 90.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   5. Taylor expanded in z around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. mul-1-neg 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in x around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. associate-*r/ 73.5%

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

      3. sub-neg 73.5%

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

      4. associate-*r/ 71.5%

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

      5. associate-/l* 73.5%

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

   10. Simplified 73.5%

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

   if -1.7500000000000001e-38 < z < 0.0011800000000000001

   1. Initial program 95.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+180}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-38} \lor \neg \left(z \leq 0.00118\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 3.8 \cdot 10^{-43}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-37) (not (<= z 3.8e-43)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-37) || !(z <= 3.8e-43)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.2d-37)) .or. (.not. (z <= 3.8d-43))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-37) || !(z <= 3.8e-43)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-37) or not (z <= 3.8e-43):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-37) || !(z <= 3.8e-43))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-37) || ~((z <= 3.8e-43)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-37], N[Not[LessEqual[z, 3.8e-43]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000014e-37 or 3.7999999999999997e-43 < z

   1. Initial program 84.2%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.3%

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

      3. clear-num 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in a around 0 84.8%

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

      1. div-sub 84.8%

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

      2. *-inverses 84.8%

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

   8. Simplified 84.8%

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

   if -7.20000000000000014e-37 < z < 3.7999999999999997e-43

   1. Initial program 94.7%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 99.0%

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

      3. clear-num 99.0%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in z around 0 81.2%

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

      1. associate-*r/ 85.9%

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

   8. Simplified 85.9%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-37} \lor \neg \left(z \leq 3.8 \cdot 10^{-43}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+80} \lor \neg \left(z \leq 8.2 \cdot 10^{-41}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+80) (not (<= z 8.2e-41)))
   (+ x (* y (- 1.0 (/ t z))))
   (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+80) || !(z <= 8.2e-41)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+80)) .or. (.not. (z <= 8.2d-41))) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+80) || !(z <= 8.2e-41)) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+80) or not (z <= 8.2e-41):
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+80) || !(z <= 8.2e-41))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+80) || ~((z <= 8.2e-41)))
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+80], N[Not[LessEqual[z, 8.2e-41]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999982e80 or 8.20000000000000028e-41 < z

   1. Initial program 81.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around 0 90.3%

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

      1. div-sub 90.3%

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

      2. *-inverses 90.3%

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

   8. Simplified 90.3%

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

   if -2.59999999999999982e80 < z < 8.20000000000000028e-41

   1. Initial program 94.0%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   6. Simplified 83.3%

      \[\leadsto x + \color{blue}{\frac{-y}{a}} \cdot \left(z - t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+80} \lor \neg \left(z \leq 8.2 \cdot 10^{-41}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 8: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-37} \lor \neg \left(z \leq 5.3 \cdot 10^{-26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e-37) (not (<= z 5.3e-26))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e-37) || !(z <= 5.3e-26)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.85d-37)) .or. (.not. (z <= 5.3d-26))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e-37) || !(z <= 5.3e-26)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e-37) or not (z <= 5.3e-26):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e-37) || !(z <= 5.3e-26))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.85e-37) || ~((z <= 5.3e-26)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e-37], N[Not[LessEqual[z, 5.3e-26]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.84999999999999987e-37 or 5.29999999999999992e-26 < z

   1. Initial program 83.9%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

   6. Simplified 75.8%

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

   if -2.84999999999999987e-37 < z < 5.29999999999999992e-26

   1. Initial program 94.9%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 98.9%

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

      2. associate-/r/ 99.0%

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

      3. clear-num 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in z around 0 80.9%

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

      1. associate-*r/ 85.4%

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

   8. Simplified 85.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-37} \lor \neg \left(z \leq 5.3 \cdot 10^{-26}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-37} \lor \neg \left(z \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e-37) (not (<= z 6.5e-6))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e-37) || !(z <= 6.5e-6)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7d-37)) .or. (.not. (z <= 6.5d-6))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e-37) || !(z <= 6.5e-6)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e-37) or not (z <= 6.5e-6):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e-37) || !(z <= 6.5e-6))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7e-37) || ~((z <= 6.5e-6)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e-37], N[Not[LessEqual[z, 6.5e-6]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000003e-37 or 6.4999999999999996e-6 < z

   1. Initial program 83.1%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 76.2%

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

      1. +-commutative 76.2%

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

   6. Simplified 76.2%

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

   if -7.0000000000000003e-37 < z < 6.4999999999999996e-6

   1. Initial program 95.1%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 84.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-37} \lor \neg \left(z \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 10: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-40} \lor \neg \left(z \leq 33\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e-40) (not (<= z 33.0))) (+ x y) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e-40) || !(z <= 33.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.8d-40)) .or. (.not. (z <= 33.0d0))) then
        tmp = x + y
    else
        tmp = x + (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e-40) || !(z <= 33.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e-40) or not (z <= 33.0):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e-40) || !(z <= 33.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.8e-40) || ~((z <= 33.0)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e-40], N[Not[LessEqual[z, 33.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000036e-40 or 33 < z

   1. Initial program 83.1%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 76.2%

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

      1. +-commutative 76.2%

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

   6. Simplified 76.2%

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

   if -8.80000000000000036e-40 < z < 33

   1. Initial program 95.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-40} \lor \neg \left(z \leq 33\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((z - t) * (y / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 12: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-106} \lor \neg \left(z \leq 3.5 \cdot 10^{-115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-106) (not (<= z 3.5e-115))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-106) || !(z <= 3.5e-115)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-7.2d-106)) .or. (.not. (z <= 3.5d-115))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-106) || !(z <= 3.5e-115)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-106) or not (z <= 3.5e-115):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-106) || !(z <= 3.5e-115))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e-106) || ~((z <= 3.5e-115)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-106], N[Not[LessEqual[z, 3.5e-115]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000025e-106 or 3.5000000000000002e-115 < z

   1. Initial program 86.1%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 70.2%

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

      1. +-commutative 70.2%

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

   6. Simplified 70.2%

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

   if -7.20000000000000025e-106 < z < 3.5000000000000002e-115

   1. Initial program 95.0%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in x around inf 62.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-106} \lor \neg \left(z \leq 3.5 \cdot 10^{-115}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 50.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.8%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 57.1%

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

5. Final simplification 57.1%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((z - a) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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