Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.9% → 91.6%

Time: 10.3s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+97}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+102}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+97)
   (- x (* y (/ (- a z) t)))
   (if (<= t 3e+102)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (- x (/ y (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+97) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3e+102) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y / (t / (a - 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 (t <= (-1.1d+97)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 3d+102) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x - (y / (t / (a - 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 (t <= -1.1e+97) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 3e+102) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+97:
		tmp = x - (y * ((a - z) / t))
	elif t <= 3e+102:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+97)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 3e+102)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+97)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 3e+102)
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+97], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+102], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e97

   1. Initial program 51.0%

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

      1. associate--l+ 57.6%

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

      2. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around 0 91.2%

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

   5. Taylor expanded in t around inf 94.9%

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

      1. associate-*r/ 94.9%

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

      2. mul-1-neg 94.9%

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

      3. sub-neg 94.9%

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

      4. sub-neg 94.9%

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

      5. mul-1-neg 94.9%

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

      6. +-commutative 94.9%

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

      7. distribute-lft-in 94.9%

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

      8. neg-mul-1 94.9%

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

      9. mul-1-neg 94.9%

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

      10. remove-double-neg 94.9%

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

      11. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

   if -1.1e97 < t < 2.9999999999999998e102

   1. Initial program 91.2%

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

      1. associate--l+ 91.8%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   if 2.9999999999999998e102 < t

   1. Initial program 66.7%

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

      1. associate--l+ 69.0%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in y around 0 88.9%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. associate-/l* 93.1%

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

      4. mul-1-neg 93.1%

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

      5. sub-neg 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+97}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+102}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 2: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ z a))))) (t_2 (- x (/ y (/ t (- a z))))))
   (if (<= t -9e+37)
     t_2
     (if (<= t -5.2e-7)
       t_1
       (if (<= t -2.5e-115)
         (+ x (/ (* y z) t))
         (if (<= t 2.1e+28) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (z / a)));
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -9e+37) {
		tmp = t_2;
	} else if (t <= -5.2e-7) {
		tmp = t_1;
	} else if (t <= -2.5e-115) {
		tmp = x + ((y * z) / t);
	} else if (t <= 2.1e+28) {
		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 + (y * (1.0d0 - (z / a)))
    t_2 = x - (y / (t / (a - z)))
    if (t <= (-9d+37)) then
        tmp = t_2
    else if (t <= (-5.2d-7)) then
        tmp = t_1
    else if (t <= (-2.5d-115)) then
        tmp = x + ((y * z) / t)
    else if (t <= 2.1d+28) 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 + (y * (1.0 - (z / a)));
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -9e+37) {
		tmp = t_2;
	} else if (t <= -5.2e-7) {
		tmp = t_1;
	} else if (t <= -2.5e-115) {
		tmp = x + ((y * z) / t);
	} else if (t <= 2.1e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (z / a)))
	t_2 = x - (y / (t / (a - z)))
	tmp = 0
	if t <= -9e+37:
		tmp = t_2
	elif t <= -5.2e-7:
		tmp = t_1
	elif t <= -2.5e-115:
		tmp = x + ((y * z) / t)
	elif t <= 2.1e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(z / a))))
	t_2 = Float64(x - Float64(y / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -9e+37)
		tmp = t_2;
	elseif (t <= -5.2e-7)
		tmp = t_1;
	elseif (t <= -2.5e-115)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 2.1e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (z / a)));
	t_2 = x - (y / (t / (a - z)));
	tmp = 0.0;
	if (t <= -9e+37)
		tmp = t_2;
	elseif (t <= -5.2e-7)
		tmp = t_1;
	elseif (t <= -2.5e-115)
		tmp = x + ((y * z) / t);
	elseif (t <= 2.1e+28)
		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[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+37], t$95$2, If[LessEqual[t, -5.2e-7], t$95$1, If[LessEqual[t, -2.5e-115], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999923e37 or 2.09999999999999989e28 < t

   1. Initial program 65.9%

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

      1. associate--l+ 69.6%

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

      2. associate-/l* 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in y around 0 92.4%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

      3. associate-/l* 90.9%

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

      4. mul-1-neg 90.9%

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

      5. sub-neg 90.9%

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

   7. Simplified 90.9%

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

   if -8.99999999999999923e37 < t < -5.19999999999999998e-7 or -2.5000000000000001e-115 < t < 2.09999999999999989e28

   1. Initial program 90.6%

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

      1. associate--l+ 91.5%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around 0 94.1%

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

   5. Taylor expanded in t around 0 80.7%

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

      1. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -5.19999999999999998e-7 < t < -2.5000000000000001e-115

   1. Initial program 91.4%

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

      1. associate--l+ 91.4%

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

      2. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 95.8%

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

   5. Taylor expanded in a around 0 83.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 3: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot z}{a}\\ t_2 := x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y z) a))) (t_2 (- x (/ y (/ t (- a z))))))
   (if (<= t -2.9e+46)
     t_2
     (if (<= t -1.65e-7)
       t_1
       (if (<= t -6.4e-115)
         (+ x (/ (* y z) t))
         (if (<= t 3.8e+22) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -2.9e+46) {
		tmp = t_2;
	} else if (t <= -1.65e-7) {
		tmp = t_1;
	} else if (t <= -6.4e-115) {
		tmp = x + ((y * z) / t);
	} else if (t <= 3.8e+22) {
		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 + y) - ((y * z) / a)
    t_2 = x - (y / (t / (a - z)))
    if (t <= (-2.9d+46)) then
        tmp = t_2
    else if (t <= (-1.65d-7)) then
        tmp = t_1
    else if (t <= (-6.4d-115)) then
        tmp = x + ((y * z) / t)
    else if (t <= 3.8d+22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * z) / a);
	double t_2 = x - (y / (t / (a - z)));
	double tmp;
	if (t <= -2.9e+46) {
		tmp = t_2;
	} else if (t <= -1.65e-7) {
		tmp = t_1;
	} else if (t <= -6.4e-115) {
		tmp = x + ((y * z) / t);
	} else if (t <= 3.8e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * z) / a)
	t_2 = x - (y / (t / (a - z)))
	tmp = 0
	if t <= -2.9e+46:
		tmp = t_2
	elif t <= -1.65e-7:
		tmp = t_1
	elif t <= -6.4e-115:
		tmp = x + ((y * z) / t)
	elif t <= 3.8e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * z) / a))
	t_2 = Float64(x - Float64(y / Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t <= -2.9e+46)
		tmp = t_2;
	elseif (t <= -1.65e-7)
		tmp = t_1;
	elseif (t <= -6.4e-115)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t <= 3.8e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * z) / a);
	t_2 = x - (y / (t / (a - z)));
	tmp = 0.0;
	if (t <= -2.9e+46)
		tmp = t_2;
	elseif (t <= -1.65e-7)
		tmp = t_1;
	elseif (t <= -6.4e-115)
		tmp = x + ((y * z) / t);
	elseif (t <= 3.8e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+46], t$95$2, If[LessEqual[t, -1.65e-7], t$95$1, If[LessEqual[t, -6.4e-115], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e46 or 3.8000000000000004e22 < t

   1. Initial program 65.4%

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

      1. associate--l+ 69.1%

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

      2. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in y around 0 92.3%

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

   5. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

      3. associate-/l* 91.5%

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

      4. mul-1-neg 91.5%

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

      5. sub-neg 91.5%

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

   7. Simplified 91.5%

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

   if -2.9000000000000002e46 < t < -1.6500000000000001e-7 or -6.4e-115 < t < 3.8000000000000004e22

   1. Initial program 90.8%

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

      1. associate--l+ 91.8%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 81.4%

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

   if -1.6500000000000001e-7 < t < -6.4e-115

   1. Initial program 91.0%

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

      1. associate--l+ 91.0%

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

      2. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in y around 0 95.6%

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

   5. Taylor expanded in a around 0 83.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+46}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-7}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-115}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+22}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 4: 93.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\left(\frac{t}{a - t} + 1\right) - \frac{z}{a - t}\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (- (+ (/ t (- a t)) 1.0) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - 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 * (((t / (a - t)) + 1.0d0) - (z / (a - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(t / Float64(a - t)) + 1.0) - Float64(z / Float64(a - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((t / (a - t)) + 1.0) - (z / (a - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.4%

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

   1. associate--l+ 80.6%

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

   2. associate-/l* 87.1%

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

3. Simplified 87.1%

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

4. Taylor expanded in y around 0 93.4%

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

5. Final simplification 93.4%

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

Alternative 5: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+101}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e+95)
   (- x (* y (/ (- a z) t)))
   (if (<= t 1.5e+101)
     (+ x (- y (/ y (/ (- a t) z))))
     (- x (/ y (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e+95) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 1.5e+101) {
		tmp = x + (y - (y / ((a - t) / z)));
	} else {
		tmp = x - (y / (t / (a - 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 (t <= (-1.9d+95)) then
        tmp = x - (y * ((a - z) / t))
    else if (t <= 1.5d+101) then
        tmp = x + (y - (y / ((a - t) / z)))
    else
        tmp = x - (y / (t / (a - 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 (t <= -1.9e+95) {
		tmp = x - (y * ((a - z) / t));
	} else if (t <= 1.5e+101) {
		tmp = x + (y - (y / ((a - t) / z)));
	} else {
		tmp = x - (y / (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e+95:
		tmp = x - (y * ((a - z) / t))
	elif t <= 1.5e+101:
		tmp = x + (y - (y / ((a - t) / z)))
	else:
		tmp = x - (y / (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e+95)
		tmp = Float64(x - Float64(y * Float64(Float64(a - z) / t)));
	elseif (t <= 1.5e+101)
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e+95)
		tmp = x - (y * ((a - z) / t));
	elseif (t <= 1.5e+101)
		tmp = x + (y - (y / ((a - t) / z)));
	else
		tmp = x - (y / (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e+95], N[(x - N[(y * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+101], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e95

   1. Initial program 51.0%

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

      1. associate--l+ 57.6%

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

      2. associate-/l* 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around 0 91.2%

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

   5. Taylor expanded in t around inf 94.9%

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

      1. associate-*r/ 94.9%

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

      2. mul-1-neg 94.9%

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

      3. sub-neg 94.9%

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

      4. sub-neg 94.9%

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

      5. mul-1-neg 94.9%

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

      6. +-commutative 94.9%

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

      7. distribute-lft-in 94.9%

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

      8. neg-mul-1 94.9%

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

      9. mul-1-neg 94.9%

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

      10. remove-double-neg 94.9%

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

      11. neg-mul-1 94.9%

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

   7. Simplified 94.9%

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

   if -1.9e95 < t < 1.49999999999999997e101

   1. Initial program 91.2%

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

      1. associate--l+ 91.8%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 91.7%

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

      1. associate-/l* 93.7%

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

   6. Simplified 93.7%

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

   if 1.49999999999999997e101 < t

   1. Initial program 66.7%

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

      1. associate--l+ 69.0%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in y around 0 88.9%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

      3. associate-/l* 93.1%

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

      4. mul-1-neg 93.1%

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

      5. sub-neg 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;x - y \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+101}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a - z}}\\ \end{array} \]

Alternative 6: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-35} \lor \neg \left(a \leq 9.5 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-35) (not (<= a 9.5e-58)))
   (+ x (* y (- 1.0 (/ z a))))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-35) || !(a <= 9.5e-58)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x + (y / (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 ((a <= (-4.8d-35)) .or. (.not. (a <= 9.5d-58))) then
        tmp = x + (y * (1.0d0 - (z / a)))
    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 a) {
	double tmp;
	if ((a <= -4.8e-35) || !(a <= 9.5e-58)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-35) or not (a <= 9.5e-58):
		tmp = x + (y * (1.0 - (z / a)))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-35) || !(a <= 9.5e-58))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / a))));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-35) || ~((a <= 9.5e-58)))
		tmp = x + (y * (1.0 - (z / a)));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-35], N[Not[LessEqual[a, 9.5e-58]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000003e-35 or 9.4999999999999994e-58 < a

   1. Initial program 80.0%

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

      1. associate--l+ 81.3%

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

      2. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around 0 92.1%

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

   5. Taylor expanded in t around 0 80.7%

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

      1. +-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -4.8000000000000003e-35 < a < 9.4999999999999994e-58

   1. Initial program 76.6%

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

      1. associate--l+ 79.8%

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

      2. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around 0 95.0%

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

   5. Taylor expanded in a around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-35} \lor \neg \left(a \leq 9.5 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+101} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e+101) (not (<= a 1.12e+129)))
   (+ x (* y (- 1.0 (/ z a))))
   (- x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e+101) || !(a <= 1.12e+129)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x - (y * (z / (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 ((a <= (-6.5d+101)) .or. (.not. (a <= 1.12d+129))) then
        tmp = x + (y * (1.0d0 - (z / a)))
    else
        tmp = x - (y * (z / (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 ((a <= -6.5e+101) || !(a <= 1.12e+129)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.5e+101) or not (a <= 1.12e+129):
		tmp = x + (y * (1.0 - (z / a)))
	else:
		tmp = x - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e+101) || !(a <= 1.12e+129))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / a))));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.5e+101) || ~((a <= 1.12e+129)))
		tmp = x + (y * (1.0 - (z / a)));
	else
		tmp = x - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e+101], N[Not[LessEqual[a, 1.12e+129]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.50000000000000016e101 or 1.11999999999999993e129 < a

   1. Initial program 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in t around 0 91.9%

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

      1. +-commutative 91.9%

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

   7. Simplified 91.9%

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

   if -6.50000000000000016e101 < a < 1.11999999999999993e129

   1. Initial program 77.5%

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

      1. associate--l+ 80.7%

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

      2. associate-/l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in y around 0 93.8%

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

   5. Taylor expanded in z around inf 88.3%

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

      1. neg-mul-1 88.3%

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

      2. distribute-neg-frac 88.3%

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

   7. Simplified 88.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+101} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 8: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+93} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+93) (not (<= a 1.12e+129))) (+ x y) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+93) || !(a <= 1.12e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / 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 ((a <= (-2.8d+93)) .or. (.not. (a <= 1.12d+129))) then
        tmp = x + y
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+93) || !(a <= 1.12e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e+93) or not (a <= 1.12e+129):
		tmp = x + y
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+93) || !(a <= 1.12e+129))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e+93) || ~((a <= 1.12e+129)))
		tmp = x + y;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e+93], N[Not[LessEqual[a, 1.12e+129]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.79999999999999989e93 or 1.11999999999999993e129 < a

   1. Initial program 81.3%

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

      1. associate--l+ 81.3%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 84.9%

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

      1. +-commutative 84.9%

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

   6. Simplified 84.9%

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

   if -2.79999999999999989e93 < a < 1.11999999999999993e129

   1. Initial program 77.1%

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

      1. associate--l+ 80.3%

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

      2. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in y around 0 93.7%

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

   5. Taylor expanded in a around 0 76.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+93} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+93} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.6e+93) (not (<= a 1.12e+129))) (+ x y) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e+93) || !(a <= 1.12e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (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 ((a <= (-3.6d+93)) .or. (.not. (a <= 1.12d+129))) then
        tmp = x + y
    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 a) {
	double tmp;
	if ((a <= -3.6e+93) || !(a <= 1.12e+129)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.6e+93) or not (a <= 1.12e+129):
		tmp = x + y
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.6e+93) || !(a <= 1.12e+129))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.6e+93) || ~((a <= 1.12e+129)))
		tmp = x + y;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.6e+93], N[Not[LessEqual[a, 1.12e+129]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5999999999999999e93 or 1.11999999999999993e129 < a

   1. Initial program 81.3%

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

      1. associate--l+ 81.3%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in a around inf 84.9%

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

      1. +-commutative 84.9%

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

   6. Simplified 84.9%

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

   if -3.5999999999999999e93 < a < 1.11999999999999993e129

   1. Initial program 77.1%

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

      1. associate--l+ 80.3%

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

      2. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in y around 0 93.7%

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

   5. Taylor expanded in a around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+93} \lor \neg \left(a \leq 1.12 \cdot 10^{+129}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 10: 61.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-258} \lor \neg \left(a \leq 2.4 \cdot 10^{-210}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e-258) (not (<= a 2.4e-210))) (+ x y) (* z (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-258) || !(a <= 2.4e-210)) {
		tmp = x + y;
	} else {
		tmp = z * (y / 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 ((a <= (-3.3d-258)) .or. (.not. (a <= 2.4d-210))) then
        tmp = x + y
    else
        tmp = z * (y / 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 ((a <= -3.3e-258) || !(a <= 2.4e-210)) {
		tmp = x + y;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e-258) or not (a <= 2.4e-210):
		tmp = x + y
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e-258) || !(a <= 2.4e-210))
		tmp = Float64(x + y);
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e-258) || ~((a <= 2.4e-210)))
		tmp = x + y;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e-258], N[Not[LessEqual[a, 2.4e-210]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3e-258 or 2.40000000000000004e-210 < a

   1. Initial program 79.7%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in a around inf 66.2%

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

      1. +-commutative 66.2%

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

   6. Simplified 66.2%

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

   if -3.3e-258 < a < 2.40000000000000004e-210

   1. Initial program 71.7%

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

      1. associate--l+ 74.1%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in z around inf 71.1%

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

      1. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in z around inf 57.8%

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

      1. associate-*l/ 61.1%

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

      2. associate-*r* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

      5. distribute-neg-frac 61.1%

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

   9. Simplified 61.1%

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

   10. Taylor expanded in a around 0 54.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-258} \lor \neg \left(a \leq 2.4 \cdot 10^{-210}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 61.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+216}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -9.4e+216) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.4e+216) {
		tmp = x;
	} else {
		tmp = x + 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 (t <= (-9.4d+216)) then
        tmp = x
    else
        tmp = x + 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 (t <= -9.4e+216) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.4e+216:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.4e+216)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.4e+216)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.4e+216], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4000000000000004e216

   1. Initial program 35.4%

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

      1. associate--l+ 48.5%

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

      2. associate-/l* 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in x around inf 62.0%

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

   if -9.4000000000000004e216 < t

   1. Initial program 82.3%

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

      1. associate--l+ 83.5%

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

      2. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in a around inf 61.6%

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

      1. +-commutative 61.6%

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

   6. Simplified 61.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+216}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 49.8% accurate, 13.0× 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 78.4%

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

   1. associate--l+ 80.6%

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

   2. associate-/l* 87.1%

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

3. Simplified 87.1%

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

4. Taylor expanded in x around inf 50.7%

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

5. Final simplification 50.7%

   \[\leadsto x \]

Developer target: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	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 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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