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

Percentage Accurate: 98.1% → 98.1%

Time: 9.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

2. Final simplification 99.1%

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

Alternative 2: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{t}{z - t}}\\ t_2 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ t (- z t))))) (t_2 (+ x (* y (/ (- z t) a)))))
   (if (<= a -9.8e+55)
     t_2
     (if (<= a -3.2e-38)
       t_1
       (if (<= a -2.1e-84)
         (+ x (/ (* y z) a))
         (if (<= a 3.1e-123)
           t_1
           (if (<= a 6e+81) (+ x (* y (/ z (- a t)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / (z - t)));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -9.8e+55) {
		tmp = t_2;
	} else if (a <= -3.2e-38) {
		tmp = t_1;
	} else if (a <= -2.1e-84) {
		tmp = x + ((y * z) / a);
	} else if (a <= 3.1e-123) {
		tmp = t_1;
	} else if (a <= 6e+81) {
		tmp = x + (y * (z / (a - t)));
	} 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 / (t / (z - t)))
    t_2 = x + (y * ((z - t) / a))
    if (a <= (-9.8d+55)) then
        tmp = t_2
    else if (a <= (-3.2d-38)) then
        tmp = t_1
    else if (a <= (-2.1d-84)) then
        tmp = x + ((y * z) / a)
    else if (a <= 3.1d-123) then
        tmp = t_1
    else if (a <= 6d+81) then
        tmp = x + (y * (z / (a - t)))
    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 / (t / (z - t)));
	double t_2 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -9.8e+55) {
		tmp = t_2;
	} else if (a <= -3.2e-38) {
		tmp = t_1;
	} else if (a <= -2.1e-84) {
		tmp = x + ((y * z) / a);
	} else if (a <= 3.1e-123) {
		tmp = t_1;
	} else if (a <= 6e+81) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (t / (z - t)))
	t_2 = x + (y * ((z - t) / a))
	tmp = 0
	if a <= -9.8e+55:
		tmp = t_2
	elif a <= -3.2e-38:
		tmp = t_1
	elif a <= -2.1e-84:
		tmp = x + ((y * z) / a)
	elif a <= 3.1e-123:
		tmp = t_1
	elif a <= 6e+81:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(t / Float64(z - t))))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -9.8e+55)
		tmp = t_2;
	elseif (a <= -3.2e-38)
		tmp = t_1;
	elseif (a <= -2.1e-84)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 3.1e-123)
		tmp = t_1;
	elseif (a <= 6e+81)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (t / (z - t)));
	t_2 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -9.8e+55)
		tmp = t_2;
	elseif (a <= -3.2e-38)
		tmp = t_1;
	elseif (a <= -2.1e-84)
		tmp = x + ((y * z) / a);
	elseif (a <= 3.1e-123)
		tmp = t_1;
	elseif (a <= 6e+81)
		tmp = x + (y * (z / (a - t)));
	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[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.8e+55], t$95$2, If[LessEqual[a, -3.2e-38], t$95$1, If[LessEqual[a, -2.1e-84], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e-123], t$95$1, If[LessEqual[a, 6e+81], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.80000000000000029e55 or 5.99999999999999995e81 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 94.3%

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

   if -9.80000000000000029e55 < a < -3.19999999999999977e-38 or -2.09999999999999998e-84 < a < 3.09999999999999998e-123

   1. Initial program 99.0%

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

      1. associate-*r/ 82.6%

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

   3. Simplified 82.6%

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

      1. associate-*r/ 99.0%

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

      2. *-commutative 99.0%

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

      3. div-inv 98.8%

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

      4. associate-*l* 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in a around 0 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. *-commutative 72.7%

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

      4. unsub-neg 72.7%

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

      5. *-commutative 72.7%

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

      6. associate-/l* 89.1%

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

   8. Simplified 89.1%

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

   if -3.19999999999999977e-38 < a < -2.09999999999999998e-84

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 82.9%

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

   if 3.09999999999999998e-123 < a < 5.99999999999999995e81

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 89.6%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+81}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 3: 81.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) a)))))
   (if (<= a -5.5e+55)
     t_1
     (if (<= a -5e-38)
       (- x (/ y (/ t (- z t))))
       (if (<= a -5e-85)
         (+ x (/ (* y z) a))
         (if (<= a 4.1e-123)
           (+ x (/ (- t z) (/ t y)))
           (if (<= a 2.45e+82) (+ x (* y (/ z (- a t)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -5.5e+55) {
		tmp = t_1;
	} else if (a <= -5e-38) {
		tmp = x - (y / (t / (z - t)));
	} else if (a <= -5e-85) {
		tmp = x + ((y * z) / a);
	} else if (a <= 4.1e-123) {
		tmp = x + ((t - z) / (t / y));
	} else if (a <= 2.45e+82) {
		tmp = x + (y * (z / (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) :: tmp
    t_1 = x + (y * ((z - t) / a))
    if (a <= (-5.5d+55)) then
        tmp = t_1
    else if (a <= (-5d-38)) then
        tmp = x - (y / (t / (z - t)))
    else if (a <= (-5d-85)) then
        tmp = x + ((y * z) / a)
    else if (a <= 4.1d-123) then
        tmp = x + ((t - z) / (t / y))
    else if (a <= 2.45d+82) then
        tmp = x + (y * (z / (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 = x + (y * ((z - t) / a));
	double tmp;
	if (a <= -5.5e+55) {
		tmp = t_1;
	} else if (a <= -5e-38) {
		tmp = x - (y / (t / (z - t)));
	} else if (a <= -5e-85) {
		tmp = x + ((y * z) / a);
	} else if (a <= 4.1e-123) {
		tmp = x + ((t - z) / (t / y));
	} else if (a <= 2.45e+82) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / a))
	tmp = 0
	if a <= -5.5e+55:
		tmp = t_1
	elif a <= -5e-38:
		tmp = x - (y / (t / (z - t)))
	elif a <= -5e-85:
		tmp = x + ((y * z) / a)
	elif a <= 4.1e-123:
		tmp = x + ((t - z) / (t / y))
	elif a <= 2.45e+82:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -5.5e+55)
		tmp = t_1;
	elseif (a <= -5e-38)
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	elseif (a <= -5e-85)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (a <= 4.1e-123)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (a <= 2.45e+82)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / a));
	tmp = 0.0;
	if (a <= -5.5e+55)
		tmp = t_1;
	elseif (a <= -5e-38)
		tmp = x - (y / (t / (z - t)));
	elseif (a <= -5e-85)
		tmp = x + ((y * z) / a);
	elseif (a <= 4.1e-123)
		tmp = x + ((t - z) / (t / y));
	elseif (a <= 2.45e+82)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+55], t$95$1, If[LessEqual[a, -5e-38], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-85], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-123], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+82], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.5000000000000004e55 or 2.45e82 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 94.3%

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

   if -5.5000000000000004e55 < a < -5.00000000000000033e-38

   1. Initial program 99.9%

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

      1. associate-*r/ 84.3%

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

   3. Simplified 84.3%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. div-inv 99.8%

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

      4. associate-*l* 87.9%

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

   5. Applied egg-rr 87.9%

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

   6. Taylor expanded in a around 0 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. *-commutative 67.8%

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

      4. unsub-neg 67.8%

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

      5. *-commutative 67.8%

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

      6. associate-/l* 83.5%

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

   8. Simplified 83.5%

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

   if -5.00000000000000033e-38 < a < -5.0000000000000002e-85

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 82.9%

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

   if -5.0000000000000002e-85 < a < 4.1e-123

   1. Initial program 98.7%

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

   2. Taylor expanded in a around 0 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. associate-/l* 91.9%

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

   4. Simplified 91.9%

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

   if 4.1e-123 < a < 2.45e82

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 89.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-85}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 4: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 115000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- t a)) (- t z))))
   (if (<= y -6.5e+107)
     t_1
     (if (<= y 8.8e-269)
       (+ x (/ (* y z) a))
       (if (<= y 1.6e-57)
         (+ x y)
         (if (<= y 115000.0) (+ x (* y (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (t - a)) * (t - z);
	double tmp;
	if (y <= -6.5e+107) {
		tmp = t_1;
	} else if (y <= 8.8e-269) {
		tmp = x + ((y * z) / a);
	} else if (y <= 1.6e-57) {
		tmp = x + y;
	} else if (y <= 115000.0) {
		tmp = x + (y * (z / a));
	} 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) :: tmp
    t_1 = (y / (t - a)) * (t - z)
    if (y <= (-6.5d+107)) then
        tmp = t_1
    else if (y <= 8.8d-269) then
        tmp = x + ((y * z) / a)
    else if (y <= 1.6d-57) then
        tmp = x + y
    else if (y <= 115000.0d0) then
        tmp = x + (y * (z / a))
    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 / (t - a)) * (t - z);
	double tmp;
	if (y <= -6.5e+107) {
		tmp = t_1;
	} else if (y <= 8.8e-269) {
		tmp = x + ((y * z) / a);
	} else if (y <= 1.6e-57) {
		tmp = x + y;
	} else if (y <= 115000.0) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (t - a)) * (t - z)
	tmp = 0
	if y <= -6.5e+107:
		tmp = t_1
	elif y <= 8.8e-269:
		tmp = x + ((y * z) / a)
	elif y <= 1.6e-57:
		tmp = x + y
	elif y <= 115000.0:
		tmp = x + (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(t - a)) * Float64(t - z))
	tmp = 0.0
	if (y <= -6.5e+107)
		tmp = t_1;
	elseif (y <= 8.8e-269)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (y <= 1.6e-57)
		tmp = Float64(x + y);
	elseif (y <= 115000.0)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (t - a)) * (t - z);
	tmp = 0.0;
	if (y <= -6.5e+107)
		tmp = t_1;
	elseif (y <= 8.8e-269)
		tmp = x + ((y * z) / a);
	elseif (y <= 1.6e-57)
		tmp = x + y;
	elseif (y <= 115000.0)
		tmp = x + (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+107], t$95$1, If[LessEqual[y, 8.8e-269], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-57], N[(x + y), $MachinePrecision], If[LessEqual[y, 115000.0], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5000000000000006e107 or 115000 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 67.6%

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

      4. sub-neg 67.6%

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

      5. +-commutative 67.6%

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

      6. neg-sub0 67.6%

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

      7. associate-+l- 67.6%

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

      8. sub0-neg 67.6%

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

      9. neg-mul-1 67.6%

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

      10. times-frac 97.2%

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

      11. fma-def 97.2%

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

      12. sub-neg 97.2%

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

      13. +-commutative 97.2%

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

      14. neg-sub0 97.2%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 97.2%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 97.2%

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

      17. neg-mul-1 97.2%

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

      18. *-commutative 97.2%

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

      19. associate-/l* 97.2%

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

      20. metadata-eval 97.2%

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

      21. /-rgt-identity 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around -inf 53.5%

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

      1. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

      1. associate-/r/ 80.1%

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

   8. Applied egg-rr 80.1%

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

   if -6.5000000000000006e107 < y < 8.79999999999999936e-269

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 79.4%

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

   if 8.79999999999999936e-269 < y < 1.6e-57

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 86.4%

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

   if 1.6e-57 < y < 115000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 75.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;y \leq 115000:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t - a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-87} \lor \neg \left(t \leq 8.2 \cdot 10^{-23}\right) \land t \leq 1.26 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+38)
   (+ x y)
   (if (or (<= t 1.8e-87) (and (not (<= t 8.2e-23)) (<= t 1.26e+61)))
     (+ x (* y (/ z a)))
     (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+38) {
		tmp = x + y;
	} else if ((t <= 1.8e-87) || (!(t <= 8.2e-23) && (t <= 1.26e+61))) {
		tmp = x + (y * (z / a));
	} 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 <= (-5.2d+38)) then
        tmp = x + y
    else if ((t <= 1.8d-87) .or. (.not. (t <= 8.2d-23)) .and. (t <= 1.26d+61)) then
        tmp = x + (y * (z / a))
    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 <= -5.2e+38) {
		tmp = x + y;
	} else if ((t <= 1.8e-87) || (!(t <= 8.2e-23) && (t <= 1.26e+61))) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+38:
		tmp = x + y
	elif (t <= 1.8e-87) or (not (t <= 8.2e-23) and (t <= 1.26e+61)):
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+38)
		tmp = Float64(x + y);
	elseif ((t <= 1.8e-87) || (!(t <= 8.2e-23) && (t <= 1.26e+61)))
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+38)
		tmp = x + y;
	elseif ((t <= 1.8e-87) || (~((t <= 8.2e-23)) && (t <= 1.26e+61)))
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+38], N[(x + y), $MachinePrecision], If[Or[LessEqual[t, 1.8e-87], And[N[Not[LessEqual[t, 8.2e-23]], $MachinePrecision], LessEqual[t, 1.26e+61]]], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999998e38 or 1.79999999999999996e-87 < t < 8.20000000000000059e-23 or 1.2600000000000001e61 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.8%

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

   if -5.1999999999999998e38 < t < 1.79999999999999996e-87 or 8.20000000000000059e-23 < t < 1.2600000000000001e61

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0 79.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-87} \lor \neg \left(t \leq 8.2 \cdot 10^{-23}\right) \land t \leq 1.26 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 76.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+38)
   (+ x y)
   (if (<= t 1.86e-87)
     (+ x (/ y (/ a z)))
     (if (<= t 7.6e-23)
       (+ x y)
       (if (<= t 2e+61) (+ x (* y (/ z a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+38) {
		tmp = x + y;
	} else if (t <= 1.86e-87) {
		tmp = x + (y / (a / z));
	} else if (t <= 7.6e-23) {
		tmp = x + y;
	} else if (t <= 2e+61) {
		tmp = x + (y * (z / a));
	} 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 <= (-5.2d+38)) then
        tmp = x + y
    else if (t <= 1.86d-87) then
        tmp = x + (y / (a / z))
    else if (t <= 7.6d-23) then
        tmp = x + y
    else if (t <= 2d+61) then
        tmp = x + (y * (z / a))
    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 <= -5.2e+38) {
		tmp = x + y;
	} else if (t <= 1.86e-87) {
		tmp = x + (y / (a / z));
	} else if (t <= 7.6e-23) {
		tmp = x + y;
	} else if (t <= 2e+61) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+38:
		tmp = x + y
	elif t <= 1.86e-87:
		tmp = x + (y / (a / z))
	elif t <= 7.6e-23:
		tmp = x + y
	elif t <= 2e+61:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+38)
		tmp = Float64(x + y);
	elseif (t <= 1.86e-87)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 7.6e-23)
		tmp = Float64(x + y);
	elseif (t <= 2e+61)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+38)
		tmp = x + y;
	elseif (t <= 1.86e-87)
		tmp = x + (y / (a / z));
	elseif (t <= 7.6e-23)
		tmp = x + y;
	elseif (t <= 2e+61)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+38], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.86e-87], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-23], N[(x + y), $MachinePrecision], If[LessEqual[t, 2e+61], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999998e38 or 1.8600000000000001e-87 < t < 7.60000000000000023e-23 or 1.9999999999999999e61 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.8%

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

   if -5.1999999999999998e38 < t < 1.8600000000000001e-87

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 78.2%

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

      1. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

   if 7.60000000000000023e-23 < t < 1.9999999999999999e61

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 69.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+38}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.86 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-23}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+42)
   (+ x y)
   (if (<= t 6.8e-88)
     (+ x (/ y (/ a z)))
     (if (<= t 1.35e-22)
       (+ x y)
       (if (<= t 1.26e+61) (- x (/ y (/ a t))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+42) {
		tmp = x + y;
	} else if (t <= 6.8e-88) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.35e-22) {
		tmp = x + y;
	} else if (t <= 1.26e+61) {
		tmp = x - (y / (a / t));
	} 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 <= (-6d+42)) then
        tmp = x + y
    else if (t <= 6.8d-88) then
        tmp = x + (y / (a / z))
    else if (t <= 1.35d-22) then
        tmp = x + y
    else if (t <= 1.26d+61) then
        tmp = x - (y / (a / t))
    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 <= -6e+42) {
		tmp = x + y;
	} else if (t <= 6.8e-88) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.35e-22) {
		tmp = x + y;
	} else if (t <= 1.26e+61) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+42:
		tmp = x + y
	elif t <= 6.8e-88:
		tmp = x + (y / (a / z))
	elif t <= 1.35e-22:
		tmp = x + y
	elif t <= 1.26e+61:
		tmp = x - (y / (a / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+42)
		tmp = Float64(x + y);
	elseif (t <= 6.8e-88)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.35e-22)
		tmp = Float64(x + y);
	elseif (t <= 1.26e+61)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e+42)
		tmp = x + y;
	elseif (t <= 6.8e-88)
		tmp = x + (y / (a / z));
	elseif (t <= 1.35e-22)
		tmp = x + y;
	elseif (t <= 1.26e+61)
		tmp = x - (y / (a / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+42], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.8e-88], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-22], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.26e+61], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000058e42 or 6.79999999999999949e-88 < t < 1.3500000000000001e-22 or 1.2600000000000001e61 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.8%

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

   if -6.00000000000000058e42 < t < 6.79999999999999949e-88

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 78.2%

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

      1. associate-/l* 80.4%

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

   4. Simplified 80.4%

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

   if 1.3500000000000001e-22 < t < 1.2600000000000001e61

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 81.9%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-22}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+61}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+107} \lor \neg \left(y \leq 1.3 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.5e+107) (not (<= y 1.3e+157)))
   (* (/ y (- t a)) (- t z))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.5e+107) || !(y <= 1.3e+157)) {
		tmp = (y / (t - a)) * (t - z);
	} 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 ((y <= (-9.5d+107)) .or. (.not. (y <= 1.3d+157))) then
        tmp = (y / (t - a)) * (t - z)
    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 ((y <= -9.5e+107) || !(y <= 1.3e+157)) {
		tmp = (y / (t - a)) * (t - z);
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.5e+107) or not (y <= 1.3e+157):
		tmp = (y / (t - a)) * (t - z)
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.5e+107) || !(y <= 1.3e+157))
		tmp = Float64(Float64(y / Float64(t - a)) * Float64(t - z));
	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 ((y <= -9.5e+107) || ~((y <= 1.3e+157)))
		tmp = (y / (t - a)) * (t - z);
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.5e+107], N[Not[LessEqual[y, 1.3e+157]], $MachinePrecision]], N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000019e107 or 1.30000000000000005e157 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 58.5%

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

      4. sub-neg 58.5%

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

      5. +-commutative 58.5%

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

      6. neg-sub0 58.5%

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

      7. associate-+l- 58.5%

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

      8. sub0-neg 58.5%

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

      9. neg-mul-1 58.5%

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

      10. times-frac 95.9%

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

      11. fma-def 95.9%

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

      12. sub-neg 95.9%

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

      13. +-commutative 95.9%

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

      14. neg-sub0 95.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 95.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 95.9%

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

      17. neg-mul-1 95.9%

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

      18. *-commutative 95.9%

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

      19. associate-/l* 95.9%

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

      20. metadata-eval 95.9%

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

      21. /-rgt-identity 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in y around -inf 52.4%

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

      1. associate-/l* 87.7%

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

   6. Simplified 87.7%

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

      1. associate-/r/ 85.2%

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

   8. Applied egg-rr 85.2%

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

   if -9.50000000000000019e107 < y < 1.30000000000000005e157

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 84.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+107} \lor \neg \left(y \leq 1.3 \cdot 10^{+157}\right):\\ \;\;\;\;\frac{y}{t - a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 9: 57.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-288}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-288) (+ x y) (if (<= a 4.2e-131) (* y (/ (- t z) t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-288) {
		tmp = x + y;
	} else if (a <= 4.2e-131) {
		tmp = y * ((t - z) / t);
	} 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 (a <= (-4.8d-288)) then
        tmp = x + y
    else if (a <= 4.2d-131) then
        tmp = y * ((t - z) / t)
    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 (a <= -4.8e-288) {
		tmp = x + y;
	} else if (a <= 4.2e-131) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-288:
		tmp = x + y
	elif a <= 4.2e-131:
		tmp = y * ((t - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-288)
		tmp = Float64(x + y);
	elseif (a <= 4.2e-131)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e-288)
		tmp = x + y;
	elseif (a <= 4.2e-131)
		tmp = y * ((t - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-288], N[(x + y), $MachinePrecision], If[LessEqual[a, 4.2e-131], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -4.7999999999999997e-288

   1. Initial program 99.1%

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

   2. Taylor expanded in t around inf 66.2%

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

   if -4.7999999999999997e-288 < a < 4.19999999999999994e-131

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 72.7%

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

      4. sub-neg 72.7%

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

      5. +-commutative 72.7%

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

      6. neg-sub0 72.7%

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

      7. associate-+l- 72.7%

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

      8. sub0-neg 72.7%

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

      9. neg-mul-1 72.7%

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

      10. times-frac 96.9%

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

      11. fma-def 96.9%

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

      12. sub-neg 96.9%

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

      13. +-commutative 96.9%

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

      14. neg-sub0 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 96.9%

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

      17. neg-mul-1 96.9%

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

      18. *-commutative 96.9%

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

      19. associate-/l* 96.9%

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

      20. metadata-eval 96.9%

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

      21. /-rgt-identity 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around -inf 64.2%

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

      1. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in a around 0 53.9%

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

      1. expm1-log1p-u 33.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

      2. expm1-udef 24.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]

   9. Applied egg-rr 24.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 33.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

       2. expm1-log1p 53.9%

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

       3. associate-*r/ 75.5%

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

   11. Simplified 75.5%

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

   if 4.19999999999999994e-131 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 64.3%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-288}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 57.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-286}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-131}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-286) (+ x y) (if (<= a 7e-131) (* (- t z) (/ y t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-286) {
		tmp = x + y;
	} else if (a <= 7e-131) {
		tmp = (t - z) * (y / t);
	} 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 (a <= (-4.5d-286)) then
        tmp = x + y
    else if (a <= 7d-131) then
        tmp = (t - z) * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-286) {
		tmp = x + y;
	} else if (a <= 7e-131) {
		tmp = (t - z) * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-286:
		tmp = x + y
	elif a <= 7e-131:
		tmp = (t - z) * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-286)
		tmp = Float64(x + y);
	elseif (a <= 7e-131)
		tmp = Float64(Float64(t - z) * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-286)
		tmp = x + y;
	elseif (a <= 7e-131)
		tmp = (t - z) * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-286], N[(x + y), $MachinePrecision], If[LessEqual[a, 7e-131], N[(N[(t - z), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -4.50000000000000005e-286

   1. Initial program 99.1%

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

   2. Taylor expanded in t around inf 66.2%

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

   if -4.50000000000000005e-286 < a < 7.0000000000000004e-131

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 72.7%

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

      4. sub-neg 72.7%

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

      5. +-commutative 72.7%

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

      6. neg-sub0 72.7%

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

      7. associate-+l- 72.7%

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

      8. sub0-neg 72.7%

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

      9. neg-mul-1 72.7%

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

      10. times-frac 96.9%

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

      11. fma-def 96.9%

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

      12. sub-neg 96.9%

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

      13. +-commutative 96.9%

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

      14. neg-sub0 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 96.9%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 96.9%

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

      17. neg-mul-1 96.9%

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

      18. *-commutative 96.9%

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

      19. associate-/l* 96.9%

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

      20. metadata-eval 96.9%

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

      21. /-rgt-identity 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around -inf 64.2%

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

      1. associate-/l* 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in a around 0 53.9%

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

      1. expm1-log1p-u 33.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

      2. expm1-udef 24.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]

   9. Applied egg-rr 24.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 33.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

       2. expm1-log1p 53.9%

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

       3. *-commutative 53.9%

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

       4. associate-*r/ 78.0%

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

       5. *-commutative 78.0%

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

   11. Simplified 78.0%

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

   if 7.0000000000000004e-131 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 64.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-286}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-131}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 59.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.8 \cdot 10^{-308}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 8.8e-308)
   (+ x y)
   (if (<= a 3e-245) (* y (/ (- z) t)) (if (<= a 1550000000.0) (+ x y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 8.8e-308) {
		tmp = x + y;
	} else if (a <= 3e-245) {
		tmp = y * (-z / t);
	} else if (a <= 1550000000.0) {
		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 (a <= 8.8d-308) then
        tmp = x + y
    else if (a <= 3d-245) then
        tmp = y * (-z / t)
    else if (a <= 1550000000.0d0) 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 (a <= 8.8e-308) {
		tmp = x + y;
	} else if (a <= 3e-245) {
		tmp = y * (-z / t);
	} else if (a <= 1550000000.0) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 8.8e-308:
		tmp = x + y
	elif a <= 3e-245:
		tmp = y * (-z / t)
	elif a <= 1550000000.0:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 8.8e-308)
		tmp = Float64(x + y);
	elseif (a <= 3e-245)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (a <= 1550000000.0)
		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 (a <= 8.8e-308)
		tmp = x + y;
	elseif (a <= 3e-245)
		tmp = y * (-z / t);
	elseif (a <= 1550000000.0)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 8.8e-308], N[(x + y), $MachinePrecision], If[LessEqual[a, 3e-245], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1550000000.0], N[(x + y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < 8.79999999999999979e-308 or 3.0000000000000002e-245 < a < 1.55e9

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 66.2%

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

   if 8.79999999999999979e-308 < a < 3.0000000000000002e-245

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 89.9%

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

      4. sub-neg 89.9%

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

      5. +-commutative 89.9%

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

      6. neg-sub0 89.9%

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

      7. associate-+l- 89.9%

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

      8. sub0-neg 89.9%

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

      9. neg-mul-1 89.9%

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

      10. times-frac 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. neg-sub0 99.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\left(0 - t\right)} + z}{-1}, \frac{y}{t - a}, x\right) \]

      15. associate-+l- 99.7%

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - \left(t - z\right)}}{-1}, \frac{y}{t - a}, x\right) \]

      16. sub0-neg 99.7%

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

      17. neg-mul-1 99.7%

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

      18. *-commutative 99.7%

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

      19. associate-/l* 99.7%

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

      20. metadata-eval 99.7%

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

      21. /-rgt-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around -inf 79.2%

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

      1. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in a around 0 69.6%

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

      1. expm1-log1p-u 45.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

      2. expm1-udef 45.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]

   9. Applied egg-rr 45.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 45.6%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot \left(t - z\right)}{t}\right)\right)} \]

       2. expm1-log1p 69.6%

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

       3. associate-*r/ 79.5%

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

   11. Simplified 79.5%

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

   12. Taylor expanded in t around 0 69.0%

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

       1. mul-1-neg 69.0%

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

       2. distribute-neg-frac 69.0%

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

   14. Simplified 69.0%

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

   if 1.55e9 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 67.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.8 \cdot 10^{-308}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-245}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;a \leq 1550000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1550000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 1550000000.0) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1550000000.0) {
		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 (a <= 1550000000.0d0) 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 (a <= 1550000000.0) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 1550000000.0:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1550000000.0)
		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 (a <= 1550000000.0)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 1550000000.0], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 1.55e9

   1. Initial program 98.9%

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

   2. Taylor expanded in t around inf 64.1%

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

   if 1.55e9 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 67.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1550000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 51.2% 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 99.1%

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

2. Taylor expanded in x around inf 49.9%

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

3. Final simplification 49.9%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (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) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (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 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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