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

Percentage Accurate: 98.0% → 98.9%

Time: 9.3s

Alternatives: 12

Speedup: 0.5×

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: 98.0% 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: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 1e+303) (+ t_1 x) (+ x (* (- z t) (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+303) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 1d+303) then
        tmp = t_1 + x
    else
        tmp = x + ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 1e+303) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= 1e+303:
		tmp = t_1 + x
	else:
		tmp = x + ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= 1e+303)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= 1e+303)
		tmp = t_1 + x;
	else
		tmp = x + ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+303], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 1e303

   1. Initial program 98.7%

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

   if 1e303 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 74.2%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-/l* 74.2%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 10^{+303}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 5e+304) (+ t_1 x) (+ x (* z (/ y (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1 + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= 5d+304) then
        tmp = t_1 + x
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= 5e+304) {
		tmp = t_1 + x;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= 5e+304:
		tmp = t_1 + x
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= 5e+304)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= 5e+304)
		tmp = t_1 + x;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+304], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 4.9999999999999997e304

   1. Initial program 98.7%

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

   if 4.9999999999999997e304 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 72.6%

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

   2. Taylor expanded in z around inf 99.8%

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

      1. associate-/l* 72.6%

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

      2. associate-/r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{z - t}{a - t} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 3: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e-46)
   (+ y x)
   (if (<= t 4e-79)
     (+ x (/ y (/ a z)))
     (if (<= t 1.2e+51) (- x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e-46) {
		tmp = y + x;
	} else if (t <= 4e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+51) {
		tmp = x - (y * (z / t));
	} else {
		tmp = y + 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 (t <= (-5.5d-46)) then
        tmp = y + x
    else if (t <= 4d-79) then
        tmp = x + (y / (a / z))
    else if (t <= 1.2d+51) then
        tmp = x - (y * (z / t))
    else
        tmp = y + 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 (t <= -5.5e-46) {
		tmp = y + x;
	} else if (t <= 4e-79) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+51) {
		tmp = x - (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e-46:
		tmp = y + x
	elif t <= 4e-79:
		tmp = x + (y / (a / z))
	elif t <= 1.2e+51:
		tmp = x - (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e-46)
		tmp = Float64(y + x);
	elseif (t <= 4e-79)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.2e+51)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e-46)
		tmp = y + x;
	elseif (t <= 4e-79)
		tmp = x + (y / (a / z));
	elseif (t <= 1.2e+51)
		tmp = x - (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e-46], N[(y + x), $MachinePrecision], If[LessEqual[t, 4e-79], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+51], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.49999999999999983e-46 or 1.1999999999999999e51 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.8%

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

   if -5.49999999999999983e-46 < t < 4e-79

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

   if 4e-79 < t < 1.1999999999999999e51

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 88.4%

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

   3. Taylor expanded in a around 0 81.5%

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

      1. associate-*r/ 81.5%

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

      2. neg-mul-1 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e-36)
   (+ y x)
   (if (<= t 2.8e-84)
     (+ x (/ y (/ a z)))
     (if (<= t 5.2e+49) (- x (/ y (/ t z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e-36) {
		tmp = y + x;
	} else if (t <= 2.8e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 5.2e+49) {
		tmp = x - (y / (t / z));
	} else {
		tmp = y + 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 (t <= (-4.7d-36)) then
        tmp = y + x
    else if (t <= 2.8d-84) then
        tmp = x + (y / (a / z))
    else if (t <= 5.2d+49) then
        tmp = x - (y / (t / z))
    else
        tmp = y + 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 (t <= -4.7e-36) {
		tmp = y + x;
	} else if (t <= 2.8e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 5.2e+49) {
		tmp = x - (y / (t / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e-36:
		tmp = y + x
	elif t <= 2.8e-84:
		tmp = x + (y / (a / z))
	elif t <= 5.2e+49:
		tmp = x - (y / (t / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e-36)
		tmp = Float64(y + x);
	elseif (t <= 2.8e-84)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 5.2e+49)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e-36)
		tmp = y + x;
	elseif (t <= 2.8e-84)
		tmp = x + (y / (a / z));
	elseif (t <= 5.2e+49)
		tmp = x - (y / (t / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e-36], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.8e-84], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+49], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7000000000000003e-36 or 5.19999999999999977e49 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.8%

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

   if -4.7000000000000003e-36 < t < 2.79999999999999982e-84

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

   if 2.79999999999999982e-84 < t < 5.19999999999999977e49

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 88.4%

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

   3. Taylor expanded in a around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-/l* 81.6%

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

      3. distribute-neg-frac 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e-36)
   (+ y x)
   (if (<= t 2e-84)
     (+ x (/ y (/ a z)))
     (if (<= t 1.15e+52) (- x (/ (* y z) t)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e-36) {
		tmp = y + x;
	} else if (t <= 2e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.15e+52) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = y + 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 (t <= (-4.7d-36)) then
        tmp = y + x
    else if (t <= 2d-84) then
        tmp = x + (y / (a / z))
    else if (t <= 1.15d+52) then
        tmp = x - ((y * z) / t)
    else
        tmp = y + 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 (t <= -4.7e-36) {
		tmp = y + x;
	} else if (t <= 2e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.15e+52) {
		tmp = x - ((y * z) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e-36:
		tmp = y + x
	elif t <= 2e-84:
		tmp = x + (y / (a / z))
	elif t <= 1.15e+52:
		tmp = x - ((y * z) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e-36)
		tmp = Float64(y + x);
	elseif (t <= 2e-84)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.15e+52)
		tmp = Float64(x - Float64(Float64(y * z) / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e-36)
		tmp = y + x;
	elseif (t <= 2e-84)
		tmp = x + (y / (a / z));
	elseif (t <= 1.15e+52)
		tmp = x - ((y * z) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e-36], N[(y + x), $MachinePrecision], If[LessEqual[t, 2e-84], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+52], N[(x - N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7000000000000003e-36 or 1.15e52 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.8%

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

   if -4.7000000000000003e-36 < t < 2.0000000000000001e-84

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

   if 2.0000000000000001e-84 < t < 1.15e52

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 88.5%

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

      2. associate-/r/ 92.0%

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

   4. Applied egg-rr 92.0%

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

   5. Taylor expanded in a around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. neg-mul-1 81.8%

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

      3. distribute-rgt-neg-in 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+52}:\\ \;\;\;\;x - \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-38} \lor \neg \left(t \leq 3.1 \cdot 10^{-83}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e-38) (not (<= t 3.1e-83)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e-38) || !(t <= 3.1e-83)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y / (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 <= (-4.2d-38)) .or. (.not. (t <= 3.1d-83))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    else
        tmp = x + (y / (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 <= -4.2e-38) || !(t <= 3.1e-83)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e-38) or not (t <= 3.1e-83):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e-38) || !(t <= 3.1e-83))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e-38) || ~((t <= 3.1e-83)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e-38], N[Not[LessEqual[t, 3.1e-83]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000026e-38 or 3.09999999999999992e-83 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   7. Simplified 87.0%

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

   if -4.20000000000000026e-38 < t < 3.09999999999999992e-83

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.1%

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

      1. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-38} \lor \neg \left(t \leq 3.1 \cdot 10^{-83}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36} \lor \neg \left(t \leq 2.75 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.7e-36) (not (<= t 2.75e-13)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-36) || !(t <= 2.75e-13)) {
		tmp = x + (y * (1.0 - (z / t)));
	} 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 ((t <= (-4.7d-36)) .or. (.not. (t <= 2.75d-13))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    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 ((t <= -4.7e-36) || !(t <= 2.75e-13)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.7e-36) or not (t <= 2.75e-13):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.7e-36) || !(t <= 2.75e-13))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	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 ((t <= -4.7e-36) || ~((t <= 2.75e-13)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.7e-36], N[Not[LessEqual[t, 2.75e-13]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $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 t < -4.7000000000000003e-36 or 2.74999999999999989e-13 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. neg-mul-1 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   7. Simplified 89.6%

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

   if -4.7000000000000003e-36 < t < 2.74999999999999989e-13

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 89.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-36} \lor \neg \left(t \leq 2.75 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 8: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-42} \lor \neg \left(t \leq 2.7 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e-42) (not (<= t 2.7e-13)))
   (+ x (* y (- 1.0 (/ z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e-42) || !(t <= 2.7e-13)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.6d-42)) .or. (.not. (t <= 2.7d-13))) then
        tmp = x + (y * (1.0d0 - (z / t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e-42) || !(t <= 2.7e-13)) {
		tmp = x + (y * (1.0 - (z / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e-42) or not (t <= 2.7e-13):
		tmp = x + (y * (1.0 - (z / t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e-42) || !(t <= 2.7e-13))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.6e-42) || ~((t <= 2.7e-13)))
		tmp = x + (y * (1.0 - (z / t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e-42], N[Not[LessEqual[t, 2.7e-13]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6000000000000002e-42 or 2.70000000000000011e-13 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. neg-mul-1 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   7. Simplified 89.6%

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

   if -3.6000000000000002e-42 < t < 2.70000000000000011e-13

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 89.6%

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

      1. associate-/l* 90.2%

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

      2. associate-/r/ 92.8%

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

   4. Applied egg-rr 92.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-42} \lor \neg \left(t \leq 2.7 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 9: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-37} \lor \neg \left(t \leq 3.2 \cdot 10^{-13}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.4e-37) (not (<= t 3.2e-13))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.4e-37) || !(t <= 3.2e-13)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.4d-37)) .or. (.not. (t <= 3.2d-13))) then
        tmp = y + x
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.4e-37) || !(t <= 3.2e-13)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.4e-37) or not (t <= 3.2e-13):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.4e-37) || !(t <= 3.2e-13))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.4e-37) || ~((t <= 3.2e-13)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.4e-37], N[Not[LessEqual[t, 3.2e-13]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4e-37 or 3.2e-13 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 75.8%

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

   if -7.4e-37 < t < 3.2e-13

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-37} \lor \neg \left(t \leq 3.2 \cdot 10^{-13}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 10: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-40} \lor \neg \left(t \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.22e-40) (not (<= t 2e-13))) (+ y x) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.22e-40) || !(t <= 2e-13)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (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 <= (-1.22d-40)) .or. (.not. (t <= 2d-13))) then
        tmp = y + x
    else
        tmp = x + (y / (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 <= -1.22e-40) || !(t <= 2e-13)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.22e-40) or not (t <= 2e-13):
		tmp = y + x
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.22e-40) || !(t <= 2e-13))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.22e-40) || ~((t <= 2e-13)))
		tmp = y + x;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.22e-40], N[Not[LessEqual[t, 2e-13]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22e-40 or 2.0000000000000001e-13 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 75.8%

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

   if -1.22e-40 < t < 2.0000000000000001e-13

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 77.8%

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

      1. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-40} \lor \neg \left(t \leq 2 \cdot 10^{-13}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 11: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-126} \lor \neg \left(t \leq 4.4 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e-126) (not (<= t 4.4e+31))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-126) || !(t <= 4.4e+31)) {
		tmp = y + x;
	} 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 ((t <= (-1d-126)) .or. (.not. (t <= 4.4d+31))) then
        tmp = y + x
    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 ((t <= -1e-126) || !(t <= 4.4e+31)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e-126) or not (t <= 4.4e+31):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e-126) || !(t <= 4.4e+31))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e-126) || ~((t <= 4.4e+31)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e-126], N[Not[LessEqual[t, 4.4e+31]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999995e-127 or 4.4000000000000002e31 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 72.8%

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

   if -9.9999999999999995e-127 < t < 4.4000000000000002e31

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 48.8%

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

      1. mul-1-neg 48.8%

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

      2. associate-/l* 54.0%

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

      3. distribute-neg-frac 54.0%

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

   4. Simplified 54.0%

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

   5. Taylor expanded in x around inf 46.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-126} \lor \neg \left(t \leq 4.4 \cdot 10^{+31}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.7% 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 97.0%

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

2. Taylor expanded in z around 0 57.7%

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

   1. mul-1-neg 57.7%

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

   2. associate-/l* 65.5%

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

   3. distribute-neg-frac 65.5%

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

4. Simplified 65.5%

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

5. Taylor expanded in x around inf 44.0%

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

6. Final simplification 44.0%

   \[\leadsto x \]

Developer target: 99.4% 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 2023333 
(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)))))