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

Percentage Accurate: 98.3% → 98.3%

Time: 6.9s

Alternatives: 8

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: 98.3% 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: 98.3% 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 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 49:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))))
   (if (<= t -4.5e-74)
     (+ x y)
     (if (<= t 1.45e-92)
       t_1
       (if (<= t 4.5e-24) (- x (/ y (/ t z))) (if (<= t 49.0) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -4.5e-74) {
		tmp = x + y;
	} else if (t <= 1.45e-92) {
		tmp = t_1;
	} else if (t <= 4.5e-24) {
		tmp = x - (y / (t / z));
	} else if (t <= 49.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    if (t <= (-4.5d-74)) then
        tmp = x + y
    else if (t <= 1.45d-92) then
        tmp = t_1
    else if (t <= 4.5d-24) then
        tmp = x - (y / (t / z))
    else if (t <= 49.0d0) then
        tmp = t_1
    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 t_1 = x + (y * (z / a));
	double tmp;
	if (t <= -4.5e-74) {
		tmp = x + y;
	} else if (t <= 1.45e-92) {
		tmp = t_1;
	} else if (t <= 4.5e-24) {
		tmp = x - (y / (t / z));
	} else if (t <= 49.0) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	tmp = 0
	if t <= -4.5e-74:
		tmp = x + y
	elif t <= 1.45e-92:
		tmp = t_1
	elif t <= 4.5e-24:
		tmp = x - (y / (t / z))
	elif t <= 49.0:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -4.5e-74)
		tmp = Float64(x + y);
	elseif (t <= 1.45e-92)
		tmp = t_1;
	elseif (t <= 4.5e-24)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (t <= 49.0)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -4.5e-74)
		tmp = x + y;
	elseif (t <= 1.45e-92)
		tmp = t_1;
	elseif (t <= 4.5e-24)
		tmp = x - (y / (t / z));
	elseif (t <= 49.0)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e-74], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.45e-92], t$95$1, If[LessEqual[t, 4.5e-24], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 49.0], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999999e-74 or 49 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 81.2%

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

   if -4.4999999999999999e-74 < t < 1.44999999999999992e-92 or 4.4999999999999997e-24 < t < 49

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 87.3%

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

   if 1.44999999999999992e-92 < t < 4.4999999999999997e-24

   1. Initial program 99.6%

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

   2. Taylor expanded in a around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in z around inf 66.8%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 49:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+66} \lor \neg \left(t \leq 5.5 \cdot 10^{+149}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.3e+66) (not (<= t 5.5e+149)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.3e+66) || !(t <= 5.5e+149)) {
		tmp = x + y;
	} 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 <= (-6.3d+66)) .or. (.not. (t <= 5.5d+149))) then
        tmp = x + y
    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 <= -6.3e+66) || !(t <= 5.5e+149)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.3e+66) or not (t <= 5.5e+149):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.3e+66) || !(t <= 5.5e+149))
		tmp = Float64(x + y);
	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 <= -6.3e+66) || ~((t <= 5.5e+149)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.3e+66], N[Not[LessEqual[t, 5.5e+149]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2999999999999998e66 or 5.49999999999999999e149 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 88.0%

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

   if -6.2999999999999998e66 < t < 5.49999999999999999e149

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 85.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+66} \lor \neg \left(t \leq 5.5 \cdot 10^{+149}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-24} \lor \neg \left(t \leq 1.45 \cdot 10^{-92}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e-24) (not (<= t 1.45e-92)))
   (+ x (- y (/ y (/ t z))))
   (- x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e-24) || !(t <= 1.45e-92)) {
		tmp = x + (y - (y / (t / z)));
	} else {
		tmp = x - (y * ((t - 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 <= (-1.3d-24)) .or. (.not. (t <= 1.45d-92))) then
        tmp = x + (y - (y / (t / z)))
    else
        tmp = x - (y * ((t - 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 <= -1.3e-24) || !(t <= 1.45e-92)) {
		tmp = x + (y - (y / (t / z)));
	} else {
		tmp = x - (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e-24) or not (t <= 1.45e-92):
		tmp = x + (y - (y / (t / z)))
	else:
		tmp = x - (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e-24) || !(t <= 1.45e-92))
		tmp = Float64(x + Float64(y - Float64(y / Float64(t / z))));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e-24) || ~((t <= 1.45e-92)))
		tmp = x + (y - (y / (t / z)));
	else
		tmp = x - (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e-24], N[Not[LessEqual[t, 1.45e-92]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e-24 or 1.44999999999999992e-92 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in z around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

      3. associate-/l* 89.5%

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

   7. Simplified 89.5%

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

   if -1.3e-24 < t < 1.44999999999999992e-92

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 90.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-24} \lor \neg \left(t \leq 1.45 \cdot 10^{-92}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 5: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e-75) (+ x y) (if (<= t 3.5e-89) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e-75) {
		tmp = x + y;
	} else if (t <= 3.5e-89) {
		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 <= (-3.8d-75)) then
        tmp = x + y
    else if (t <= 3.5d-89) 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 <= -3.8e-75) {
		tmp = x + y;
	} else if (t <= 3.5e-89) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e-75:
		tmp = x + y
	elif t <= 3.5e-89:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e-75)
		tmp = Float64(x + y);
	elseif (t <= 3.5e-89)
		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 <= -3.8e-75)
		tmp = x + y;
	elseif (t <= 3.5e-89)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e-75], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.5e-89], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.79999999999999994e-75 or 3.4999999999999997e-89 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.7%

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

   if -3.79999999999999994e-75 < t < 3.4999999999999997e-89

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 85.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 62.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e+39) x (if (<= a 5.4e+51) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e+39) {
		tmp = x;
	} else if (a <= 5.4e+51) {
		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 <= (-5.5d+39)) then
        tmp = x
    else if (a <= 5.4d+51) 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 <= -5.5e+39) {
		tmp = x;
	} else if (a <= 5.4e+51) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e+39:
		tmp = x
	elif a <= 5.4e+51:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e+39)
		tmp = x;
	elseif (a <= 5.4e+51)
		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 <= -5.5e+39)
		tmp = x;
	elseif (a <= 5.4e+51)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e+39], x, If[LessEqual[a, 5.4e+51], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999997e39 or 5.39999999999999983e51 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 70.8%

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

   if -5.4999999999999997e39 < a < 5.39999999999999983e51

   1. Initial program 98.7%

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

   2. Taylor expanded in t around inf 65.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+51}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 53.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.5e+218) y (if (<= y 7.2e+188) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+218) {
		tmp = y;
	} else if (y <= 7.2e+188) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-3.5d+218)) then
        tmp = y
    else if (y <= 7.2d+188) then
        tmp = x
    else
        tmp = 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 (y <= -3.5e+218) {
		tmp = y;
	} else if (y <= 7.2e+188) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.5e+218:
		tmp = y
	elif y <= 7.2e+188:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.5e+218)
		tmp = y;
	elseif (y <= 7.2e+188)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.5e+218)
		tmp = y;
	elseif (y <= 7.2e+188)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.5e+218], y, If[LessEqual[y, 7.2e+188], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000019e218 or 7.20000000000000041e188 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 51.1%

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

   3. Taylor expanded in t around inf 45.2%

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

   if -3.50000000000000019e218 < y < 7.20000000000000041e188

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 59.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+218}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+188}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 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 99.2%

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

2. Taylor expanded in x around inf 51.1%

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

3. Final simplification 51.1%

   \[\leadsto x \]

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 2023196 
(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)))))