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

Percentage Accurate: 98.3% → 98.3%

Time: 6.4s

Alternatives: 9

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 98.1%

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

2. Final simplification 98.1%

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

Alternative 2: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -51000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -51000000000000.0)
   (+ x y)
   (if (<= t 9.8e-98)
     (+ x (/ z (/ a y)))
     (if (<= t 5.4e+41) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -51000000000000.0) {
		tmp = x + y;
	} else if (t <= 9.8e-98) {
		tmp = x + (z / (a / y));
	} else if (t <= 5.4e+41) {
		tmp = x - (y / (t / z));
	} 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 <= (-51000000000000.0d0)) then
        tmp = x + y
    else if (t <= 9.8d-98) then
        tmp = x + (z / (a / y))
    else if (t <= 5.4d+41) then
        tmp = x - (y / (t / z))
    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 <= -51000000000000.0) {
		tmp = x + y;
	} else if (t <= 9.8e-98) {
		tmp = x + (z / (a / y));
	} else if (t <= 5.4e+41) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -51000000000000.0:
		tmp = x + y
	elif t <= 9.8e-98:
		tmp = x + (z / (a / y))
	elif t <= 5.4e+41:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -51000000000000.0)
		tmp = Float64(x + y);
	elseif (t <= 9.8e-98)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 5.4e+41)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -51000000000000.0)
		tmp = x + y;
	elseif (t <= 9.8e-98)
		tmp = x + (z / (a / y));
	elseif (t <= 5.4e+41)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -51000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.8e-98], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+41], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1e13 or 5.39999999999999999e41 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 83.7%

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

   if -5.1e13 < t < 9.80000000000000028e-98

   1. Initial program 95.7%

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

   2. Taylor expanded in t around 0 74.5%

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

      1. associate-/l* 80.5%

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

   4. Simplified 80.5%

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

      1. associate-/r/ 81.4%

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

   6. Applied egg-rr 81.4%

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

      1. *-commutative 81.4%

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

      2. clear-num 81.4%

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

      3. un-div-inv 81.4%

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

   8. Applied egg-rr 81.4%

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

   if 9.80000000000000028e-98 < t < 5.39999999999999999e41

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. associate-/l* 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -51000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8300000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8300000000.0)
   (+ x y)
   (if (<= t 8.8e-98)
     (+ x (/ (- z t) (/ a y)))
     (if (<= t 5.5e+41) (- x (/ y (/ t z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8300000000.0) {
		tmp = x + y;
	} else if (t <= 8.8e-98) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 5.5e+41) {
		tmp = x - (y / (t / z));
	} 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 <= (-8300000000.0d0)) then
        tmp = x + y
    else if (t <= 8.8d-98) then
        tmp = x + ((z - t) / (a / y))
    else if (t <= 5.5d+41) then
        tmp = x - (y / (t / z))
    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 <= -8300000000.0) {
		tmp = x + y;
	} else if (t <= 8.8e-98) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 5.5e+41) {
		tmp = x - (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8300000000.0:
		tmp = x + y
	elif t <= 8.8e-98:
		tmp = x + ((z - t) / (a / y))
	elif t <= 5.5e+41:
		tmp = x - (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8300000000.0)
		tmp = Float64(x + y);
	elseif (t <= 8.8e-98)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	elseif (t <= 5.5e+41)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8300000000.0)
		tmp = x + y;
	elseif (t <= 8.8e-98)
		tmp = x + ((z - t) / (a / y));
	elseif (t <= 5.5e+41)
		tmp = x - (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8300000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 8.8e-98], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+41], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.3e9 or 5.5000000000000003e41 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 83.7%

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

   if -8.3e9 < t < 8.79999999999999985e-98

   1. Initial program 95.7%

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

   2. Taylor expanded in a around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-/l* 81.8%

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

   4. Simplified 81.8%

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

   if 8.79999999999999985e-98 < t < 5.5000000000000003e41

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. associate-/l* 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8300000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-98}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-96} \lor \neg \left(t \leq 9.5 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.9e-96) (not (<= t 9.5e-98)))
   (+ x (/ (- t z) (/ t y)))
   (+ x (/ (- z t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e-96) || !(t <= 9.5e-98)) {
		tmp = x + ((t - z) / (t / y));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.9d-96)) .or. (.not. (t <= 9.5d-98))) then
        tmp = x + ((t - z) / (t / y))
    else
        tmp = x + ((z - t) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.9e-96) || !(t <= 9.5e-98)) {
		tmp = x + ((t - z) / (t / y));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.9e-96) or not (t <= 9.5e-98):
		tmp = x + ((t - z) / (t / y))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.9e-96) || !(t <= 9.5e-98))
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.9e-96) || ~((t <= 9.5e-98)))
		tmp = x + ((t - z) / (t / y));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.9e-96], N[Not[LessEqual[t, 9.5e-98]], $MachinePrecision]], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.89999999999999994e-96 or 9.5000000000000001e-98 < t

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. associate-/l* 82.2%

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

   4. Simplified 82.2%

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

   if -2.89999999999999994e-96 < t < 9.5000000000000001e-98

   1. Initial program 95.4%

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

   2. Taylor expanded in a around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-/l* 89.8%

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

   4. Simplified 89.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-96} \lor \neg \left(t \leq 9.5 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -34000000000 \lor \neg \left(t \leq 1.7 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -34000000000.0) (not (<= t 1.7e-9)))
   (+ x y)
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -34000000000.0) || !(t <= 1.7e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-34000000000.0d0)) .or. (.not. (t <= 1.7d-9))) then
        tmp = x + y
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -34000000000.0) || !(t <= 1.7e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -34000000000.0) or not (t <= 1.7e-9):
		tmp = x + y
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -34000000000.0) || !(t <= 1.7e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -34000000000.0) || ~((t <= 1.7e-9)))
		tmp = x + y;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -34000000000.0], N[Not[LessEqual[t, 1.7e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e10 or 1.6999999999999999e-9 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -3.4e10 < t < 1.6999999999999999e-9

   1. Initial program 96.3%

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

   2. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 77.5%

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

   4. Simplified 77.5%

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

      1. associate-/r/ 78.3%

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

   6. Applied egg-rr 78.3%

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

      1. *-commutative 78.3%

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

      2. clear-num 78.3%

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

      3. un-div-inv 78.3%

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

   8. Applied egg-rr 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -34000000000 \lor \neg \left(t \leq 1.7 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4000000000000.0)
   (+ x y)
   (if (<= t 5.6e-11) (+ x (* y (/ z a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4000000000000.0) {
		tmp = x + y;
	} else if (t <= 5.6e-11) {
		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 <= (-4000000000000.0d0)) then
        tmp = x + y
    else if (t <= 5.6d-11) 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 <= -4000000000000.0) {
		tmp = x + y;
	} else if (t <= 5.6e-11) {
		tmp = x + (y * (z / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4000000000000.0:
		tmp = x + y
	elif t <= 5.6e-11:
		tmp = x + (y * (z / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4000000000000.0)
		tmp = Float64(x + y);
	elseif (t <= 5.6e-11)
		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 <= -4000000000000.0)
		tmp = x + y;
	elseif (t <= 5.6e-11)
		tmp = x + (y * (z / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4000000000000.0], N[(x + y), $MachinePrecision], If[LessEqual[t, 5.6e-11], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4e12 or 5.6e-11 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -4e12 < t < 5.6e-11

   1. Initial program 96.3%

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

   2. Taylor expanded in t around 0 77.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4000000000000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+15) (+ x y) (if (<= t 3.5e-10) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+15) {
		tmp = x + y;
	} else if (t <= 3.5e-10) {
		tmp = x + (z * (y / 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 <= (-2.1d+15)) then
        tmp = x + y
    else if (t <= 3.5d-10) then
        tmp = x + (z * (y / 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 <= -2.1e+15) {
		tmp = x + y;
	} else if (t <= 3.5e-10) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+15:
		tmp = x + y
	elif t <= 3.5e-10:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+15)
		tmp = Float64(x + y);
	elseif (t <= 3.5e-10)
		tmp = Float64(x + Float64(z * Float64(y / 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 <= -2.1e+15)
		tmp = x + y;
	elseif (t <= 3.5e-10)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+15], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.5e-10], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e15 or 3.4999999999999998e-10 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -2.1e15 < t < 3.4999999999999998e-10

   1. Initial program 96.3%

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

   2. Taylor expanded in t around 0 71.5%

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

      1. associate-/l* 77.5%

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

   4. Simplified 77.5%

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

      1. associate-/r/ 78.3%

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

   6. Applied egg-rr 78.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-10}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e-134) (+ x y) (if (<= t 5e+41) x (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e-134) {
		tmp = x + y;
	} else if (t <= 5e+41) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.3d-134)) then
        tmp = x + y
    else if (t <= 5d+41) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e-134) {
		tmp = x + y;
	} else if (t <= 5e+41) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.3e-134:
		tmp = x + y
	elif t <= 5e+41:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e-134)
		tmp = Float64(x + y);
	elseif (t <= 5e+41)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.3e-134)
		tmp = x + y;
	elseif (t <= 5e+41)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e-134], N[(x + y), $MachinePrecision], If[LessEqual[t, 5e+41], x, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000019e-134 or 5.00000000000000022e41 < t

   1. Initial program 98.7%

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

   2. Taylor expanded in t around inf 73.7%

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

   if -3.30000000000000019e-134 < t < 5.00000000000000022e41

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 60.3%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-134}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 50.4% 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 98.1%

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

2. Taylor expanded in x around inf 51.9%

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

3. Final simplification 51.9%

   \[\leadsto x \]

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 2023200 
(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)))))