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

Percentage Accurate: 98.4% → 98.4%

Time: 8.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (z - a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Final simplification 97.7%

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

Alternative 2: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-46} \lor \neg \left(z \leq 3500\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e-46) (not (<= z 3500.0)))
   (+ x (* y (/ (- z t) z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-46) || !(z <= 3500.0)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (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 ((z <= (-1.95d-46)) .or. (.not. (z <= 3500.0d0))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (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 ((z <= -1.95e-46) || !(z <= 3500.0)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e-46) or not (z <= 3500.0):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e-46) || !(z <= 3500.0))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e-46) || ~((z <= 3500.0)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e-46], N[Not[LessEqual[z, 3500.0]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-46 or 3500 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 87.1%

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

   if -1.9500000000000001e-46 < z < 3500

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 80.1%

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

   4. Simplified 80.1%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-46} \lor \neg \left(z \leq 3500\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+14} \lor \neg \left(t \leq 3 \cdot 10^{-96}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+14) (not (<= t 3e-96)))
   (- x (* y (/ t (- z a))))
   (+ x (/ y (/ (- z a) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+14) || !(t <= 3e-96)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - 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 <= (-1.05d+14)) .or. (.not. (t <= 3d-96))) then
        tmp = x - (y * (t / (z - a)))
    else
        tmp = x + (y / ((z - 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 <= -1.05e+14) || !(t <= 3e-96)) {
		tmp = x - (y * (t / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+14) or not (t <= 3e-96):
		tmp = x - (y * (t / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+14) || !(t <= 3e-96))
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+14) || ~((t <= 3e-96)))
		tmp = x - (y * (t / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+14], N[Not[LessEqual[t, 3e-96]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e14 or 3e-96 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in t around inf 84.7%

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

      1. neg-mul-1 84.7%

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

      2. distribute-neg-frac 84.7%

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

   4. Simplified 84.7%

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

      1. *-commutative 84.7%

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

      2. add-sqr-sqrt 42.0%

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

      3. sqrt-unprod 43.4%

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

      4. sqr-neg 43.4%

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

      5. sqrt-unprod 26.2%

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

      6. add-sqr-sqrt 44.4%

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

      7. cancel-sign-sub 44.4%

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

      8. distribute-frac-neg 44.4%

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

      9. *-commutative 44.4%

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

      10. clear-num 44.4%

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

      11. un-div-inv 45.1%

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

      12. add-sqr-sqrt 18.9%

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

      13. sqrt-unprod 41.3%

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

      14. sqr-neg 41.3%

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

      15. sqrt-unprod 43.4%

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

      16. add-sqr-sqrt 86.1%

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

   6. Applied egg-rr 86.1%

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

      1. div-inv 84.7%

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

      2. clear-num 84.7%

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

   8. Applied egg-rr 84.7%

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

   if -1.05e14 < t < 3e-96

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+14} \lor \neg \left(t \leq 3 \cdot 10^{-96}\right):\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7000000000000:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7000000000000.0)
   (- x (* y (/ t (- z a))))
   (if (<= t 3.2e-96) (+ x (/ y (/ (- z a) z))) (- x (* t (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7000000000000.0) {
		tmp = x - (y * (t / (z - a)));
	} else if (t <= 3.2e-96) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (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 <= (-7000000000000.0d0)) then
        tmp = x - (y * (t / (z - a)))
    else if (t <= 3.2d-96) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - (t * (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 <= -7000000000000.0) {
		tmp = x - (y * (t / (z - a)));
	} else if (t <= 3.2e-96) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7000000000000.0:
		tmp = x - (y * (t / (z - a)))
	elif t <= 3.2e-96:
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7000000000000.0)
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	elseif (t <= 3.2e-96)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7000000000000.0)
		tmp = x - (y * (t / (z - a)));
	elseif (t <= 3.2e-96)
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7000000000000.0], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-96], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e12

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 88.1%

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

      1. neg-mul-1 88.1%

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

      2. distribute-neg-frac 88.1%

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

   4. Simplified 88.1%

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

      1. *-commutative 88.1%

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

      2. add-sqr-sqrt 88.0%

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

      3. sqrt-unprod 52.1%

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

      4. sqr-neg 52.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 38.2%

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

      7. cancel-sign-sub 38.2%

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

      8. distribute-frac-neg 38.2%

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

      9. *-commutative 38.2%

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

      10. clear-num 38.2%

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

      11. un-div-inv 39.6%

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

      12. add-sqr-sqrt 39.6%

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

      13. sqrt-unprod 23.3%

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

      14. sqr-neg 23.3%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 89.4%

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

   6. Applied egg-rr 89.4%

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

      1. div-inv 88.0%

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

      2. clear-num 88.1%

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

   8. Applied egg-rr 88.1%

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

   if -7e12 < t < 3.20000000000000012e-96

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   if 3.20000000000000012e-96 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-/l* 83.1%

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

      4. sub-neg 83.1%

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

      5. associate-/r/ 84.0%

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

   7. Simplified 84.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7000000000000:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 5: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+16)
   (- x (/ y (/ (- z a) t)))
   (if (<= t 3.4e-96) (+ x (/ y (/ (- z a) z))) (- x (* t (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+16) {
		tmp = x - (y / ((z - a) / t));
	} else if (t <= 3.4e-96) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (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 <= (-2.6d+16)) then
        tmp = x - (y / ((z - a) / t))
    else if (t <= 3.4d-96) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x - (t * (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 <= -2.6e+16) {
		tmp = x - (y / ((z - a) / t));
	} else if (t <= 3.4e-96) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x - (t * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+16:
		tmp = x - (y / ((z - a) / t))
	elif t <= 3.4e-96:
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x - (t * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+16)
		tmp = Float64(x - Float64(y / Float64(Float64(z - a) / t)));
	elseif (t <= 3.4e-96)
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x - Float64(t * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.6e+16)
		tmp = x - (y / ((z - a) / t));
	elseif (t <= 3.4e-96)
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x - (t * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+16], N[(x - N[(y / N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-96], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e16

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 88.1%

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

      1. neg-mul-1 88.1%

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

      2. distribute-neg-frac 88.1%

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

   4. Simplified 88.1%

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

      1. *-commutative 88.1%

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

      2. add-sqr-sqrt 88.0%

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

      3. sqrt-unprod 52.1%

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

      4. sqr-neg 52.1%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 38.2%

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

      7. cancel-sign-sub 38.2%

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

      8. distribute-frac-neg 38.2%

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

      9. *-commutative 38.2%

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

      10. clear-num 38.2%

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

      11. un-div-inv 39.6%

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

      12. add-sqr-sqrt 39.6%

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

      13. sqrt-unprod 23.3%

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

      14. sqr-neg 23.3%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 89.4%

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

   6. Applied egg-rr 89.4%

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

   if -2.6e16 < t < 3.4000000000000001e-96

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-/l* 97.2%

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

   4. Simplified 97.2%

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

   if 3.4000000000000001e-96 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-/l* 83.1%

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

      4. sub-neg 83.1%

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

      5. associate-/r/ 84.0%

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

   7. Simplified 84.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{y}{\frac{z - a}{t}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-96}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]

Alternative 6: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+22} \lor \neg \left(z \leq 15500000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+22) (not (<= z 15500000.0))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+22) || !(z <= 15500000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / 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 ((z <= (-2.4d+22)) .or. (.not. (z <= 15500000.0d0))) then
        tmp = x + y
    else
        tmp = x + ((y * t) / 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 ((z <= -2.4e+22) || !(z <= 15500000.0)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+22) or not (z <= 15500000.0):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+22) || !(z <= 15500000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+22) || ~((z <= 15500000.0)))
		tmp = x + y;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+22], N[Not[LessEqual[z, 15500000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e22 or 1.55e7 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 78.6%

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

      1. +-commutative 78.6%

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

   4. Simplified 78.6%

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

   if -2.4e22 < z < 1.55e7

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 74.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+22} \lor \neg \left(z \leq 15500000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 7: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+105} \lor \neg \left(z \leq 280000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+105) (not (<= z 280000000000.0)))
   (+ x y)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+105) || !(z <= 280000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / 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 ((z <= (-5.5d+105)) .or. (.not. (z <= 280000000000.0d0))) then
        tmp = x + y
    else
        tmp = x + (t * (y / 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 ((z <= -5.5e+105) || !(z <= 280000000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+105) or not (z <= 280000000000.0):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+105) || !(z <= 280000000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+105) || ~((z <= 280000000000.0)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+105], N[Not[LessEqual[z, 280000000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999979e105 or 2.8e11 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.0%

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

      1. +-commutative 81.0%

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

   4. Simplified 81.0%

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

   if -5.49999999999999979e105 < z < 2.8e11

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in t around 0 72.3%

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

      1. associate-*r/ 73.6%

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

   7. Simplified 73.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+105} \lor \neg \left(z \leq 280000000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+105} \lor \neg \left(z \leq 5000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+105) (not (<= z 5000000.0))) (+ x y) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+105) || !(z <= 5000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (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 ((z <= (-5.5d+105)) .or. (.not. (z <= 5000000.0d0))) then
        tmp = x + y
    else
        tmp = x + (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 ((z <= -5.5e+105) || !(z <= 5000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+105) or not (z <= 5000000.0):
		tmp = x + y
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+105) || !(z <= 5000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+105) || ~((z <= 5000000.0)))
		tmp = x + y;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+105], N[Not[LessEqual[z, 5000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999979e105 or 5e6 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 81.0%

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

      1. +-commutative 81.0%

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

   4. Simplified 81.0%

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

   if -5.49999999999999979e105 < z < 5e6

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+105} \lor \neg \left(z \leq 5000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 63.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{+199}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 2.6e+199) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.6e+199) {
		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 <= 2.6d+199) 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 <= 2.6e+199) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.6e+199:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.6e+199)
		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 <= 2.6e+199)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.6e+199], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 2.6000000000000001e199

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 66.7%

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

      1. +-commutative 66.7%

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

   4. Simplified 66.7%

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

   if 2.6000000000000001e199 < a

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf 72.8%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{+199}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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 97.7%

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

2. Taylor expanded in x around inf 53.3%

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

3. Final simplification 53.3%

   \[\leadsto x \]

Developer target: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023319 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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