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

Percentage Accurate: 98.3% → 98.4%

Time: 9.5s

Alternatives: 13

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: 98.3% 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

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

FPCore

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

C

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

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) / (t - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. clear-num 96.8%

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

   2. un-div-inv 97.6%

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

4. Applied egg-rr 97.6%

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

5. Final simplification 97.6%

   \[\leadsto x - \frac{y}{\frac{z - a}{t - z}} \]
6. Add Preprocessing

Alternative 2: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5000000000000.0) (not (<= z 1.25e-15)))
   (+ 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 ((z <= -5000000000000.0) || !(z <= 1.25e-15)) {
		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 ((z <= (-5000000000000.0d0)) .or. (.not. (z <= 1.25d-15))) 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 ((z <= -5000000000000.0) || !(z <= 1.25e-15)) {
		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 (z <= -5000000000000.0) or not (z <= 1.25e-15):
		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 ((z <= -5000000000000.0) || !(z <= 1.25e-15))
		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 ((z <= -5000000000000.0) || ~((z <= 1.25e-15)))
		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[Or[LessEqual[z, -5000000000000.0], N[Not[LessEqual[z, 1.25e-15]], $MachinePrecision]], 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 2 regimes

2. if z < -5e12 or 1.25e-15 < z

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 87.1%

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

   if -5e12 < z < 1.25e-15

   1. Initial program 94.1%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.1%

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

      1. mul-1-neg 91.1%

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

      2. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1080000000000 \lor \neg \left(z \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1080000000000.0) (not (<= z 7e-16)))
   (+ x (/ y (/ (- z a) z)))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1080000000000.0) || !(z <= 7e-16)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y * (t / (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 ((z <= (-1080000000000.0d0)) .or. (.not. (z <= 7d-16))) then
        tmp = x + (y / ((z - a) / z))
    else
        tmp = x + (y * (t / (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 ((z <= -1080000000000.0) || !(z <= 7e-16)) {
		tmp = x + (y / ((z - a) / z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1080000000000.0) or not (z <= 7e-16):
		tmp = x + (y / ((z - a) / z))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1080000000000.0) || !(z <= 7e-16))
		tmp = Float64(x + Float64(y / Float64(Float64(z - a) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1080000000000.0) || ~((z <= 7e-16)))
		tmp = x + (y / ((z - a) / z));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1080000000000.0], N[Not[LessEqual[z, 7e-16]], $MachinePrecision]], N[(x + N[(y / N[(N[(z - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.08e12 or 7.00000000000000035e-16 < z

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 87.1%

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

   if -1.08e12 < z < 7.00000000000000035e-16

   1. Initial program 94.1%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.1%

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

      1. associate-*r/ 91.1%

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

      2. mul-1-neg 91.1%

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

      3. distribute-lft-neg-out 91.1%

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

      4. *-commutative 91.1%

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

      5. *-lft-identity 91.1%

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

      6. times-frac 88.2%

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

      7. /-rgt-identity 88.2%

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

      8. distribute-neg-frac 88.2%

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

      9. distribute-neg-frac2 88.2%

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

      10. neg-sub0 88.2%

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

      11. sub-neg 88.2%

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

      12. +-commutative 88.2%

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

      13. associate--r+ 88.2%

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

      14. neg-sub0 88.2%

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

      15. remove-double-neg 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1080000000000 \lor \neg \left(z \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+58} \lor \neg \left(z \leq 1.05 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.86e+58) (not (<= z 1.05e-34)))
   (+ x (* y (/ (- z t) z)))
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.86e+58) || !(z <= 1.05e-34)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / (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 ((z <= (-1.86d+58)) .or. (.not. (z <= 1.05d-34))) then
        tmp = x + (y * ((z - t) / z))
    else
        tmp = x + (y * (t / (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 ((z <= -1.86e+58) || !(z <= 1.05e-34)) {
		tmp = x + (y * ((z - t) / z));
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.86e+58) or not (z <= 1.05e-34):
		tmp = x + (y * ((z - t) / z))
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.86e+58) || !(z <= 1.05e-34))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.86e+58) || ~((z <= 1.05e-34)))
		tmp = x + (y * ((z - t) / z));
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.86e+58], N[Not[LessEqual[z, 1.05e-34]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.86000000000000001e58 or 1.05e-34 < z

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 85.8%

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

   if -1.86000000000000001e58 < z < 1.05e-34

   1. Initial program 94.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 88.3%

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

      1. associate-*r/ 88.3%

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

      2. mul-1-neg 88.3%

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

      3. distribute-lft-neg-out 88.3%

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

      4. *-commutative 88.3%

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

      5. *-lft-identity 88.3%

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

      6. times-frac 86.3%

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

      7. /-rgt-identity 86.3%

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

      8. distribute-neg-frac 86.3%

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

      9. distribute-neg-frac2 86.3%

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

      10. neg-sub0 86.3%

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

      11. sub-neg 86.3%

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

      12. +-commutative 86.3%

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

      13. associate--r+ 86.3%

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

      14. neg-sub0 86.3%

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

      15. remove-double-neg 86.3%

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

   5. Simplified 86.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+58} \lor \neg \left(z \leq 1.05 \cdot 10^{-34}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+72} \lor \neg \left(z \leq 3.6 \cdot 10^{+118}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.55e+72) (not (<= z 3.6e+118)))
   (+ x y)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.55e+72) || !(z <= 3.6e+118)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / (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 ((z <= (-3.55d+72)) .or. (.not. (z <= 3.6d+118))) then
        tmp = x + y
    else
        tmp = x + (y * (t / (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 ((z <= -3.55e+72) || !(z <= 3.6e+118)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.55e+72) or not (z <= 3.6e+118):
		tmp = x + y
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.55e+72) || !(z <= 3.6e+118))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.55e+72) || ~((z <= 3.6e+118)))
		tmp = x + y;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.55e+72], N[Not[LessEqual[z, 3.6e+118]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5499999999999996e72 or 3.6e118 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.8%

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

      1. +-commutative 76.8%

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

   7. Simplified 76.8%

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

   if -3.5499999999999996e72 < z < 3.6e118

   1. Initial program 95.4%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.8%

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

      1. associate-*r/ 85.8%

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

      2. mul-1-neg 85.8%

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

      3. distribute-lft-neg-out 85.8%

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

      4. *-commutative 85.8%

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

      5. *-lft-identity 85.8%

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

      6. times-frac 84.7%

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

      7. /-rgt-identity 84.7%

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

      8. distribute-neg-frac 84.7%

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

      9. distribute-neg-frac2 84.7%

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

      10. neg-sub0 84.7%

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

      11. sub-neg 84.7%

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

      12. +-commutative 84.7%

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

      13. associate--r+ 84.7%

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

      14. neg-sub0 84.7%

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

      15. remove-double-neg 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+72} \lor \neg \left(z \leq 3.6 \cdot 10^{+118}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+54)
   (+ x (* y (/ (- z t) z)))
   (if (<= z 9.8e-14) (+ x (* y (/ t (- a z)))) (+ x (* z (/ y (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+54) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 9.8e-14) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (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 (z <= (-2.4d+54)) then
        tmp = x + (y * ((z - t) / z))
    else if (z <= 9.8d-14) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (z * (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 (z <= -2.4e+54) {
		tmp = x + (y * ((z - t) / z));
	} else if (z <= 9.8e-14) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (z * (y / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+54:
		tmp = x + (y * ((z - t) / z))
	elif z <= 9.8e-14:
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (z * (y / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+54)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	elseif (z <= 9.8e-14)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+54)
		tmp = x + (y * ((z - t) / z));
	elseif (z <= 9.8e-14)
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (z * (y / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+54], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e-14], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999998e54

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 89.2%

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

   if -2.39999999999999998e54 < z < 9.79999999999999989e-14

   1. Initial program 94.6%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 88.7%

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

      1. associate-*r/ 88.7%

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

      2. mul-1-neg 88.7%

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

      3. distribute-lft-neg-out 88.7%

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

      4. *-commutative 88.7%

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

      5. *-lft-identity 88.7%

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

      6. times-frac 86.8%

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

      7. /-rgt-identity 86.8%

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

      8. distribute-neg-frac 86.8%

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

      9. distribute-neg-frac2 86.8%

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

      10. neg-sub0 86.8%

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

      11. sub-neg 86.8%

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

      12. +-commutative 86.8%

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

      13. associate--r+ 86.8%

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

      14. neg-sub0 86.8%

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

      15. remove-double-neg 86.8%

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

   5. Simplified 86.8%

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

   if 9.79999999999999989e-14 < z

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 71.2%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

   7. Simplified 84.1%

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

Alternative 7: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-9} \lor \neg \left(z \leq 1.9 \cdot 10^{-18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e-9) (not (<= z 1.9e-18))) (+ x y) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-9) || !(z <= 1.9e-18)) {
		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 <= (-4.8d-9)) .or. (.not. (z <= 1.9d-18))) 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 <= -4.8e-9) || !(z <= 1.9e-18)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e-9) or not (z <= 1.9e-18):
		tmp = x + y
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e-9) || !(z <= 1.9e-18))
		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 <= -4.8e-9) || ~((z <= 1.9e-18)))
		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, -4.8e-9], N[Not[LessEqual[z, 1.9e-18]], $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 < -4.8e-9 or 1.8999999999999999e-18 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. +-commutative 71.5%

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

   7. Simplified 71.5%

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

   if -4.8e-9 < z < 1.8999999999999999e-18

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*l/ 80.5%

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

   9. Applied egg-rr 80.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-9} \lor \neg \left(z \leq 1.9 \cdot 10^{-18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+52} \lor \neg \left(z \leq 6 \cdot 10^{-22}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.7e+52) (not (<= z 6e-22))) (+ x y) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+52) || !(z <= 6e-22)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.7d+52)) .or. (.not. (z <= 6d-22))) then
        tmp = x + y
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.7e+52) || !(z <= 6e-22)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.7e+52) or not (z <= 6e-22):
		tmp = x + y
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.7e+52) || !(z <= 6e-22))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.7e+52) || ~((z <= 6e-22)))
		tmp = x + y;
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.7e+52], N[Not[LessEqual[z, 6e-22]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e52 or 5.9999999999999998e-22 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

   7. Simplified 75.2%

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

   if -2.7e52 < z < 5.9999999999999998e-22

   1. Initial program 94.5%

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

      1. clear-num 94.4%

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

      2. un-div-inv 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in z around 0 76.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+52} \lor \neg \left(z \leq 6 \cdot 10^{-22}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+51} \lor \neg \left(z \leq 2.35 \cdot 10^{-18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.6e+51) (not (<= z 2.35e-18))) (+ x y) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.6e+51) || !(z <= 2.35e-18)) {
		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 <= (-8.6d+51)) .or. (.not. (z <= 2.35d-18))) 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 <= -8.6e+51) || !(z <= 2.35e-18)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.6e+51) or not (z <= 2.35e-18):
		tmp = x + y
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.6e+51) || !(z <= 2.35e-18))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.6e+51) || ~((z <= 2.35e-18)))
		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, -8.6e+51], N[Not[LessEqual[z, 2.35e-18]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5999999999999994e51 or 2.3499999999999998e-18 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.2%

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

      1. +-commutative 75.2%

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

   7. Simplified 75.2%

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

   if -8.5999999999999994e51 < z < 2.3499999999999998e-18

   1. Initial program 94.5%

      \[x + y \cdot \frac{z - t}{z - a} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+51} \lor \neg \left(z \leq 2.35 \cdot 10^{-18}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e+55) x (if (<= a 3.7e+130) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e+55) {
		tmp = x;
	} else if (a <= 3.7e+130) {
		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 <= (-2.4d+55)) then
        tmp = x
    else if (a <= 3.7d+130) 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 <= -2.4e+55) {
		tmp = x;
	} else if (a <= 3.7e+130) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e+55:
		tmp = x
	elif a <= 3.7e+130:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e+55)
		tmp = x;
	elseif (a <= 3.7e+130)
		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 <= -2.4e+55)
		tmp = x;
	elseif (a <= 3.7e+130)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e+55], x, If[LessEqual[a, 3.7e+130], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3999999999999999e55 or 3.7000000000000001e130 < a

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. fma-define 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 62.8%

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

   if -2.3999999999999999e55 < a < 3.7000000000000001e130

   1. Initial program 96.0%

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

      1. +-commutative 96.0%

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

      2. fma-define 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 62.7%

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

      1. +-commutative 62.7%

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

   7. Simplified 62.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+130}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-178}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1e-142) x (if (<= x 1.85e-178) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1e-142) {
		tmp = x;
	} else if (x <= 1.85e-178) {
		tmp = 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 (x <= (-1d-142)) then
        tmp = x
    else if (x <= 1.85d-178) then
        tmp = 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 (x <= -1e-142) {
		tmp = x;
	} else if (x <= 1.85e-178) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1e-142:
		tmp = x
	elif x <= 1.85e-178:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1e-142)
		tmp = x;
	elseif (x <= 1.85e-178)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1e-142)
		tmp = x;
	elseif (x <= 1.85e-178)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1e-142], x, If[LessEqual[x, 1.85e-178], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1e-142 or 1.85000000000000002e-178 < x

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-define 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 63.0%

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

   if -1e-142 < x < 1.85000000000000002e-178

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. fma-define 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 43.5%

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

      1. +-commutative 43.5%

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

   7. Simplified 43.5%

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

   8. Taylor expanded in y around inf 39.9%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 98.3% 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 96.9%

   \[x + y \cdot \frac{z - t}{z - a} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 13: 51.2% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in y around 0 49.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.4% 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 2024165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

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