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

Percentage Accurate: 85.5% → 98.2%

Time: 9.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.5% accurate, 1.0× speedup

Math

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

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(Float64(y * 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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.7%

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

   1. associate-/l* 98.1%

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

   2. *-commutative 98.1%

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

4. Applied egg-rr 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{z - a}\\ t_2 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 0.00042:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- z a))))) (t_2 (- x (* t (/ y z)))))
   (if (<= z -1.3e-39)
     t_1
     (if (<= z 4e-149)
       (+ x (* t (/ y a)))
       (if (<= z 1.4e-125)
         t_2
         (if (<= z 0.00042)
           t_1
           (if (<= z 7.5e+33)
             t_2
             (if (<= z 1.5e+112) (+ x (* y (/ t a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -1.3e-39) {
		tmp = t_1;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.4e-125) {
		tmp = t_2;
	} else if (z <= 0.00042) {
		tmp = t_1;
	} else if (z <= 7.5e+33) {
		tmp = t_2;
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / (z - a)))
    t_2 = x - (t * (y / z))
    if (z <= (-1.3d-39)) then
        tmp = t_1
    else if (z <= 4d-149) then
        tmp = x + (t * (y / a))
    else if (z <= 1.4d-125) then
        tmp = t_2
    else if (z <= 0.00042d0) then
        tmp = t_1
    else if (z <= 7.5d+33) then
        tmp = t_2
    else if (z <= 1.5d+112) then
        tmp = x + (y * (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (z - a)));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -1.3e-39) {
		tmp = t_1;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 1.4e-125) {
		tmp = t_2;
	} else if (z <= 0.00042) {
		tmp = t_1;
	} else if (z <= 7.5e+33) {
		tmp = t_2;
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / (z - a)))
	t_2 = x - (t * (y / z))
	tmp = 0
	if z <= -1.3e-39:
		tmp = t_1
	elif z <= 4e-149:
		tmp = x + (t * (y / a))
	elif z <= 1.4e-125:
		tmp = t_2
	elif z <= 0.00042:
		tmp = t_1
	elif z <= 7.5e+33:
		tmp = t_2
	elif z <= 1.5e+112:
		tmp = x + (y * (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(z - a))))
	t_2 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -1.3e-39)
		tmp = t_1;
	elseif (z <= 4e-149)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 1.4e-125)
		tmp = t_2;
	elseif (z <= 0.00042)
		tmp = t_1;
	elseif (z <= 7.5e+33)
		tmp = t_2;
	elseif (z <= 1.5e+112)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / (z - a)));
	t_2 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -1.3e-39)
		tmp = t_1;
	elseif (z <= 4e-149)
		tmp = x + (t * (y / a));
	elseif (z <= 1.4e-125)
		tmp = t_2;
	elseif (z <= 0.00042)
		tmp = t_1;
	elseif (z <= 7.5e+33)
		tmp = t_2;
	elseif (z <= 1.5e+112)
		tmp = x + (y * (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-39], t$95$1, If[LessEqual[z, 4e-149], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-125], t$95$2, If[LessEqual[z, 0.00042], t$95$1, If[LessEqual[z, 7.5e+33], t$95$2, If[LessEqual[z, 1.5e+112], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e-39 or 1.4e-125 < z < 4.2000000000000002e-4 or 1.4999999999999999e112 < z

   1. Initial program 74.6%

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

   3. Taylor expanded in t around 0 64.4%

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

      1. associate-/l* 86.3%

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

   5. Simplified 86.3%

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

   if -1.3e-39 < z < 3.99999999999999992e-149

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. associate-/l* 87.8%

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

   5. Simplified 87.8%

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

   if 3.99999999999999992e-149 < z < 1.4e-125 or 4.2000000000000002e-4 < z < 7.50000000000000046e33

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 89.2%

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

      1. neg-mul-1 89.2%

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

      2. distribute-neg-frac2 89.2%

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

      3. sub-neg 89.2%

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

      4. distribute-neg-in 89.2%

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

      5. remove-double-neg 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in z around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

      3. associate-/l* 81.6%

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

   10. Simplified 81.6%

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

   if 7.50000000000000046e33 < z < 1.4999999999999999e112

   1. Initial program 81.6%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 87.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-125}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 0.00042:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= z -4.2e-12)
     (+ x y)
     (if (<= z 4e-149)
       t_1
       (if (<= z 7.5e-105)
         (* y (/ (- z t) z))
         (if (<= z 1.5e+112) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -4.2e-12) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = t_1;
	} else if (z <= 7.5e-105) {
		tmp = y * ((z - t) / z);
	} else if (z <= 1.5e+112) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    if (z <= (-4.2d-12)) then
        tmp = x + y
    else if (z <= 4d-149) then
        tmp = t_1
    else if (z <= 7.5d-105) then
        tmp = y * ((z - t) / z)
    else if (z <= 1.5d+112) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -4.2e-12) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = t_1;
	} else if (z <= 7.5e-105) {
		tmp = y * ((z - t) / z);
	} else if (z <= 1.5e+112) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if z <= -4.2e-12:
		tmp = x + y
	elif z <= 4e-149:
		tmp = t_1
	elif z <= 7.5e-105:
		tmp = y * ((z - t) / z)
	elif z <= 1.5e+112:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -4.2e-12)
		tmp = Float64(x + y);
	elseif (z <= 4e-149)
		tmp = t_1;
	elseif (z <= 7.5e-105)
		tmp = Float64(y * Float64(Float64(z - t) / z));
	elseif (z <= 1.5e+112)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -4.2e-12)
		tmp = x + y;
	elseif (z <= 4e-149)
		tmp = t_1;
	elseif (z <= 7.5e-105)
		tmp = y * ((z - t) / z);
	elseif (z <= 1.5e+112)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-12], N[(x + y), $MachinePrecision], If[LessEqual[z, 4e-149], t$95$1, If[LessEqual[z, 7.5e-105], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+112], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999988e-12 or 1.4999999999999999e112 < z

   1. Initial program 67.6%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -4.19999999999999988e-12 < z < 3.99999999999999992e-149 or 7.5000000000000006e-105 < z < 1.4999999999999999e112

   1. Initial program 94.4%

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

      1. associate-/l* 96.5%

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

      2. *-commutative 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 80.5%

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

   if 3.99999999999999992e-149 < z < 7.5000000000000006e-105

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.1%

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

   4. Taylor expanded in a around 0 61.1%

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

      1. associate-/l* 60.9%

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

   6. Simplified 60.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e-17)
   (+ x y)
   (if (<= z 4e-149)
     (+ x (* t (/ y a)))
     (if (<= z 7.5e-105)
       (* y (/ (- z t) z))
       (if (<= z 1.5e+112) (+ x (* y (/ t a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e-17) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.5e-105) {
		tmp = y * ((z - t) / z);
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.1d-17)) then
        tmp = x + y
    else if (z <= 4d-149) then
        tmp = x + (t * (y / a))
    else if (z <= 7.5d-105) then
        tmp = y * ((z - t) / z)
    else if (z <= 1.5d+112) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e-17) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.5e-105) {
		tmp = y * ((z - t) / z);
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e-17:
		tmp = x + y
	elif z <= 4e-149:
		tmp = x + (t * (y / a))
	elif z <= 7.5e-105:
		tmp = y * ((z - t) / z)
	elif z <= 1.5e+112:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e-17)
		tmp = Float64(x + y);
	elseif (z <= 4e-149)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 7.5e-105)
		tmp = Float64(y * Float64(Float64(z - t) / z));
	elseif (z <= 1.5e+112)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e-17)
		tmp = x + y;
	elseif (z <= 4e-149)
		tmp = x + (t * (y / a));
	elseif (z <= 7.5e-105)
		tmp = y * ((z - t) / z);
	elseif (z <= 1.5e+112)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e-17], N[(x + y), $MachinePrecision], If[LessEqual[z, 4e-149], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-105], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+112], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1000000000000003e-17 or 1.4999999999999999e112 < z

   1. Initial program 67.6%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -5.1000000000000003e-17 < z < 3.99999999999999992e-149

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if 3.99999999999999992e-149 < z < 7.5000000000000006e-105

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 74.1%

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

   4. Taylor expanded in a around 0 61.1%

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

      1. associate-/l* 60.9%

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

   6. Simplified 60.9%

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

   if 7.5000000000000006e-105 < z < 1.4999999999999999e112

   1. Initial program 93.5%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 73.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-17}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-125}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e-13)
   (+ x y)
   (if (<= z 4e-149)
     (+ x (* t (/ y a)))
     (if (<= z 3.2e-125)
       (- x (* t (/ y z)))
       (if (<= z 1.5e+112) (+ x (* y (/ t a))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e-13) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.2e-125) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d-13)) then
        tmp = x + y
    else if (z <= 4d-149) then
        tmp = x + (t * (y / a))
    else if (z <= 3.2d-125) then
        tmp = x - (t * (y / z))
    else if (z <= 1.5d+112) then
        tmp = x + (y * (t / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e-13) {
		tmp = x + y;
	} else if (z <= 4e-149) {
		tmp = x + (t * (y / a));
	} else if (z <= 3.2e-125) {
		tmp = x - (t * (y / z));
	} else if (z <= 1.5e+112) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e-13:
		tmp = x + y
	elif z <= 4e-149:
		tmp = x + (t * (y / a))
	elif z <= 3.2e-125:
		tmp = x - (t * (y / z))
	elif z <= 1.5e+112:
		tmp = x + (y * (t / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e-13)
		tmp = Float64(x + y);
	elseif (z <= 4e-149)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 3.2e-125)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= 1.5e+112)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e-13)
		tmp = x + y;
	elseif (z <= 4e-149)
		tmp = x + (t * (y / a));
	elseif (z <= 3.2e-125)
		tmp = x - (t * (y / z));
	elseif (z <= 1.5e+112)
		tmp = x + (y * (t / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e-13], N[(x + y), $MachinePrecision], If[LessEqual[z, 4e-149], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-125], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+112], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.7999999999999997e-13 or 1.4999999999999999e112 < z

   1. Initial program 67.6%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -4.7999999999999997e-13 < z < 3.99999999999999992e-149

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if 3.99999999999999992e-149 < z < 3.1999999999999998e-125

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac2 86.4%

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

      3. sub-neg 86.4%

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

      4. distribute-neg-in 86.4%

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

      5. remove-double-neg 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in z around inf 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

      3. associate-/l* 85.9%

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

   10. Simplified 85.9%

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

   if 3.1999999999999998e-125 < z < 1.4999999999999999e112

   1. Initial program 94.5%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 68.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-125}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+112}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4800000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4800000000000.0) (not (<= z 1.5e+113)))
   (+ x (* y (/ z (- z a))))
   (- x (* y (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4800000000000.0) || !(z <= 1.5e+113)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4800000000000.0d0)) .or. (.not. (z <= 1.5d+113))) then
        tmp = x + (y * (z / (z - a)))
    else
        tmp = x - (y * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4800000000000.0) || !(z <= 1.5e+113)) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = x - (y * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4800000000000.0) or not (z <= 1.5e+113):
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = x - (y * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4800000000000.0) || !(z <= 1.5e+113))
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4800000000000.0) || ~((z <= 1.5e+113)))
		tmp = x + (y * (z / (z - a)));
	else
		tmp = x - (y * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4800000000000.0], N[Not[LessEqual[z, 1.5e+113]], $MachinePrecision]], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e12 or 1.5e113 < z

   1. Initial program 65.6%

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

   3. Taylor expanded in t around 0 62.5%

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

      1. associate-/l* 93.1%

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

   5. Simplified 93.1%

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

   if -4.8e12 < z < 1.5e113

   1. Initial program 94.6%

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

      1. associate-/l* 97.0%

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

      2. *-commutative 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around inf 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac2 89.3%

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

      3. sub-neg 89.3%

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

      4. distribute-neg-in 89.3%

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

      5. remove-double-neg 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in t around 0 89.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4800000000000 \lor \neg \left(z \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2850000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2850000000000.0)
   (+ x (* y (/ z (- z a))))
   (if (<= z 4.5e+112) (- 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 (z <= -2850000000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4.5e+112) {
		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 (z <= (-2850000000000.0d0)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 4.5d+112) 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 (z <= -2850000000000.0) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 4.5e+112) {
		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 z <= -2850000000000.0:
		tmp = x + (y * (z / (z - a)))
	elif z <= 4.5e+112:
		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 (z <= -2850000000000.0)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 4.5e+112)
		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 (z <= -2850000000000.0)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 4.5e+112)
		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[LessEqual[z, -2850000000000.0], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+112], 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 3 regimes

2. if z < -2.85e12

   1. Initial program 66.7%

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

   3. Taylor expanded in t around 0 63.4%

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

      1. associate-/l* 93.3%

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

   5. Simplified 93.3%

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

   if -2.85e12 < z < 4.4999999999999999e112

   1. Initial program 94.6%

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

      1. associate-/l* 97.0%

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

      2. *-commutative 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around inf 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac2 89.3%

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

      3. sub-neg 89.3%

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

      4. distribute-neg-in 89.3%

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

      5. remove-double-neg 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in t around 0 89.3%

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

   if 4.4999999999999999e112 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 92.9%

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

   5. Simplified 92.9%

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

      1. clear-num 92.9%

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

      2. un-div-inv 92.9%

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

   7. Applied egg-rr 92.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2850000000000:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+113}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+14)
   (+ x (* y (/ z (- z a))))
   (if (<= z 1.05e+113) (- x (* t (/ y (- z a)))) (+ x (/ y (/ (- z a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+14) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.05e+113) {
		tmp = x - (t * (y / (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 (z <= (-1.05d+14)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 1.05d+113) then
        tmp = x - (t * (y / (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 (z <= -1.05e+14) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 1.05e+113) {
		tmp = x - (t * (y / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+14:
		tmp = x + (y * (z / (z - a)))
	elif z <= 1.05e+113:
		tmp = x - (t * (y / (z - a)))
	else:
		tmp = x + (y / ((z - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+14)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 1.05e+113)
		tmp = Float64(x - Float64(t * Float64(y / 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 (z <= -1.05e+14)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 1.05e+113)
		tmp = x - (t * (y / (z - a)));
	else
		tmp = x + (y / ((z - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+14], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+113], N[(x - N[(t * N[(y / 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 3 regimes

2. if z < -1.05e14

   1. Initial program 66.7%

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

   3. Taylor expanded in t around 0 63.4%

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

      1. associate-/l* 93.3%

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

   5. Simplified 93.3%

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

   if -1.05e14 < z < 1.0499999999999999e113

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 90.1%

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

      3. distribute-rgt-neg-in 90.1%

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

      4. distribute-frac-neg 90.1%

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

   5. Simplified 90.1%

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

   if 1.0499999999999999e113 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in t around 0 61.3%

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

      1. associate-/l* 92.9%

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

   5. Simplified 92.9%

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

      1. clear-num 92.9%

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

      2. un-div-inv 92.9%

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

   7. Applied egg-rr 92.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+113}:\\ \;\;\;\;x - t \cdot \frac{y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.7e-141) x (if (<= x 8.8e-269) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e-141) {
		tmp = x;
	} else if (x <= 8.8e-269) {
		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 <= (-2.7d-141)) then
        tmp = x
    else if (x <= 8.8d-269) 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 <= -2.7e-141) {
		tmp = x;
	} else if (x <= 8.8e-269) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.7e-141:
		tmp = x
	elif x <= 8.8e-269:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.7e-141)
		tmp = x;
	elseif (x <= 8.8e-269)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.7e-141)
		tmp = x;
	elseif (x <= 8.8e-269)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.7e-141], x, If[LessEqual[x, 8.8e-269], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000003e-141 or 8.79999999999999936e-269 < x

   1. Initial program 84.3%

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

   3. Taylor expanded in x around inf 61.8%

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

   if -2.7000000000000003e-141 < x < 8.79999999999999936e-269

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in z around inf 42.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-269}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -9e+128) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+128) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+128)) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+128) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+128:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+128)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+128)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+128], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.0000000000000003e128

   1. Initial program 77.7%

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

   3. Taylor expanded in x around inf 71.7%

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

   if -9.0000000000000003e128 < a

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf 63.5%

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

      1. +-commutative 63.5%

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

   5. Simplified 63.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+128}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 83.7%

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

3. Taylor expanded in x around inf 53.9%

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

4. Final simplification 53.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 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 2024059 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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