Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.2% → 99.7%

Time: 12.1s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / 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) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + a \cdot \frac{y - z}{-1 + \left(z - t\right)} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* a (/ (- y z) (+ -1.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((y - z) / (-1.0 + (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 + (a * ((y - z) / ((-1.0d0) + (z - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (a * ((y - z) / (-1.0 + (z - t))));
}

Python

def code(x, y, z, t, a):
	return x + (a * ((y - z) / (-1.0 + (z - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(a * Float64(Float64(y - z) / Float64(-1.0 + Float64(z - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (a * ((y - z) / (-1.0 + (z - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{\left(t - z\right) + 1}\right), \color{blue}{a}\right)\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\left(t - z\right) + 1\right)\right), a\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\left(t - z\right) + 1\right)\right), a\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{+.f64}\left(\left(t - z\right), 1\right)\right), a\right)\right) \]

   6. --lowering--.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), a\right)\right) \]

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

   \[\leadsto x + a \cdot \frac{y - z}{-1 + \left(z - t\right)} \]
6. Add Preprocessing

Alternative 2: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{t}{a}}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-122}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ t a)))))
   (if (<= z -3.5e+70)
     (- x a)
     (if (<= z -3.8e-102)
       t_1
       (if (<= z 3e-122)
         (+ x (* a (- z y)))
         (if (<= z 3.3e+75) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (t / a));
	double tmp;
	if (z <= -3.5e+70) {
		tmp = x - a;
	} else if (z <= -3.8e-102) {
		tmp = t_1;
	} else if (z <= 3e-122) {
		tmp = x + (a * (z - y));
	} else if (z <= 3.3e+75) {
		tmp = t_1;
	} else {
		tmp = x - 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (t / a))
    if (z <= (-3.5d+70)) then
        tmp = x - a
    else if (z <= (-3.8d-102)) then
        tmp = t_1
    else if (z <= 3d-122) then
        tmp = x + (a * (z - y))
    else if (z <= 3.3d+75) then
        tmp = t_1
    else
        tmp = x - a
    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 <= -3.5e+70) {
		tmp = x - a;
	} else if (z <= -3.8e-102) {
		tmp = t_1;
	} else if (z <= 3e-122) {
		tmp = x + (a * (z - y));
	} else if (z <= 3.3e+75) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (t / a))
	tmp = 0
	if z <= -3.5e+70:
		tmp = x - a
	elif z <= -3.8e-102:
		tmp = t_1
	elif z <= 3e-122:
		tmp = x + (a * (z - y))
	elif z <= 3.3e+75:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(t / a)))
	tmp = 0.0
	if (z <= -3.5e+70)
		tmp = Float64(x - a);
	elseif (z <= -3.8e-102)
		tmp = t_1;
	elseif (z <= 3e-122)
		tmp = Float64(x + Float64(a * Float64(z - y)));
	elseif (z <= 3.3e+75)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	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 <= -3.5e+70)
		tmp = x - a;
	elseif (z <= -3.8e-102)
		tmp = t_1;
	elseif (z <= 3e-122)
		tmp = x + (a * (z - y));
	elseif (z <= 3.3e+75)
		tmp = t_1;
	else
		tmp = x - a;
	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, -3.5e+70], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.8e-102], t$95$1, If[LessEqual[z, 3e-122], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+75], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000002e70 or 3.29999999999999998e75 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 88.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 88.2%

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

   if -3.50000000000000002e70 < z < -3.80000000000000026e-102 or 3.00000000000000004e-122 < z < 3.29999999999999998e75

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 73.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 73.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 70.5%

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

   if -3.80000000000000026e-102 < z < 3.00000000000000004e-122

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 84.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 84.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(y - z\right) \cdot a}{\color{blue}{1} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{a}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a}{1 - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a}}{1 - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 84.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   7. Applied egg-rr 84.6%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{a}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 84.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-102}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-122}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-119}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+62)
   (- x a)
   (if (<= z 1.18e-119)
     (+ x (* a (/ y (+ z -1.0))))
     (if (<= z 1.8e+75) (+ x (* a (/ (- z y) t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+62) {
		tmp = x - a;
	} else if (z <= 1.18e-119) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if (z <= 1.8e+75) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - 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 <= (-3.2d+62)) then
        tmp = x - a
    else if (z <= 1.18d-119) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    else if (z <= 1.8d+75) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - 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 <= -3.2e+62) {
		tmp = x - a;
	} else if (z <= 1.18e-119) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if (z <= 1.8e+75) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+62:
		tmp = x - a
	elif z <= 1.18e-119:
		tmp = x + (a * (y / (z + -1.0)))
	elif z <= 1.8e+75:
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+62)
		tmp = Float64(x - a);
	elseif (z <= 1.18e-119)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	elseif (z <= 1.8e+75)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+62)
		tmp = x - a;
	elseif (z <= 1.18e-119)
		tmp = x + (a * (y / (z + -1.0)));
	elseif (z <= 1.8e+75)
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+62], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.18e-119], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+75], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999984e62 or 1.8e75 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 87.6%

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

   if -3.19999999999999984e62 < z < 1.17999999999999996e-119

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 81.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 - z}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y}{1 - z}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{y}{1 - z}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      4. --lowering--.f64 80.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 80.8%

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

   if 1.17999999999999996e-119 < z < 1.8e75

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), t\right)\right) \]

      6. --lowering--.f64 68.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 68.6%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{t} \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{t}\right), \color{blue}{a}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), t\right), a\right)\right) \]

      5. --lowering--.f64 72.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), a\right)\right) \]

   7. Applied egg-rr 72.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-119}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-125}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+61)
   (- x a)
   (if (<= z 5.2e-125)
     (+ x (* a (/ y (+ z -1.0))))
     (if (<= z 1.55e+75) (- x (/ y (/ t a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+61) {
		tmp = x - a;
	} else if (z <= 5.2e-125) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if (z <= 1.55e+75) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - 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 <= (-3.3d+61)) then
        tmp = x - a
    else if (z <= 5.2d-125) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    else if (z <= 1.55d+75) then
        tmp = x - (y / (t / a))
    else
        tmp = x - 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 <= -3.3e+61) {
		tmp = x - a;
	} else if (z <= 5.2e-125) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if (z <= 1.55e+75) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+61:
		tmp = x - a
	elif z <= 5.2e-125:
		tmp = x + (a * (y / (z + -1.0)))
	elif z <= 1.55e+75:
		tmp = x - (y / (t / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+61)
		tmp = Float64(x - a);
	elseif (z <= 5.2e-125)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	elseif (z <= 1.55e+75)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+61)
		tmp = x - a;
	elseif (z <= 5.2e-125)
		tmp = x + (a * (y / (z + -1.0)));
	elseif (z <= 1.55e+75)
		tmp = x - (y / (t / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+61], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.2e-125], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+75], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999998e61 or 1.5500000000000001e75 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 87.6%

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

   if -3.2999999999999998e61 < z < 5.20000000000000011e-125

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 81.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 81.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 - z}\right)}\right) \]
   7. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y}{1 - z}}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{y}{1 - z}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      4. --lowering--.f64 80.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   8. Simplified 80.8%

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

   if 5.20000000000000011e-125 < z < 1.5500000000000001e75

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 72.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 72.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 65.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+61}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-125}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{z - t}{a}}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 600000000000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- z t) a)))))
   (if (<= t -1.05e+17)
     t_1
     (if (<= t 600000000000.0) (+ x (* (- y z) (/ a (+ z -1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((z - t) / a));
	double tmp;
	if (t <= -1.05e+17) {
		tmp = t_1;
	} else if (t <= 600000000000.0) {
		tmp = x + ((y - z) * (a / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) / ((z - t) / a))
    if (t <= (-1.05d+17)) then
        tmp = t_1
    else if (t <= 600000000000.0d0) then
        tmp = x + ((y - z) * (a / (z + (-1.0d0))))
    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 - t) / a));
	double tmp;
	if (t <= -1.05e+17) {
		tmp = t_1;
	} else if (t <= 600000000000.0) {
		tmp = x + ((y - z) * (a / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((z - t) / a))
	tmp = 0
	if t <= -1.05e+17:
		tmp = t_1
	elif t <= 600000000000.0:
		tmp = x + ((y - z) * (a / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (t <= -1.05e+17)
		tmp = t_1;
	elseif (t <= 600000000000.0)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / Float64(z + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((z - t) / a));
	tmp = 0.0;
	if (t <= -1.05e+17)
		tmp = t_1;
	elseif (t <= 600000000000.0)
		tmp = x + ((y - z) * (a / (z + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+17], t$95$1, If[LessEqual[t, 600000000000.0], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e17 or 6e11 < t

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1 + \left(t - z\right)}{a}\right)\right)\right) \]

      2. associate-+r- N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\left(1 + t\right) - z}{a}\right)\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{1 + t}{a} - \color{blue}{\frac{z}{a}}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\left(\frac{1 + t}{a}\right), \color{blue}{\left(\frac{z}{a}\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(1 + t\right), a\right), \left(\frac{\color{blue}{z}}{a}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, t\right), a\right), \left(\frac{z}{a}\right)\right)\right)\right) \]

      7. /-lowering-/.f64 97.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(1, t\right), a\right), \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right)\right) \]

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\color{blue}{\left(\frac{t}{a}\right)}, \mathsf{/.f64}\left(z, a\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 97.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(t, a\right), \mathsf{/.f64}\left(\color{blue}{z}, a\right)\right)\right)\right) \]

   7. Simplified 97.2%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y - z}{\frac{t}{a} - \frac{z}{a}}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{t}{a} - \frac{z}{a}\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\color{blue}{\frac{t}{a}} - \frac{z}{a}\right)\right)\right) \]

      4. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{t - z}{\color{blue}{a}}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{a}\right)\right)\right) \]

      6. --lowering--.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right)\right)\right) \]

   9. Applied egg-rr 99.8%

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

   if -1.05e17 < t < 6e11

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 81.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 81.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(y - z\right) \cdot a}{\color{blue}{1} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{a}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a}{1 - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a}}{1 - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 97.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   7. Applied egg-rr 97.3%

      \[\leadsto x - \color{blue}{\left(y - z\right) \cdot \frac{a}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - t}{a}}\\ \mathbf{elif}\;t \leq 600000000000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z - t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.42e+20)
   (+ x (* a (/ (- z y) t)))
   (if (<= t 8.5e+70) (+ x (* (- y z) (/ a (+ z -1.0)))) (- x (/ y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.42e+20) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 8.5e+70) {
		tmp = x + ((y - z) * (a / (z + -1.0)));
	} 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 (t <= (-1.42d+20)) then
        tmp = x + (a * ((z - y) / t))
    else if (t <= 8.5d+70) then
        tmp = x + ((y - z) * (a / (z + (-1.0d0))))
    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 (t <= -1.42e+20) {
		tmp = x + (a * ((z - y) / t));
	} else if (t <= 8.5e+70) {
		tmp = x + ((y - z) * (a / (z + -1.0)));
	} else {
		tmp = x - (y / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.42e+20:
		tmp = x + (a * ((z - y) / t))
	elif t <= 8.5e+70:
		tmp = x + ((y - z) * (a / (z + -1.0)))
	else:
		tmp = x - (y / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.42e+20)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (t <= 8.5e+70)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / Float64(z + -1.0))));
	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 (t <= -1.42e+20)
		tmp = x + (a * ((z - y) / t));
	elseif (t <= 8.5e+70)
		tmp = x + ((y - z) * (a / (z + -1.0)));
	else
		tmp = x - (y / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.42e+20], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+70], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.42e20

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{t}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), t\right)\right) \]

      6. --lowering--.f64 69.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), t\right)\right) \]

   5. Simplified 69.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{t}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{t} \cdot \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{t}\right), \color{blue}{a}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), t\right), a\right)\right) \]

      5. --lowering--.f64 79.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), a\right)\right) \]

   7. Applied egg-rr 79.7%

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

   if -1.42e20 < t < 8.4999999999999996e70

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 80.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 80.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(y - z\right) \cdot a}{\color{blue}{1} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{a}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a}{1 - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a}}{1 - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 96.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   7. Applied egg-rr 96.3%

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

   if 8.4999999999999996e70 < t

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   5. Simplified 87.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(t, a\right)\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 90.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+20}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+70}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{z}{-1 + \left(z - t\right)}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ z (+ -1.0 (- z t)))))))
   (if (<= z -7.8e+54)
     t_1
     (if (<= z 1.55e+75) (+ x (/ (* y a) (- -1.0 t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (z / (-1.0 + (z - t))));
	double tmp;
	if (z <= -7.8e+54) {
		tmp = t_1;
	} else if (z <= 1.55e+75) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * (z / ((-1.0d0) + (z - t))))
    if (z <= (-7.8d+54)) then
        tmp = t_1
    else if (z <= 1.55d+75) then
        tmp = x + ((y * a) / ((-1.0d0) - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (z / (-1.0 + (z - t))));
	double tmp;
	if (z <= -7.8e+54) {
		tmp = t_1;
	} else if (z <= 1.55e+75) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (z / (-1.0 + (z - t))))
	tmp = 0
	if z <= -7.8e+54:
		tmp = t_1
	elif z <= 1.55e+75:
		tmp = x + ((y * a) / (-1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(z / Float64(-1.0 + Float64(z - t)))))
	tmp = 0.0
	if (z <= -7.8e+54)
		tmp = t_1;
	elseif (z <= 1.55e+75)
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (z / (-1.0 + (z - t))));
	tmp = 0.0;
	if (z <= -7.8e+54)
		tmp = t_1;
	elseif (z <= 1.55e+75)
		tmp = x + ((y * a) / (-1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(z / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+54], t$95$1, If[LessEqual[z, 1.55e+75], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8000000000000005e54 or 1.5500000000000001e75 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - z}{\left(t - z\right) + 1}\right), \color{blue}{a}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\left(t - z\right) + 1\right)\right), a\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\left(t - z\right) + 1\right)\right), a\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{+.f64}\left(\left(t - z\right), 1\right)\right), a\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), a\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)}\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(a \cdot \color{blue}{\frac{z}{\left(1 + t\right) - z}}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{z}{\left(1 + t\right) - z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \color{blue}{\left(\left(1 + t\right) - z\right)}\right)\right)\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \left(\left(1 + t\right) + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      9. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \left(1 + \color{blue}{\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)}\right)\right)\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \left(1 + \left(t + -1 \cdot \color{blue}{z}\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(1, \color{blue}{\left(t + -1 \cdot z\right)}\right)\right)\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(1, \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(1, \left(t - \color{blue}{z}\right)\right)\right)\right)\right) \]

      14. --lowering--.f64 89.9%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(z, \mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right)\right)\right) \]

   7. Simplified 89.9%

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

   if -7.8000000000000005e54 < z < 1.5500000000000001e75

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 85.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.2%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+54}:\\ \;\;\;\;x - a \cdot \frac{z}{-1 + \left(z - t\right)}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{-1 + \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.3e+54)
   (- x a)
   (if (<= z 1.55e+75) (+ x (/ (* y a) (- -1.0 t))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.3e+54) {
		tmp = x - a;
	} else if (z <= 1.55e+75) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.3d+54)) then
        tmp = x - a
    else if (z <= 1.55d+75) then
        tmp = x + ((y * a) / ((-1.0d0) - t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.3e+54) {
		tmp = x - a;
	} else if (z <= 1.55e+75) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.3e+54:
		tmp = x - a
	elif z <= 1.55e+75:
		tmp = x + ((y * a) / (-1.0 - t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.3e+54)
		tmp = Float64(x - a);
	elseif (z <= 1.55e+75)
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.3e+54)
		tmp = x - a;
	elseif (z <= 1.55e+75)
		tmp = x + ((y * a) / (-1.0 - t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.3e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.55e+75], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000018e54 or 1.5500000000000001e75 < z

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 87.6%

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

   if -5.30000000000000018e54 < z < 1.5500000000000001e75

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 85.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 85.2%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 + t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+54) (- x a) (if (<= z 1.3e-7) (+ x (* a (- z y))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 1.3e-7) {
		tmp = x + (a * (z - y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.1d+54)) then
        tmp = x - a
    else if (z <= 1.3d-7) then
        tmp = x + (a * (z - y))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 1.3e-7) {
		tmp = x + (a * (z - y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+54:
		tmp = x - a
	elif z <= 1.3e-7:
		tmp = x + (a * (z - y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+54)
		tmp = Float64(x - a);
	elseif (z <= 1.3e-7)
		tmp = Float64(x + Float64(a * Float64(z - y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e+54)
		tmp = x - a;
	elseif (z <= 1.3e-7)
		tmp = x + (a * (z - y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.3e-7], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000009e54 or 1.29999999999999999e-7 < z

   1. Initial program 97.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 82.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 82.2%

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

   if -5.10000000000000009e54 < z < 1.29999999999999999e-7

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 76.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 76.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(y - z\right) \cdot a}{\color{blue}{1} - z}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{a}{1 - z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{a}{1 - z}\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{a}}{1 - z}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \color{blue}{\left(1 - z\right)}\right)\right)\right) \]

      6. --lowering--.f64 76.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right) \]

   7. Applied egg-rr 76.2%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{a}\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 74.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+54) (- x a) (if (<= z 8.8e-8) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 8.8e-8) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.1d+54)) then
        tmp = x - a
    else if (z <= 8.8d-8) then
        tmp = x - (y * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 8.8e-8) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+54:
		tmp = x - a
	elif z <= 8.8e-8:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+54)
		tmp = Float64(x - a);
	elseif (z <= 8.8e-8)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e+54)
		tmp = x - a;
	elseif (z <= 8.8e-8)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, 8.8e-8], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000009e54 or 8.7999999999999994e-8 < z

   1. Initial program 97.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 82.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 82.2%

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

   if -5.10000000000000009e54 < z < 8.7999999999999994e-8

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot \left(y - z\right)}{1 - z}\right)}\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(y - z\right)\right), \color{blue}{\left(1 - z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y - z\right)\right), \left(\color{blue}{1} - z\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \left(1 - z\right)\right)\right) \]

      5. --lowering--.f64 76.2%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 76.2%

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

   6. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 72.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+54}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+54) (- x a) (if (<= z 2.15e-38) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 2.15e-38) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.1d+54)) then
        tmp = x - a
    else if (z <= 2.15d-38) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+54) {
		tmp = x - a;
	} else if (z <= 2.15e-38) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+54:
		tmp = x - a
	elif z <= 2.15e-38:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+54)
		tmp = Float64(x - a);
	elseif (z <= 2.15e-38)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.1e+54)
		tmp = x - a;
	elseif (z <= 2.15e-38)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+54], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.15e-38], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000009e54 or 2.1500000000000001e-38 < z

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 78.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 78.3%

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

   if -5.10000000000000009e54 < z < 2.1500000000000001e-38

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 54.9%

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

Alternative 12: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-117}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.25e-236) x (if (<= x 2.35e-117) (- 0.0 a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e-236) {
		tmp = x;
	} else if (x <= 2.35e-117) {
		tmp = 0.0 - a;
	} 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 <= (-1.25d-236)) then
        tmp = x
    else if (x <= 2.35d-117) then
        tmp = 0.0d0 - a
    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 <= -1.25e-236) {
		tmp = x;
	} else if (x <= 2.35e-117) {
		tmp = 0.0 - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.25e-236:
		tmp = x
	elif x <= 2.35e-117:
		tmp = 0.0 - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.25e-236)
		tmp = x;
	elseif (x <= 2.35e-117)
		tmp = Float64(0.0 - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.25e-236)
		tmp = x;
	elseif (x <= 2.35e-117)
		tmp = 0.0 - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.25e-236], x, If[LessEqual[x, 2.35e-117], N[(0.0 - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2499999999999999e-236 or 2.35000000000000004e-117 < x

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 62.8%

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

   if -1.2499999999999999e-236 < x < 2.35000000000000004e-117

   1. Initial program 94.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 44.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 44.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot a} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{a} \]

      3. --lowering--.f64 39.5%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{a}\right) \]

   8. Simplified 39.5%

      \[\leadsto \color{blue}{0 - a} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-lowering-neg.f64 39.5%

         \[\leadsto \mathsf{neg.f64}\left(a\right) \]

   10. Applied egg-rr 39.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-117}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \frac{a}{-1 + \left(z - t\right)} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* (- y z) (/ a (+ -1.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * (a / (-1.0 + (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 / ((-1.0d0) + (z - t))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * (a / (-1.0 + (z - t))));
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * (a / (-1.0 + (z - t))))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(a / Float64(-1.0 + Float64(z - t)))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * (a / (-1.0 + (z - t))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{\frac{\left(t - z\right) + 1}{a}}{y - z}}}\right)\right) \]

   2. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\frac{\left(t - z\right) + 1}{a}} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

   3. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\left(t - z\right) + 1} \cdot \left(\color{blue}{y} - z\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{a}{\left(t - z\right) + 1}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \left(\left(t - z\right) + 1\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\left(t - z\right), 1\right)\right), \left(y - z\right)\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), \left(y - z\right)\right)\right) \]

   8. --lowering--.f64 98.7%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 98.7%

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

5. Final simplification 98.7%

   \[\leadsto x + \left(y - z\right) \cdot \frac{a}{-1 + \left(z - t\right)} \]
6. Add Preprocessing

Alternative 14: 53.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 51.8%

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

Developer Target 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * 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) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))