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

Percentage Accurate: 96.9% → 99.5%

Time: 11.7s

Alternatives: 15

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: 96.9% 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: 99.5% 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 97.6%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 99.2%

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

4. Applied egg-rr 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-276}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{z + -1}{a}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ t (- z y))))))
   (if (<= t -5.2e+27)
     t_1
     (if (<= t 4e-276)
       (- x a)
       (if (<= t 1.85e-21) (+ x (/ y (/ (+ z -1.0) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (t / (z - y)));
	double tmp;
	if (t <= -5.2e+27) {
		tmp = t_1;
	} else if (t <= 4e-276) {
		tmp = x - a;
	} else if (t <= 1.85e-21) {
		tmp = x + (y / ((z + -1.0) / 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) :: tmp
    t_1 = x + (a / (t / (z - y)))
    if (t <= (-5.2d+27)) then
        tmp = t_1
    else if (t <= 4d-276) then
        tmp = x - a
    else if (t <= 1.85d-21) then
        tmp = x + (y / ((z + (-1.0d0)) / 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 + (a / (t / (z - y)));
	double tmp;
	if (t <= -5.2e+27) {
		tmp = t_1;
	} else if (t <= 4e-276) {
		tmp = x - a;
	} else if (t <= 1.85e-21) {
		tmp = x + (y / ((z + -1.0) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (t / (z - y)))
	tmp = 0
	if t <= -5.2e+27:
		tmp = t_1
	elif t <= 4e-276:
		tmp = x - a
	elif t <= 1.85e-21:
		tmp = x + (y / ((z + -1.0) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(t / Float64(z - y))))
	tmp = 0.0
	if (t <= -5.2e+27)
		tmp = t_1;
	elseif (t <= 4e-276)
		tmp = Float64(x - a);
	elseif (t <= 1.85e-21)
		tmp = Float64(x + Float64(y / Float64(Float64(z + -1.0) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (t / (z - y)));
	tmp = 0.0;
	if (t <= -5.2e+27)
		tmp = t_1;
	elseif (t <= 4e-276)
		tmp = x - a;
	elseif (t <= 1.85e-21)
		tmp = x + (y / ((z + -1.0) / a));
	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[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+27], t$95$1, If[LessEqual[t, 4e-276], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.85e-21], N[(x + N[(y / N[(N[(z + -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000018e27 or 1.8500000000000001e-21 < t

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.1%

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

   5. Simplified 87.1%

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

      1. associate-/r/ N/A

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

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

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

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

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

      4. --lowering--.f64 85.6%

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

   7. Applied egg-rr 85.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 85.6%

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

   9. Applied egg-rr 85.6%

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

   if -5.20000000000000018e27 < t < 4e-276

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 72.4%

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

   5. Simplified 72.4%

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

   if 4e-276 < t < 1.8500000000000001e-21

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 81.6%

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

   6. Taylor expanded in t around 0

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

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

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

      2. --lowering--.f64 81.6%

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

   8. Simplified 81.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-276}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{z + -1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-275}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ t (- z y))))))
   (if (<= t -2.7e+28)
     t_1
     (if (<= t 3.2e-275) (- x a) (if (<= t 1.26e-18) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / (t / (z - y)));
	double tmp;
	if (t <= -2.7e+28) {
		tmp = t_1;
	} else if (t <= 3.2e-275) {
		tmp = x - a;
	} else if (t <= 1.26e-18) {
		tmp = x - (y * 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) :: tmp
    t_1 = x + (a / (t / (z - y)))
    if (t <= (-2.7d+28)) then
        tmp = t_1
    else if (t <= 3.2d-275) then
        tmp = x - a
    else if (t <= 1.26d-18) then
        tmp = x - (y * 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 + (a / (t / (z - y)));
	double tmp;
	if (t <= -2.7e+28) {
		tmp = t_1;
	} else if (t <= 3.2e-275) {
		tmp = x - a;
	} else if (t <= 1.26e-18) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / (t / (z - y)))
	tmp = 0
	if t <= -2.7e+28:
		tmp = t_1
	elif t <= 3.2e-275:
		tmp = x - a
	elif t <= 1.26e-18:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(t / Float64(z - y))))
	tmp = 0.0
	if (t <= -2.7e+28)
		tmp = t_1;
	elseif (t <= 3.2e-275)
		tmp = Float64(x - a);
	elseif (t <= 1.26e-18)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / (t / (z - y)));
	tmp = 0.0;
	if (t <= -2.7e+28)
		tmp = t_1;
	elseif (t <= 3.2e-275)
		tmp = x - a;
	elseif (t <= 1.26e-18)
		tmp = x - (y * a);
	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[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+28], t$95$1, If[LessEqual[t, 3.2e-275], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.26e-18], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000002e28 or 1.26000000000000004e-18 < t

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.8%

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

   5. Simplified 87.8%

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

      1. associate-/r/ N/A

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

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

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

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

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

      4. --lowering--.f64 86.3%

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

   7. Applied egg-rr 86.3%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 86.3%

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

   9. Applied egg-rr 86.3%

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

   if -2.7000000000000002e28 < t < 3.2e-275

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 72.4%

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

   5. Simplified 72.4%

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

   if 3.2e-275 < t < 1.26000000000000004e-18

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in t 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 72.8%

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

   8. Simplified 72.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-275}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-281}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -8.2e+27)
     t_1
     (if (<= t 7.2e-281) (- x a) (if (<= t 1.3e-18) (- x (* y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -8.2e+27) {
		tmp = t_1;
	} else if (t <= 7.2e-281) {
		tmp = x - a;
	} else if (t <= 1.3e-18) {
		tmp = x - (y * 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) :: tmp
    t_1 = x + (a * ((z - y) / t))
    if (t <= (-8.2d+27)) then
        tmp = t_1
    else if (t <= 7.2d-281) then
        tmp = x - a
    else if (t <= 1.3d-18) then
        tmp = x - (y * 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 + (a * ((z - y) / t));
	double tmp;
	if (t <= -8.2e+27) {
		tmp = t_1;
	} else if (t <= 7.2e-281) {
		tmp = x - a;
	} else if (t <= 1.3e-18) {
		tmp = x - (y * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -8.2e+27:
		tmp = t_1
	elif t <= 7.2e-281:
		tmp = x - a
	elif t <= 1.3e-18:
		tmp = x - (y * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -8.2e+27)
		tmp = t_1;
	elseif (t <= 7.2e-281)
		tmp = Float64(x - a);
	elseif (t <= 1.3e-18)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -8.2e+27)
		tmp = t_1;
	elseif (t <= 7.2e-281)
		tmp = x - a;
	elseif (t <= 1.3e-18)
		tmp = x - (y * a);
	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[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+27], t$95$1, If[LessEqual[t, 7.2e-281], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.3e-18], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2000000000000005e27 or 1.3e-18 < t

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.8%

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

   5. Simplified 87.8%

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

      1. associate-/r/ N/A

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

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

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

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

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

      4. --lowering--.f64 86.3%

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

   7. Applied egg-rr 86.3%

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

   if -8.2000000000000005e27 < t < 7.20000000000000013e-281

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 72.4%

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

   5. Simplified 72.4%

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

   if 7.20000000000000013e-281 < t < 1.3e-18

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in t 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 72.8%

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

   8. Simplified 72.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-281}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+94)
   (+ x (* a (/ z (- (+ t 1.0) z))))
   (if (<= z 5.4e+14)
     (+ x (/ (- y z) (/ (- -1.0 t) a)))
     (+ x (* a (/ (- y z) (+ z -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+94) {
		tmp = x + (a * (z / ((t + 1.0) - z)));
	} else if (z <= 5.4e+14) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	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 <= (-4d+94)) then
        tmp = x + (a * (z / ((t + 1.0d0) - z)))
    else if (z <= 5.4d+14) then
        tmp = x + ((y - z) / (((-1.0d0) - t) / a))
    else
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    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 <= -4e+94) {
		tmp = x + (a * (z / ((t + 1.0) - z)));
	} else if (z <= 5.4e+14) {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+94:
		tmp = x + (a * (z / ((t + 1.0) - z)))
	elif z <= 5.4e+14:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	else:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+94)
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t + 1.0) - z))));
	elseif (z <= 5.4e+14)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+94)
		tmp = x + (a * (z / ((t + 1.0) - z)));
	elseif (z <= 5.4e+14)
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	else
		tmp = x + (a * ((y - z) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+94], N[(x + N[(a * N[(z / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+14], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e94

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   4. 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. --lowering--.f64 N/A

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

      9. +-lowering-+.f64 92.0%

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

   5. Simplified 92.0%

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

   if -4.0000000000000001e94 < z < 5.4e14

   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

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

   5. Simplified 97.8%

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

   if 5.4e14 < z

   1. Initial program 95.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 90.6%

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

   7. Simplified 90.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z y) (/ t a)))))
   (if (<= t -9.5e+28)
     t_1
     (if (<= t 1.7e+60) (+ x (* a (/ (- y z) (+ z -1.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) / (t / a));
	double tmp;
	if (t <= -9.5e+28) {
		tmp = t_1;
	} else if (t <= 1.7e+60) {
		tmp = x + (a * ((y - z) / (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 + ((z - y) / (t / a))
    if (t <= (-9.5d+28)) then
        tmp = t_1
    else if (t <= 1.7d+60) then
        tmp = x + (a * ((y - z) / (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 + ((z - y) / (t / a));
	double tmp;
	if (t <= -9.5e+28) {
		tmp = t_1;
	} else if (t <= 1.7e+60) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) / (t / a))
	tmp = 0
	if t <= -9.5e+28:
		tmp = t_1
	elif t <= 1.7e+60:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) / Float64(t / a)))
	tmp = 0.0
	if (t <= -9.5e+28)
		tmp = t_1;
	elseif (t <= 1.7e+60)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / 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 + ((z - y) / (t / a));
	tmp = 0.0;
	if (t <= -9.5e+28)
		tmp = t_1;
	elseif (t <= 1.7e+60)
		tmp = x + (a * ((y - z) / (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[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+28], t$95$1, If[LessEqual[t, 1.7e+60], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999927e28 or 1.7e60 < t

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 91.5%

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

   5. Simplified 91.5%

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

   if -9.49999999999999927e28 < t < 1.7e60

   1. Initial program 96.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 96.2%

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

   7. Simplified 96.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+50}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- (+ t 1.0) z))))))
   (if (<= z -1.62e+94)
     t_1
     (if (<= z 5.1e+50) (+ x (* a (/ y (+ z (- -1.0 t))))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t + 1.0) - z)));
	double tmp;
	if (z <= -1.62e+94) {
		tmp = t_1;
	} else if (z <= 5.1e+50) {
		tmp = x + (a * (y / (z + (-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 / ((t + 1.0d0) - z)))
    if (z <= (-1.62d+94)) then
        tmp = t_1
    else if (z <= 5.1d+50) then
        tmp = x + (a * (y / (z + ((-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 / ((t + 1.0) - z)));
	double tmp;
	if (z <= -1.62e+94) {
		tmp = t_1;
	} else if (z <= 5.1e+50) {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / ((t + 1.0) - z)))
	tmp = 0
	if z <= -1.62e+94:
		tmp = t_1
	elif z <= 5.1e+50:
		tmp = x + (a * (y / (z + (-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(Float64(t + 1.0) - z))))
	tmp = 0.0
	if (z <= -1.62e+94)
		tmp = t_1;
	elseif (z <= 5.1e+50)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + 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 / ((t + 1.0) - z)));
	tmp = 0.0;
	if (z <= -1.62e+94)
		tmp = t_1;
	elseif (z <= 5.1e+50)
		tmp = x + (a * (y / (z + (-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[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.62e+94], t$95$1, If[LessEqual[z, 5.1e+50], N[(x + N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.61999999999999997e94 or 5.0999999999999998e50 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   4. 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. --lowering--.f64 N/A

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

      9. +-lowering-+.f64 92.6%

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

   5. Simplified 92.6%

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

   if -1.61999999999999997e94 < z < 5.0999999999999998e50

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 92.5%

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

      1. associate-/r/ N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 92.4%

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

   7. Applied egg-rr 92.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+94}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+50}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \left(a \cdot \frac{1}{-1 - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- (+ t 1.0) z))))))
   (if (<= z -4.1e+23)
     t_1
     (if (<= z 2.3e-38) (+ x (* y (* a (/ 1.0 (- -1.0 t))))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / ((t + 1.0) - z)));
	double tmp;
	if (z <= -4.1e+23) {
		tmp = t_1;
	} else if (z <= 2.3e-38) {
		tmp = x + (y * (a * (1.0 / (-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 / ((t + 1.0d0) - z)))
    if (z <= (-4.1d+23)) then
        tmp = t_1
    else if (z <= 2.3d-38) then
        tmp = x + (y * (a * (1.0d0 / ((-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 / ((t + 1.0) - z)));
	double tmp;
	if (z <= -4.1e+23) {
		tmp = t_1;
	} else if (z <= 2.3e-38) {
		tmp = x + (y * (a * (1.0 / (-1.0 - t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / ((t + 1.0) - z)))
	tmp = 0
	if z <= -4.1e+23:
		tmp = t_1
	elif z <= 2.3e-38:
		tmp = x + (y * (a * (1.0 / (-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(Float64(t + 1.0) - z))))
	tmp = 0.0
	if (z <= -4.1e+23)
		tmp = t_1;
	elseif (z <= 2.3e-38)
		tmp = Float64(x + Float64(y * Float64(a * Float64(1.0 / 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 / ((t + 1.0) - z)));
	tmp = 0.0;
	if (z <= -4.1e+23)
		tmp = t_1;
	elseif (z <= 2.3e-38)
		tmp = x + (y * (a * (1.0 / (-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[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+23], t$95$1, If[LessEqual[z, 2.3e-38], N[(x + N[(y * N[(a * N[(1.0 / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999996e23 or 2.30000000000000002e-38 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   4. 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. --lowering--.f64 N/A

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

      9. +-lowering-+.f64 87.3%

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

   5. Simplified 87.3%

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

   if -4.09999999999999996e23 < z < 2.30000000000000002e-38

   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 91.6%

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

   5. Simplified 91.6%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 97.7%

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

   7. Applied egg-rr 97.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-38}:\\ \;\;\;\;x + y \cdot \left(a \cdot \frac{1}{-1 - t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- (+ t 1.0) z))))))
   (if (<= z -8.5e+20)
     t_1
     (if (<= z 1.95e-38) (+ 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 / ((t + 1.0) - z)));
	double tmp;
	if (z <= -8.5e+20) {
		tmp = t_1;
	} else if (z <= 1.95e-38) {
		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 / ((t + 1.0d0) - z)))
    if (z <= (-8.5d+20)) then
        tmp = t_1
    else if (z <= 1.95d-38) 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 / ((t + 1.0) - z)));
	double tmp;
	if (z <= -8.5e+20) {
		tmp = t_1;
	} else if (z <= 1.95e-38) {
		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 / ((t + 1.0) - z)))
	tmp = 0
	if z <= -8.5e+20:
		tmp = t_1
	elif z <= 1.95e-38:
		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(Float64(t + 1.0) - z))))
	tmp = 0.0
	if (z <= -8.5e+20)
		tmp = t_1;
	elseif (z <= 1.95e-38)
		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 / ((t + 1.0) - z)));
	tmp = 0.0;
	if (z <= -8.5e+20)
		tmp = t_1;
	elseif (z <= 1.95e-38)
		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[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+20], t$95$1, If[LessEqual[z, 1.95e-38], 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 < -8.5e20 or 1.95e-38 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{\left(1 + t\right) - z}} \]
   4. 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. --lowering--.f64 N/A

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

      9. +-lowering-+.f64 87.3%

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

   5. Simplified 87.3%

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

   if -8.5e20 < z < 1.95e-38

   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 91.6%

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

   5. Simplified 91.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+20}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+94)
   (- x a)
   (if (<= z 9.2e+52) (+ 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 <= -1.65e+94) {
		tmp = x - a;
	} else if (z <= 9.2e+52) {
		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 <= (-1.65d+94)) then
        tmp = x - a
    else if (z <= 9.2d+52) 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 <= -1.65e+94) {
		tmp = x - a;
	} else if (z <= 9.2e+52) {
		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 <= -1.65e+94:
		tmp = x - a
	elif z <= 9.2e+52:
		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 <= -1.65e+94)
		tmp = Float64(x - a);
	elseif (z <= 9.2e+52)
		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 <= -1.65e+94)
		tmp = x - a;
	elseif (z <= 9.2e+52)
		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, -1.65e+94], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.2e+52], 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 < -1.65e94 or 9.1999999999999999e52 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 82.4%

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

   5. Simplified 82.4%

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

   if -1.65e94 < z < 9.1999999999999999e52

   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 84.8%

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

   5. Simplified 84.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+94}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+95}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;x + a \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+95)
   (- x a)
   (if (<= z 3.5e+54) (+ x (* a (/ y (- z t)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+95) {
		tmp = x - a;
	} else if (z <= 3.5e+54) {
		tmp = x + (a * (y / (z - 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 <= (-2.5d+95)) then
        tmp = x - a
    else if (z <= 3.5d+54) then
        tmp = x + (a * (y / (z - 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 <= -2.5e+95) {
		tmp = x - a;
	} else if (z <= 3.5e+54) {
		tmp = x + (a * (y / (z - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+95:
		tmp = x - a
	elif z <= 3.5e+54:
		tmp = x + (a * (y / (z - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+95)
		tmp = Float64(x - a);
	elseif (z <= 3.5e+54)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z - 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 <= -2.5e+95)
		tmp = x - a;
	elseif (z <= 3.5e+54)
		tmp = x + (a * (y / (z - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+95], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.5e+54], N[(x + N[(a * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000012e95 or 3.5000000000000001e54 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 82.4%

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

   5. Simplified 82.4%

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

   if -2.50000000000000012e95 < z < 3.5000000000000001e54

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 92.6%

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

      1. associate-/r/ N/A

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

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

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

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

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

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

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 92.5%

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

   7. Applied egg-rr 92.5%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 73.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+95}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+54}:\\ \;\;\;\;x + a \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 35000000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+22) (- x a) (if (<= z 35000000000000.0) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+22) {
		tmp = x - a;
	} else if (z <= 35000000000000.0) {
		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 <= (-7d+22)) then
        tmp = x - a
    else if (z <= 35000000000000.0d0) 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 <= -7e+22) {
		tmp = x - a;
	} else if (z <= 35000000000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+22:
		tmp = x - a
	elif z <= 35000000000000.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+22)
		tmp = Float64(x - a);
	elseif (z <= 35000000000000.0)
		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 <= -7e+22)
		tmp = x - a;
	elseif (z <= 35000000000000.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+22], N[(x - a), $MachinePrecision], If[LessEqual[z, 35000000000000.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7e22 or 3.5e13 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 77.1%

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

   5. Simplified 77.1%

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

   if -7e22 < z < 3.5e13

   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 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t 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 72.8%

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

   8. Simplified 72.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+22}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 35000000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+18}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+18) (- x a) (if (<= z 4.1e+15) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+18) {
		tmp = x - a;
	} else if (z <= 4.1e+15) {
		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 <= (-8.8d+18)) then
        tmp = x - a
    else if (z <= 4.1d+15) 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 <= -8.8e+18) {
		tmp = x - a;
	} else if (z <= 4.1e+15) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+18:
		tmp = x - a
	elif z <= 4.1e+15:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+18)
		tmp = Float64(x - a);
	elseif (z <= 4.1e+15)
		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 <= -8.8e+18)
		tmp = x - a;
	elseif (z <= 4.1e+15)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+18], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.1e+15], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e18 or 4.1e15 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 77.7%

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

   5. Simplified 77.7%

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

   if -8.8e18 < z < 4.1e15

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 57.7%

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

Alternative 14: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-172}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5e-181) x (if (<= x 1.2e-172) (- 0.0 a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5e-181) {
		tmp = x;
	} else if (x <= 1.2e-172) {
		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 <= (-5d-181)) then
        tmp = x
    else if (x <= 1.2d-172) 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 <= -5e-181) {
		tmp = x;
	} else if (x <= 1.2e-172) {
		tmp = 0.0 - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5e-181:
		tmp = x
	elif x <= 1.2e-172:
		tmp = 0.0 - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5e-181)
		tmp = x;
	elseif (x <= 1.2e-172)
		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 <= -5e-181)
		tmp = x;
	elseif (x <= 1.2e-172)
		tmp = 0.0 - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5e-181], x, If[LessEqual[x, 1.2e-172], N[(0.0 - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000001e-181 or 1.2e-172 < 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 64.3%

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

   if -5.0000000000000001e-181 < x < 1.2e-172

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 36.4%

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

   5. Simplified 36.4%

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

   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 35.6%

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

   8. Simplified 35.6%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 35.6%

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

   10. Applied egg-rr 35.6%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-172}:\\ \;\;\;\;0 - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.9% 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 97.6%

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

3. Taylor expanded in x around inf

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

5. Simplified 51.0%

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

Developer Target 1: 99.5% 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 2024161 
(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))))