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

Percentage Accurate: 96.9% → 97.2%

Time: 11.3s

Alternatives: 11

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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) + 1.0d0)) * (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 97.3%

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

4. Applied egg-rr 97.3%

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

5. Final simplification 97.3%

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

Alternative 2: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+191}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z y) (/ t a)))))
   (if (<= t -3.35e+72)
     t_1
     (if (<= t 4.5e+191) (+ 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 <= -3.35e+72) {
		tmp = t_1;
	} else if (t <= 4.5e+191) {
		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 <= (-3.35d+72)) then
        tmp = t_1
    else if (t <= 4.5d+191) 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 <= -3.35e+72) {
		tmp = t_1;
	} else if (t <= 4.5e+191) {
		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 <= -3.35e+72:
		tmp = t_1
	elif t <= 4.5e+191:
		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 <= -3.35e+72)
		tmp = t_1;
	elseif (t <= 4.5e+191)
		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 <= -3.35e+72)
		tmp = t_1;
	elseif (t <= 4.5e+191)
		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, -3.35e+72], t$95$1, If[LessEqual[t, 4.5e+191], 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 < -3.3499999999999999e72 or 4.5000000000000002e191 < t

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.7%

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

   5. Simplified 90.7%

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

   if -3.3499999999999999e72 < t < 4.5000000000000002e191

   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 80.6%

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

   5. Simplified 80.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 92.2%

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

   7. Applied egg-rr 92.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+72}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+191}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 800000000000:\\ \;\;\;\;x + \frac{a \cdot y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- (+ t 1.0) z))))))
   (if (<= z -9e+37)
     t_1
     (if (<= z 800000000000.0) (+ x (/ (* a y) (- -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 <= -9e+37) {
		tmp = t_1;
	} else if (z <= 800000000000.0) {
		tmp = x + ((a * y) / (-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 <= (-9d+37)) then
        tmp = t_1
    else if (z <= 800000000000.0d0) then
        tmp = x + ((a * y) / ((-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 <= -9e+37) {
		tmp = t_1;
	} else if (z <= 800000000000.0) {
		tmp = x + ((a * y) / (-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 <= -9e+37:
		tmp = t_1
	elif z <= 800000000000.0:
		tmp = x + ((a * y) / (-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 <= -9e+37)
		tmp = t_1;
	elseif (z <= 800000000000.0)
		tmp = Float64(x + Float64(Float64(a * y) / 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 <= -9e+37)
		tmp = t_1;
	elseif (z <= 800000000000.0)
		tmp = x + ((a * y) / (-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, -9e+37], t$95$1, If[LessEqual[z, 800000000000.0], N[(x + N[(N[(a * y), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999923e37 or 8e11 < z

   1. Initial program 94.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.0%

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

   5. Simplified 82.0%

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

   if -8.99999999999999923e37 < z < 8e11

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 86.8%

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

   5. Simplified 86.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+37}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \mathbf{elif}\;z \leq 800000000000:\\ \;\;\;\;x + \frac{a \cdot y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t + 1\right) - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -72000:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+113)
   (- x a)
   (if (<= z -72000.0)
     (+ x (/ (* a y) z))
     (if (<= z 1.4e-13) (- x (* a y)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+113) {
		tmp = x - a;
	} else if (z <= -72000.0) {
		tmp = x + ((a * y) / z);
	} else if (z <= 1.4e-13) {
		tmp = x - (a * 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 <= (-1.3d+113)) then
        tmp = x - a
    else if (z <= (-72000.0d0)) then
        tmp = x + ((a * y) / z)
    else if (z <= 1.4d-13) then
        tmp = x - (a * 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 <= -1.3e+113) {
		tmp = x - a;
	} else if (z <= -72000.0) {
		tmp = x + ((a * y) / z);
	} else if (z <= 1.4e-13) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+113:
		tmp = x - a
	elif z <= -72000.0:
		tmp = x + ((a * y) / z)
	elif z <= 1.4e-13:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+113)
		tmp = Float64(x - a);
	elseif (z <= -72000.0)
		tmp = Float64(x + Float64(Float64(a * y) / z));
	elseif (z <= 1.4e-13)
		tmp = Float64(x - Float64(a * 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 <= -1.3e+113)
		tmp = x - a;
	elseif (z <= -72000.0)
		tmp = x + ((a * y) / z);
	elseif (z <= 1.4e-13)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+113], N[(x - a), $MachinePrecision], If[LessEqual[z, -72000.0], N[(x + N[(N[(a * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-13], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e113 or 1.4000000000000001e-13 < z

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 74.6%

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

   5. Simplified 74.6%

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

   if -1.3e113 < z < -72000

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 83.7%

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

   5. Simplified 83.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 83.9%

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

   7. Applied egg-rr 83.9%

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

   8. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 80.7%

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

   10. Simplified 80.7%

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

   11. Taylor expanded in z around inf

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

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

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

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

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

       3. *-lowering-*.f64 79.4%

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

   13. Simplified 79.4%

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

   if -72000 < z < 1.4000000000000001e-13

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 88.1%

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

   5. Simplified 88.1%

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

   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 74.7%

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

   8. Simplified 74.7%

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

Alternative 5: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 6800000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.8e+30)
   (+ x (/ (- z y) (/ t a)))
   (if (<= t 6800000000000.0)
     (+ x (* a (/ y (+ z -1.0))))
     (+ x (* (/ a t) (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+30) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 6800000000000.0) {
		tmp = x + (a * (y / (z + -1.0)));
	} else {
		tmp = x + ((a / t) * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.8d+30)) then
        tmp = x + ((z - y) / (t / a))
    else if (t <= 6800000000000.0d0) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    else
        tmp = x + ((a / t) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.8e+30) {
		tmp = x + ((z - y) / (t / a));
	} else if (t <= 6800000000000.0) {
		tmp = x + (a * (y / (z + -1.0)));
	} else {
		tmp = x + ((a / t) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.8e+30:
		tmp = x + ((z - y) / (t / a))
	elif t <= 6800000000000.0:
		tmp = x + (a * (y / (z + -1.0)))
	else:
		tmp = x + ((a / t) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.8e+30)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (t <= 6800000000000.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	else
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.8e+30)
		tmp = x + ((z - y) / (t / a));
	elseif (t <= 6800000000000.0)
		tmp = x + (a * (y / (z + -1.0)));
	else
		tmp = x + ((a / t) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.8e+30], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6800000000000.0], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e30

   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 87.4%

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

   5. Simplified 87.4%

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

   if -1.8000000000000001e30 < t < 6.8e12

   1. Initial program 96.8%

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

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

   5. Simplified 87.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 83.2%

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

   10. Simplified 83.2%

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

   if 6.8e12 < t

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 77.9%

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

   5. Simplified 77.9%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

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

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

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

      6. --lowering--.f64 77.9%

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

   7. Applied egg-rr 77.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 6800000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 210000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ a t) (- z y)))))
   (if (<= t -5.8e+29)
     t_1
     (if (<= t 210000000000.0) (+ x (* a (/ y (+ z -1.0)))) 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 <= -5.8e+29) {
		tmp = t_1;
	} else if (t <= 210000000000.0) {
		tmp = x + (a * (y / (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 + ((a / t) * (z - y))
    if (t <= (-5.8d+29)) then
        tmp = t_1
    else if (t <= 210000000000.0d0) then
        tmp = x + (a * (y / (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 + ((a / t) * (z - y));
	double tmp;
	if (t <= -5.8e+29) {
		tmp = t_1;
	} else if (t <= 210000000000.0) {
		tmp = x + (a * (y / (z + -1.0)));
	} 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 <= -5.8e+29:
		tmp = t_1
	elif t <= 210000000000.0:
		tmp = x + (a * (y / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -5.8e+29)
		tmp = t_1;
	elseif (t <= 210000000000.0)
		tmp = Float64(x + Float64(a * Float64(y / 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 + ((a / t) * (z - y));
	tmp = 0.0;
	if (t <= -5.8e+29)
		tmp = t_1;
	elseif (t <= 210000000000.0)
		tmp = x + (a * (y / (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[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+29], t$95$1, If[LessEqual[t, 210000000000.0], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7999999999999999e29 or 2.1e11 < t

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.3%

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

   5. Simplified 82.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

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

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

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

      6. --lowering--.f64 82.3%

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

   7. Applied egg-rr 82.3%

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

   if -5.7999999999999999e29 < t < 2.1e11

   1. Initial program 96.8%

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

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

   5. Simplified 87.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 98.4%

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

   7. Applied egg-rr 98.4%

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

   8. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 83.2%

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

   10. Simplified 83.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 210000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 14000000000:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ a t) (- z y)))))
   (if (<= t -1.35e+28) t_1 (if (<= t 14000000000.0) (- x (* a y)) 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 <= -1.35e+28) {
		tmp = t_1;
	} else if (t <= 14000000000.0) {
		tmp = x - (a * y);
	} 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 <= (-1.35d+28)) then
        tmp = t_1
    else if (t <= 14000000000.0d0) then
        tmp = x - (a * y)
    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 <= -1.35e+28) {
		tmp = t_1;
	} else if (t <= 14000000000.0) {
		tmp = x - (a * y);
	} 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 <= -1.35e+28:
		tmp = t_1
	elif t <= 14000000000.0:
		tmp = x - (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -1.35e+28)
		tmp = t_1;
	elseif (t <= 14000000000.0)
		tmp = Float64(x - Float64(a * y));
	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 <= -1.35e+28)
		tmp = t_1;
	elseif (t <= 14000000000.0)
		tmp = x - (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+28], t$95$1, If[LessEqual[t, 14000000000.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3500000000000001e28 or 1.4e10 < t

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.3%

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

   5. Simplified 82.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

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

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

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

      6. --lowering--.f64 82.3%

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

   7. Applied egg-rr 82.3%

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

   if -1.3500000000000001e28 < t < 1.4e10

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 69.0%

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

   5. Simplified 69.0%

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

   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 67.5%

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

   8. Simplified 67.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq 14000000000:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7600000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7600000000.0) (- x a) (if (<= z 1.4e-13) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7600000000.0) {
		tmp = x - a;
	} else if (z <= 1.4e-13) {
		tmp = x - (a * 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 <= (-7600000000.0d0)) then
        tmp = x - a
    else if (z <= 1.4d-13) then
        tmp = x - (a * 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 <= -7600000000.0) {
		tmp = x - a;
	} else if (z <= 1.4e-13) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7600000000.0:
		tmp = x - a
	elif z <= 1.4e-13:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7600000000.0)
		tmp = Float64(x - a);
	elseif (z <= 1.4e-13)
		tmp = Float64(x - Float64(a * 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 <= -7600000000.0)
		tmp = x - a;
	elseif (z <= 1.4e-13)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7600000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.4e-13], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6e9 or 1.4000000000000001e-13 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 73.1%

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

   5. Simplified 73.1%

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

   if -7.6e9 < z < 1.4000000000000001e-13

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.6%

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

   5. Simplified 87.6%

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

   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 73.7%

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

   8. Simplified 73.7%

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

Alternative 9: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -620000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -620000000000.0) (- x a) (if (<= z 8.5e-47) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -620000000000.0) {
		tmp = x - a;
	} else if (z <= 8.5e-47) {
		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 <= (-620000000000.0d0)) then
        tmp = x - a
    else if (z <= 8.5d-47) 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 <= -620000000000.0) {
		tmp = x - a;
	} else if (z <= 8.5e-47) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -620000000000.0:
		tmp = x - a
	elif z <= 8.5e-47:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -620000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 8.5e-47)
		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 <= -620000000000.0)
		tmp = x - a;
	elseif (z <= 8.5e-47)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -620000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 8.5e-47], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e11 or 8.4999999999999999e-47 < z

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 72.7%

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

   5. Simplified 72.7%

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

   if -6.2e11 < z < 8.4999999999999999e-47

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.1%

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

Alternative 10: 53.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+200}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 6.5e+200) x (- 0.0 a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 6.5e+200) {
		tmp = x;
	} else {
		tmp = 0.0 - 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 (a <= 6.5d+200) then
        tmp = x
    else
        tmp = 0.0d0 - 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 (a <= 6.5e+200) {
		tmp = x;
	} else {
		tmp = 0.0 - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 6.5e+200:
		tmp = x
	else:
		tmp = 0.0 - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 6.5e+200)
		tmp = x;
	else
		tmp = Float64(0.0 - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 6.5e+200)
		tmp = x;
	else
		tmp = 0.0 - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 6.5e+200], x, N[(0.0 - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.49999999999999963e200

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 60.6%

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

   if 6.49999999999999963e200 < a

   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 inf

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

      1. --lowering--.f64 29.2%

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

   5. Simplified 29.2%

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

   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 29.2%

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

   8. Simplified 29.2%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 29.2%

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

   10. Applied egg-rr 29.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+200}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.8% 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 97.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 53.7%

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

Developer Target 1: 99.6% 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 2024158 
(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))))