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

Percentage Accurate: 97.0% → 99.5%

Time: 12.9s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% 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

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (a / (((-1.0d0) + (z - t)) / (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

   1. *-commutative 99.9%

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

   2. clear-num 99.9%

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

   3. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-261}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 1650:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))))
   (if (<= t -8.6e-13)
     t_1
     (if (<= t 7.3e-261) (- x (* a y)) (if (<= t 1650.0) (- x a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -8.6e-13) {
		tmp = t_1;
	} else if (t <= 7.3e-261) {
		tmp = x - (a * y);
	} else if (t <= 1650.0) {
		tmp = x - 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 - (y * (a / t))
    if (t <= (-8.6d-13)) then
        tmp = t_1
    else if (t <= 7.3d-261) then
        tmp = x - (a * y)
    else if (t <= 1650.0d0) then
        tmp = x - a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double tmp;
	if (t <= -8.6e-13) {
		tmp = t_1;
	} else if (t <= 7.3e-261) {
		tmp = x - (a * y);
	} else if (t <= 1650.0) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	tmp = 0
	if t <= -8.6e-13:
		tmp = t_1
	elif t <= 7.3e-261:
		tmp = x - (a * y)
	elif t <= 1650.0:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	tmp = 0.0
	if (t <= -8.6e-13)
		tmp = t_1;
	elseif (t <= 7.3e-261)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 1650.0)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	tmp = 0.0;
	if (t <= -8.6e-13)
		tmp = t_1;
	elseif (t <= 7.3e-261)
		tmp = x - (a * y);
	elseif (t <= 1650.0)
		tmp = x - a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e-13], t$95$1, If[LessEqual[t, 7.3e-261], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1650.0], N[(x - a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5999999999999997e-13 or 1650 < t

   1. Initial program 97.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 77.0%

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

   6. Taylor expanded in t around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*r/ 79.4%

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

   8. Simplified 79.4%

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

   if -8.5999999999999997e-13 < t < 7.29999999999999974e-261

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.4%

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

   6. Taylor expanded in t around 0 76.3%

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

   7. Taylor expanded in z around 0 69.0%

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

   if 7.29999999999999974e-261 < t < 1650

   1. Initial program 95.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.6%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-261}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 1650:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-263}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -8.6e-13)
     t_1
     (if (<= t 3.4e-263) (- x (* a y)) (if (<= t 2400.0) (- x a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -8.6e-13) {
		tmp = t_1;
	} else if (t <= 3.4e-263) {
		tmp = x - (a * y);
	} else if (t <= 2400.0) {
		tmp = x - 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 * (y / t))
    if (t <= (-8.6d-13)) then
        tmp = t_1
    else if (t <= 3.4d-263) then
        tmp = x - (a * y)
    else if (t <= 2400.0d0) then
        tmp = x - 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 * (y / t));
	double tmp;
	if (t <= -8.6e-13) {
		tmp = t_1;
	} else if (t <= 3.4e-263) {
		tmp = x - (a * y);
	} else if (t <= 2400.0) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -8.6e-13:
		tmp = t_1
	elif t <= 3.4e-263:
		tmp = x - (a * y)
	elif t <= 2400.0:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -8.6e-13)
		tmp = t_1;
	elseif (t <= 3.4e-263)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 2400.0)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -8.6e-13)
		tmp = t_1;
	elseif (t <= 3.4e-263)
		tmp = x - (a * y);
	elseif (t <= 2400.0)
		tmp = x - 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[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e-13], t$95$1, If[LessEqual[t, 3.4e-263], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2400.0], N[(x - a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5999999999999997e-13 or 2400 < t

   1. Initial program 97.2%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 83.4%

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

   6. Taylor expanded in y around inf 80.3%

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

   if -8.5999999999999997e-13 < t < 3.40000000000000004e-263

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.4%

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

   6. Taylor expanded in t around 0 76.3%

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

   7. Taylor expanded in z around 0 69.0%

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

   if 3.40000000000000004e-263 < t < 2400

   1. Initial program 95.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.6%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-263}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 2400:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-268}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 1450:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.6e-13)
   (- x (* a (/ y t)))
   (if (<= t 2.15e-268)
     (- x (* a y))
     (if (<= t 1450.0) (- x a) (- x (/ a (/ t y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.6e-13) {
		tmp = x - (a * (y / t));
	} else if (t <= 2.15e-268) {
		tmp = x - (a * y);
	} else if (t <= 1450.0) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / 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 <= (-8.6d-13)) then
        tmp = x - (a * (y / t))
    else if (t <= 2.15d-268) then
        tmp = x - (a * y)
    else if (t <= 1450.0d0) then
        tmp = x - a
    else
        tmp = x - (a / (t / 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 <= -8.6e-13) {
		tmp = x - (a * (y / t));
	} else if (t <= 2.15e-268) {
		tmp = x - (a * y);
	} else if (t <= 1450.0) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.6e-13:
		tmp = x - (a * (y / t))
	elif t <= 2.15e-268:
		tmp = x - (a * y)
	elif t <= 1450.0:
		tmp = x - a
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.6e-13)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= 2.15e-268)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 1450.0)
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8.6e-13)
		tmp = x - (a * (y / t));
	elseif (t <= 2.15e-268)
		tmp = x - (a * y);
	elseif (t <= 1450.0)
		tmp = x - a;
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.6e-13], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e-268], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1450.0], N[(x - a), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.5999999999999997e-13

   1. Initial program 95.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.7%

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

   6. Taylor expanded in y around inf 72.9%

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

   if -8.5999999999999997e-13 < t < 2.15e-268

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.4%

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

   6. Taylor expanded in t around 0 76.3%

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

   7. Taylor expanded in z around 0 69.0%

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

   if 2.15e-268 < t < 1450

   1. Initial program 95.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.6%

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

   if 1450 < t

   1. Initial program 98.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 89.0%

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

   6. Taylor expanded in y around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. clear-num 87.4%

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

      3. un-div-inv 87.4%

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

   8. Applied egg-rr 87.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-268}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 1450:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0001 \lor \neg \left(y \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.0001) (not (<= y 2e-11)))
   (- x (* a (/ y (- (+ t 1.0) z))))
   (- x (* a (/ z (+ z (- -1.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.0001) || !(y <= 2e-11)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-0.0001d0)) .or. (.not. (y <= 2d-11))) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x - (a * (z / (z + ((-1.0d0) - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.0001) || !(y <= 2e-11)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.0001) or not (y <= 2e-11):
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x - (a * (z / (z + (-1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.0001) || !(y <= 2e-11))
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + Float64(-1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -0.0001) || ~((y <= 2e-11)))
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x - (a * (z / (z + (-1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.0001], N[Not[LessEqual[y, 2e-11]], $MachinePrecision]], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000005e-4 or 1.99999999999999988e-11 < y

   1. Initial program 97.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 91.7%

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

   if -1.00000000000000005e-4 < y < 1.99999999999999988e-11

   1. Initial program 97.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 96.7%

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

      1. mul-1-neg 96.7%

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

      2. associate--l+ 96.7%

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

      3. +-commutative 96.7%

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

      4. distribute-neg-frac2 96.7%

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

      5. +-commutative 96.7%

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

      6. distribute-neg-in 96.7%

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

      7. metadata-eval 96.7%

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

      8. unsub-neg 96.7%

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

      9. associate--r- 96.7%

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

   7. Simplified 96.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0001 \lor \neg \left(y \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00051 \lor \neg \left(y \leq 1.45 \cdot 10^{-11}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.00051) (not (<= y 1.45e-11)))
   (- x (* a (/ y (- (+ t 1.0) z))))
   (+ x (/ a (+ (/ (+ t 1.0) z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.00051) || !(y <= 1.45e-11)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a / (((t + 1.0) / 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 ((y <= (-0.00051d0)) .or. (.not. (y <= 1.45d-11))) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x + (a / (((t + 1.0d0) / 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 ((y <= -0.00051) || !(y <= 1.45e-11)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.00051) or not (y <= 1.45e-11):
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x + (a / (((t + 1.0) / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.00051) || !(y <= 1.45e-11))
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -0.00051) || ~((y <= 1.45e-11)))
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.00051], N[Not[LessEqual[y, 1.45e-11]], $MachinePrecision]], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1e-4 or 1.45e-11 < y

   1. Initial program 97.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 91.7%

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

   if -5.1e-4 < y < 1.45e-11

   1. Initial program 97.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 96.8%

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

      1. mul-1-neg 96.8%

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

      2. div-sub 96.8%

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

      3. *-inverses 96.8%

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

   9. Simplified 96.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00051 \lor \neg \left(y \leq 1.45 \cdot 10^{-11}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+86}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+98)
   (+ x (/ a (+ -1.0 (/ t z))))
   (if (<= z 1.06e+86)
     (- x (* a (/ y (- (+ t 1.0) z))))
     (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+98) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 1.06e+86) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.1d+98)) then
        tmp = x + (a / ((-1.0d0) + (t / z)))
    else if (z <= 1.06d+86) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+98) {
		tmp = x + (a / (-1.0 + (t / z)));
	} else if (z <= 1.06e+86) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+98:
		tmp = x + (a / (-1.0 + (t / z)))
	elif z <= 1.06e+86:
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+98)
		tmp = Float64(x + Float64(a / Float64(-1.0 + Float64(t / z))));
	elseif (z <= 1.06e+86)
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+98)
		tmp = x + (a / (-1.0 + (t / z)));
	elseif (z <= 1.06e+86)
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+98], N[(x + N[(a / N[(-1.0 + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+86], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000019e98

   1. Initial program 90.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. div-sub 93.4%

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

      3. *-inverses 93.4%

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

   9. Simplified 93.4%

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

   10. Taylor expanded in t around inf 93.4%

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

   if -3.10000000000000019e98 < z < 1.06e86

   1. Initial program 98.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 92.5%

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

   if 1.06e86 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 97.1%

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

      1. mul-1-neg 94.8%

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

   5. Simplified 97.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+98}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+86}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85} \lor \neg \left(z \leq 2.6 \cdot 10^{+82}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+85) (not (<= z 2.6e+82)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+85) || !(z <= 2.6e+82)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+85)) .or. (.not. (z <= 2.6d+82))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+85) || !(z <= 2.6e+82)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+85) or not (z <= 2.6e+82):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+85) || !(z <= 2.6e+82))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+85) || ~((z <= 2.6e+82)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+85], N[Not[LessEqual[z, 2.6e+82]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999994e85 or 2.5999999999999998e82 < z

   1. Initial program 94.5%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.3%

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

   if -8.4999999999999994e85 < z < 2.5999999999999998e82

   1. Initial program 98.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 87.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+85} \lor \neg \left(z \leq 2.6 \cdot 10^{+82}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8500000000000 \lor \neg \left(z \leq 3900000\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8500000000000.0) (not (<= z 3900000.0)))
   (+ x (* a (/ (- y z) z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8500000000000.0) || !(z <= 3900000.0)) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8500000000000.0d0)) .or. (.not. (z <= 3900000.0d0))) then
        tmp = x + (a * ((y - z) / z))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8500000000000.0) || !(z <= 3900000.0)) {
		tmp = x + (a * ((y - z) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8500000000000.0) or not (z <= 3900000.0):
		tmp = x + (a * ((y - z) / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8500000000000.0) || !(z <= 3900000.0))
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8500000000000.0) || ~((z <= 3900000.0)))
		tmp = x + (a * ((y - z) / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8500000000000.0], N[Not[LessEqual[z, 3900000.0]], $MachinePrecision]], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e12 or 3.9e6 < z

   1. Initial program 94.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. mul-1-neg 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in z around 0 86.2%

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

      1. neg-mul-1 86.2%

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

      2. unsub-neg 86.2%

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

   10. Simplified 86.2%

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

   if -8.5e12 < z < 3.9e6

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8500000000000 \lor \neg \left(z \leq 3900000\right):\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 8000:\\ \;\;\;\;x - y \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+18)
   (- x (* a (/ y t)))
   (if (<= t 8000.0) (- x (* y (/ a (- 1.0 z)))) (- x (/ a (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+18) {
		tmp = x - (a * (y / t));
	} else if (t <= 8000.0) {
		tmp = x - (y * (a / (1.0 - z)));
	} else {
		tmp = x - (a / (t / 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 <= (-1.05d+18)) then
        tmp = x - (a * (y / t))
    else if (t <= 8000.0d0) then
        tmp = x - (y * (a / (1.0d0 - z)))
    else
        tmp = x - (a / (t / 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 <= -1.05e+18) {
		tmp = x - (a * (y / t));
	} else if (t <= 8000.0) {
		tmp = x - (y * (a / (1.0 - z)));
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+18:
		tmp = x - (a * (y / t))
	elif t <= 8000.0:
		tmp = x - (y * (a / (1.0 - z)))
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+18)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= 8000.0)
		tmp = Float64(x - Float64(y * Float64(a / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+18)
		tmp = x - (a * (y / t));
	elseif (t <= 8000.0)
		tmp = x - (y * (a / (1.0 - z)));
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+18], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8000.0], N[(x - N[(y * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e18

   1. Initial program 95.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 84.0%

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

   6. Taylor expanded in y around inf 76.5%

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

   if -1.05e18 < t < 8e3

   1. Initial program 97.5%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 76.2%

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

   6. Taylor expanded in t around 0 74.3%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   8. Simplified 78.3%

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

   if 8e3 < t

   1. Initial program 98.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 89.0%

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

   6. Taylor expanded in y around inf 87.3%

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

      1. *-commutative 87.3%

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

      2. clear-num 87.4%

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

      3. un-div-inv 87.4%

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

   8. Applied egg-rr 87.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 8000:\\ \;\;\;\;x - y \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -68000000000:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -68000000000.0)
   (+ x (* a (/ (- y z) z)))
   (if (<= z 50000000.0)
     (+ x (* a (/ y (- -1.0 t))))
     (+ x (/ a (/ z (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -68000000000.0) {
		tmp = x + (a * ((y - z) / z));
	} else if (z <= 50000000.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a / (z / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-68000000000.0d0)) then
        tmp = x + (a * ((y - z) / z))
    else if (z <= 50000000.0d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + (a / (z / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -68000000000.0) {
		tmp = x + (a * ((y - z) / z));
	} else if (z <= 50000000.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + (a / (z / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -68000000000.0:
		tmp = x + (a * ((y - z) / z))
	elif z <= 50000000.0:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + (a / (z / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -68000000000.0)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	elseif (z <= 50000000.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(a / Float64(z / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -68000000000.0)
		tmp = x + (a * ((y - z) / z));
	elseif (z <= 50000000.0)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + (a / (z / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -68000000000.0], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 50000000.0], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e10

   1. Initial program 93.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.8%

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

      1. mul-1-neg 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in z around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. unsub-neg 87.8%

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

   10. Simplified 87.8%

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

   if -6.8e10 < z < 5e7

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.9%

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

   if 5e7 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.7%

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

      1. mul-1-neg 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in z around 0 84.7%

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

      1. neg-mul-1 84.7%

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

      2. unsub-neg 84.7%

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

   10. Simplified 84.7%

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

       1. *-commutative 84.7%

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

       2. clear-num 84.7%

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

       3. un-div-inv 84.7%

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

   12. Applied egg-rr 84.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -68000000000:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 50000000:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -47000000:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -47000000.0)
   (+ x (* a (/ (- y z) z)))
   (if (<= z 7e+78) (+ x (* a (/ y (- -1.0 t)))) (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -47000000.0) {
		tmp = x + (a * ((y - z) / z));
	} else if (z <= 7e+78) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-47000000.0d0)) then
        tmp = x + (a * ((y - z) / z))
    else if (z <= 7d+78) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -47000000.0) {
		tmp = x + (a * ((y - z) / z));
	} else if (z <= 7e+78) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -47000000.0:
		tmp = x + (a * ((y - z) / z))
	elif z <= 7e+78:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -47000000.0)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / z)));
	elseif (z <= 7e+78)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -47000000.0)
		tmp = x + (a * ((y - z) / z));
	elseif (z <= 7e+78)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -47000000.0], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+78], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7e7

   1. Initial program 93.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.8%

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

      1. mul-1-neg 87.8%

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

   7. Simplified 87.8%

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

   8. Taylor expanded in z around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. unsub-neg 87.8%

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

   10. Simplified 87.8%

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

   if -4.7e7 < z < 7.0000000000000003e78

   1. Initial program 98.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 89.4%

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

   if 7.0000000000000003e78 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 97.1%

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

      1. mul-1-neg 94.8%

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

   5. Simplified 97.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -47000000:\\ \;\;\;\;x + a \cdot \frac{y - z}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+78}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-23} \lor \neg \left(z \leq 4.5 \cdot 10^{-49}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e-23) (not (<= z 4.5e-49))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-23) || !(z <= 4.5e-49)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.2d-23)) .or. (.not. (z <= 4.5d-49))) then
        tmp = x - a
    else
        tmp = x - (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-23) || !(z <= 4.5e-49)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e-23) or not (z <= 4.5e-49):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e-23) || !(z <= 4.5e-49))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e-23) || ~((z <= 4.5e-49)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e-23], N[Not[LessEqual[z, 4.5e-49]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000004e-23 or 4.5000000000000002e-49 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.1%

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

   if -9.2000000000000004e-23 < z < 4.5000000000000002e-49

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 95.7%

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

   6. Taylor expanded in t around 0 69.9%

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

   7. Taylor expanded in z around 0 69.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-23} \lor \neg \left(z \leq 4.5 \cdot 10^{-49}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.6% 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 97.3%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 15: 59.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+239}:\\ \;\;\;\;a \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.5e+239) (* a (/ y z)) (- x a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e+239) {
		tmp = a * (y / z);
	} 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 (y <= (-9.5d+239)) then
        tmp = a * (y / z)
    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 (y <= -9.5e+239) {
		tmp = a * (y / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e+239:
		tmp = a * (y / z)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e+239)
		tmp = Float64(a * Float64(y / z));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e+239)
		tmp = a * (y / z);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e+239], N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000008e239

   1. Initial program 99.9%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in y around inf 40.4%

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

      1. associate-/l* 53.3%

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

   10. Simplified 53.3%

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

   if -9.5000000000000008e239 < y

   1. Initial program 97.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 65.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+239}:\\ \;\;\;\;a \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+116}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 2.7e+116) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.7e+116) {
		tmp = x - 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 (t <= 2.7d+116) then
        tmp = x - 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 (t <= 2.7e+116) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.7e+116:
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.7e+116)
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.7e+116)
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.7e+116], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 2.7e116

   1. Initial program 97.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.1%

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

   if 2.7e116 < t

   1. Initial program 97.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 45.0%

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

      1. mul-1-neg 45.0%

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

   7. Simplified 45.0%

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

   8. Taylor expanded in x around inf 66.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+116}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.2% 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 97.3%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 59.1%

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

   1. mul-1-neg 59.1%

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

7. Simplified 59.1%

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

8. Taylor expanded in x around inf 54.5%

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

9. Final simplification 54.5%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 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 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

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