Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 93.7%

Time: 16.7s

Alternatives: 15

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + t\_1\\ \mathbf{elif}\;z \leq 480000000:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{\frac{x}{z} \cdot y}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ y (* z (- b y)))))
   (if (<= z -1.02e-5)
     (+ (* (/ x z) (/ y (- b y))) t_1)
     (if (<= z 480000000.0)
       (* x (+ (/ y t_2) (/ (* z (- t a)) (* x t_2))))
       (+ t_1 (/ (* (/ x z) y) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -1.02e-5) {
		tmp = ((x / z) * (y / (b - y))) + t_1;
	} else if (z <= 480000000.0) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = t_1 + (((x / z) * y) / (b - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = y + (z * (b - y))
    if (z <= (-1.02d-5)) then
        tmp = ((x / z) * (y / (b - y))) + t_1
    else if (z <= 480000000.0d0) then
        tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
    else
        tmp = t_1 + (((x / z) * y) / (b - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -1.02e-5) {
		tmp = ((x / z) * (y / (b - y))) + t_1;
	} else if (z <= 480000000.0) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = t_1 + (((x / z) * y) / (b - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -1.02e-5:
		tmp = ((x / z) * (y / (b - y))) + t_1
	elif z <= 480000000.0:
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
	else:
		tmp = t_1 + (((x / z) * y) / (b - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -1.02e-5)
		tmp = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + t_1);
	elseif (z <= 480000000.0)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_2))));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(x / z) * y) / Float64(b - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -1.02e-5)
		tmp = ((x / z) * (y / (b - y))) + t_1;
	elseif (z <= 480000000.0)
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	else
		tmp = t_1 + (((x / z) * y) / (b - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e-5], N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 480000000.0], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0200000000000001e-5

   1. Initial program 56.6%

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

   3. Taylor expanded in z around -inf 74.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.7%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.7%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.7%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 74.9%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 85.4%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 85.4%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 85.4%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 81.1%

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

      1. times-frac 97.2%

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

   8. Simplified 97.2%

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

   if -1.0200000000000001e-5 < z < 4.8e8

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf 92.9%

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

   if 4.8e8 < z

   1. Initial program 53.2%

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

   3. Taylor expanded in z around -inf 74.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.9%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.9%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.9%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 75.0%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 86.6%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 88.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 88.3%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 89.1%

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

      1. times-frac 97.4%

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

   8. Simplified 97.4%

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

      1. associate-*r/ 98.9%

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

   10. Applied egg-rr 98.9%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 480000000:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{x}{z} \cdot y}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-198}:\\ \;\;\;\;\frac{t\_1}{z \cdot \left(\left(b + \frac{y}{z}\right) - y\right)}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -4.2e+27)
     t_2
     (if (<= z -4.9e-198)
       (/ t_1 (* z (- (+ b (/ y z)) y)))
       (if (<= z 1.38e-213)
         x
         (if (<= z 440000000.0) (/ t_1 (+ y (* z (- b y)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.2e+27) {
		tmp = t_2;
	} else if (z <= -4.9e-198) {
		tmp = t_1 / (z * ((b + (y / z)) - y));
	} else if (z <= 1.38e-213) {
		tmp = x;
	} else if (z <= 440000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-4.2d+27)) then
        tmp = t_2
    else if (z <= (-4.9d-198)) then
        tmp = t_1 / (z * ((b + (y / z)) - y))
    else if (z <= 1.38d-213) then
        tmp = x
    else if (z <= 440000000.0d0) then
        tmp = t_1 / (y + (z * (b - y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.2e+27) {
		tmp = t_2;
	} else if (z <= -4.9e-198) {
		tmp = t_1 / (z * ((b + (y / z)) - y));
	} else if (z <= 1.38e-213) {
		tmp = x;
	} else if (z <= 440000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -4.2e+27:
		tmp = t_2
	elif z <= -4.9e-198:
		tmp = t_1 / (z * ((b + (y / z)) - y))
	elif z <= 1.38e-213:
		tmp = x
	elif z <= 440000000.0:
		tmp = t_1 / (y + (z * (b - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -4.2e+27)
		tmp = t_2;
	elseif (z <= -4.9e-198)
		tmp = Float64(t_1 / Float64(z * Float64(Float64(b + Float64(y / z)) - y)));
	elseif (z <= 1.38e-213)
		tmp = x;
	elseif (z <= 440000000.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -4.2e+27)
		tmp = t_2;
	elseif (z <= -4.9e-198)
		tmp = t_1 / (z * ((b + (y / z)) - y));
	elseif (z <= 1.38e-213)
		tmp = x;
	elseif (z <= 440000000.0)
		tmp = t_1 / (y + (z * (b - y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+27], t$95$2, If[LessEqual[z, -4.9e-198], N[(t$95$1 / N[(z * N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-213], x, If[LessEqual[z, 440000000.0], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.19999999999999989e27 or 4.4e8 < z

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 74.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.0%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.0%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 74.1%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 85.5%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 86.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in y around inf 86.8%

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

      1. mul-1-neg 86.8%

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

   8. Simplified 86.8%

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

   if -4.19999999999999989e27 < z < -4.9000000000000002e-198

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 53.9%

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

   4. Taylor expanded in z around inf 54.0%

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

   if -4.9000000000000002e-198 < z < 1.37999999999999998e-213

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 73.1%

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

   if 1.37999999999999998e-213 < z < 4.4e8

   1. Initial program 79.3%

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

   3. Taylor expanded in x around 0 52.5%

      \[\leadsto \color{blue}{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-198}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{z \cdot \left(\left(b + \frac{y}{z}\right) - y\right)}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 440000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 320000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z (- b y)))))
        (t_2 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -4.2e+27)
     t_2
     (if (<= z -3.2e-200)
       t_1
       (if (<= z 2.2e-213) x (if (<= z 320000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.2e+27) {
		tmp = t_2;
	} else if (z <= -3.2e-200) {
		tmp = t_1;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 320000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * (b - y)))
    t_2 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-4.2d+27)) then
        tmp = t_2
    else if (z <= (-3.2d-200)) then
        tmp = t_1
    else if (z <= 2.2d-213) then
        tmp = x
    else if (z <= 320000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * (b - y)));
	double t_2 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -4.2e+27) {
		tmp = t_2;
	} else if (z <= -3.2e-200) {
		tmp = t_1;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 320000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * (b - y)))
	t_2 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -4.2e+27:
		tmp = t_2
	elif z <= -3.2e-200:
		tmp = t_1
	elif z <= 2.2e-213:
		tmp = x
	elif z <= 320000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -4.2e+27)
		tmp = t_2;
	elseif (z <= -3.2e-200)
		tmp = t_1;
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 320000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * (b - y)));
	t_2 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -4.2e+27)
		tmp = t_2;
	elseif (z <= -3.2e-200)
		tmp = t_1;
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 320000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+27], t$95$2, If[LessEqual[z, -3.2e-200], t$95$1, If[LessEqual[z, 2.2e-213], x, If[LessEqual[z, 320000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999989e27 or 3.2e8 < z

   1. Initial program 53.5%

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

   3. Taylor expanded in z around -inf 74.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.0%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.0%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 74.1%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 85.5%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 86.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in y around inf 86.8%

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

      1. mul-1-neg 86.8%

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

   8. Simplified 86.8%

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

   if -4.19999999999999989e27 < z < -3.19999999999999983e-200 or 2.2000000000000001e-213 < z < 3.2e8

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 53.3%

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

   if -3.19999999999999983e-200 < z < 2.2000000000000001e-213

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 73.1%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-200}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 320000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{t + \left(x \cdot \frac{y}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 13:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- t a) (- b y)) (/ x z))))
   (if (<= z -3.4e+24)
     t_1
     (if (<= z -1.9e-86)
       (/ (+ t (- (* x (/ y z)) a)) b)
       (if (<= z 2.2e-213)
         x
         (if (<= z 13.0) (/ (* z (- t a)) (+ y (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -3.4e+24) {
		tmp = t_1;
	} else if (z <= -1.9e-86) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 13.0) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t - a) / (b - y)) - (x / z)
    if (z <= (-3.4d+24)) then
        tmp = t_1
    else if (z <= (-1.9d-86)) then
        tmp = (t + ((x * (y / z)) - a)) / b
    else if (z <= 2.2d-213) then
        tmp = x
    else if (z <= 13.0d0) then
        tmp = (z * (t - a)) / (y + (z * b))
    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 b) {
	double t_1 = ((t - a) / (b - y)) - (x / z);
	double tmp;
	if (z <= -3.4e+24) {
		tmp = t_1;
	} else if (z <= -1.9e-86) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 13.0) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t - a) / (b - y)) - (x / z)
	tmp = 0
	if z <= -3.4e+24:
		tmp = t_1
	elif z <= -1.9e-86:
		tmp = (t + ((x * (y / z)) - a)) / b
	elif z <= 2.2e-213:
		tmp = x
	elif z <= 13.0:
		tmp = (z * (t - a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z))
	tmp = 0.0
	if (z <= -3.4e+24)
		tmp = t_1;
	elseif (z <= -1.9e-86)
		tmp = Float64(Float64(t + Float64(Float64(x * Float64(y / z)) - a)) / b);
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 13.0)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t - a) / (b - y)) - (x / z);
	tmp = 0.0;
	if (z <= -3.4e+24)
		tmp = t_1;
	elseif (z <= -1.9e-86)
		tmp = (t + ((x * (y / z)) - a)) / b;
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 13.0)
		tmp = (z * (t - a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+24], t$95$1, If[LessEqual[z, -1.9e-86], N[(N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.2e-213], x, If[LessEqual[z, 13.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.4000000000000001e24 or 13 < z

   1. Initial program 54.3%

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

   3. Taylor expanded in z around -inf 72.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 72.8%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 72.8%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 72.8%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 73.0%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 84.8%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 85.6%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 85.6%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in y around inf 86.6%

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

      1. mul-1-neg 86.6%

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

   8. Simplified 86.6%

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

   if -3.4000000000000001e24 < z < -1.9e-86

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf 95.4%

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

      1. associate--l+ 95.4%

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

      2. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in b around inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. associate--l+ 65.8%

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

   8. Simplified 65.8%

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

   if -1.9e-86 < z < 2.2000000000000001e-213

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 62.7%

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

   if 2.2000000000000001e-213 < z < 13

   1. Initial program 78.8%

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

   3. Taylor expanded in x around 0 51.4%

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

   4. Taylor expanded in b around inf 50.9%

      \[\leadsto \frac{z \cdot \left(t - a\right)}{y + z \cdot \color{blue}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+24}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-86}:\\ \;\;\;\;\frac{t + \left(x \cdot \frac{y}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 13:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -360000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{t + \left(x \cdot \frac{y}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -360000.0)
     t_1
     (if (<= z -1.3e-88)
       (/ (+ t (- (* x (/ y z)) a)) b)
       (if (<= z 2.2e-213)
         x
         (if (<= z 1.0) (/ (* z (- t a)) (+ y (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -360000.0) {
		tmp = t_1;
	} else if (z <= -1.3e-88) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-360000.0d0)) then
        tmp = t_1
    else if (z <= (-1.3d-88)) then
        tmp = (t + ((x * (y / z)) - a)) / b
    else if (z <= 2.2d-213) then
        tmp = x
    else if (z <= 1.0d0) then
        tmp = (z * (t - a)) / (y + (z * b))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -360000.0) {
		tmp = t_1;
	} else if (z <= -1.3e-88) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 2.2e-213) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -360000.0:
		tmp = t_1
	elif z <= -1.3e-88:
		tmp = (t + ((x * (y / z)) - a)) / b
	elif z <= 2.2e-213:
		tmp = x
	elif z <= 1.0:
		tmp = (z * (t - a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -360000.0)
		tmp = t_1;
	elseif (z <= -1.3e-88)
		tmp = Float64(Float64(t + Float64(Float64(x * Float64(y / z)) - a)) / b);
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 1.0)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -360000.0)
		tmp = t_1;
	elseif (z <= -1.3e-88)
		tmp = (t + ((x * (y / z)) - a)) / b;
	elseif (z <= 2.2e-213)
		tmp = x;
	elseif (z <= 1.0)
		tmp = (z * (t - a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -360000.0], t$95$1, If[LessEqual[z, -1.3e-88], N[(N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.2e-213], x, If[LessEqual[z, 1.0], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e5 or 1 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in z around inf 77.6%

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

   if -3.6e5 < z < -1.30000000000000007e-88

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 94.9%

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

      1. associate--l+ 94.9%

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

      2. associate-/l* 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in b around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate--l+ 67.2%

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

   8. Simplified 67.2%

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

   if -1.30000000000000007e-88 < z < 2.2000000000000001e-213

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 62.7%

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

   if 2.2000000000000001e-213 < z < 1

   1. Initial program 78.8%

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

   3. Taylor expanded in x around 0 51.4%

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

   4. Taylor expanded in b around inf 50.9%

      \[\leadsto \frac{z \cdot \left(t - a\right)}{y + z \cdot \color{blue}{b}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.05e-24)
     t_2
     (if (<= z -1.1e-200)
       t_1
       (if (<= z 2.1e-213) x (if (<= z 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e-24) {
		tmp = t_2;
	} else if (z <= -1.1e-200) {
		tmp = t_1;
	} else if (z <= 2.1e-213) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.05d-24)) then
        tmp = t_2
    else if (z <= (-1.1d-200)) then
        tmp = t_1
    else if (z <= 2.1d-213) then
        tmp = x
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e-24) {
		tmp = t_2;
	} else if (z <= -1.1e-200) {
		tmp = t_1;
	} else if (z <= 2.1e-213) {
		tmp = x;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.05e-24:
		tmp = t_2
	elif z <= -1.1e-200:
		tmp = t_1
	elif z <= 2.1e-213:
		tmp = x
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.05e-24)
		tmp = t_2;
	elseif (z <= -1.1e-200)
		tmp = t_1;
	elseif (z <= 2.1e-213)
		tmp = x;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.05e-24)
		tmp = t_2;
	elseif (z <= -1.1e-200)
		tmp = t_1;
	elseif (z <= 2.1e-213)
		tmp = x;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-24], t$95$2, If[LessEqual[z, -1.1e-200], t$95$1, If[LessEqual[z, 2.1e-213], x, If[LessEqual[z, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e-24 or 1 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in z around inf 76.0%

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

   if -1.05e-24 < z < -1.10000000000000007e-200 or 2.0999999999999998e-213 < z < 1

   1. Initial program 83.8%

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

   3. Taylor expanded in x around 0 52.0%

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

   4. Taylor expanded in b around inf 51.7%

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

   if -1.10000000000000007e-200 < z < 2.0999999999999998e-213

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 73.1%

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

Alternative 7: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27} \lor \neg \left(z \leq 50000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+27) (not (<= z 50000000000000.0)))
   (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y)))
   (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+27) || !(z <= 50000000000000.0)) {
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d+27)) .or. (.not. (z <= 50000000000000.0d0))) then
        tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    else
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+27) || !(z <= 50000000000000.0)) {
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+27) or not (z <= 50000000000000.0):
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	else:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+27) || !(z <= 50000000000000.0))
		tmp = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+27) || ~((z <= 50000000000000.0)))
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	else
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+27], N[Not[LessEqual[z, 50000000000000.0]], $MachinePrecision]], N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999989e27 or 5e13 < z

   1. Initial program 52.0%

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

   3. Taylor expanded in z around -inf 74.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.1%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.1%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.1%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 75.1%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 86.8%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 87.7%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 87.7%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 84.4%

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

      1. times-frac 98.4%

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

   8. Simplified 98.4%

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

   if -4.19999999999999989e27 < z < 5e13

   1. Initial program 86.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27} \lor \neg \left(z \leq 50000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-9} \lor \neg \left(z \leq 50000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e-9) (not (<= z 50000000000000.0)))
   (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y)))
   (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-9) || !(z <= 50000000000000.0)) {
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.5d-9)) .or. (.not. (z <= 50000000000000.0d0))) then
        tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    else
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-9) || !(z <= 50000000000000.0)) {
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e-9) or not (z <= 50000000000000.0):
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	else:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e-9) || !(z <= 50000000000000.0))
		tmp = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e-9) || ~((z <= 50000000000000.0)))
		tmp = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	else
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e-9], N[Not[LessEqual[z, 50000000000000.0]], $MachinePrecision]], N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e-9 or 5e13 < z

   1. Initial program 53.9%

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

   3. Taylor expanded in z around -inf 74.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.4%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 74.4%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 74.4%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 75.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 86.6%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 87.4%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 87.4%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 85.0%

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

      1. times-frac 98.5%

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

   8. Simplified 98.5%

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

   if -8.5e-9 < z < 5e13

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf 70.4%

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

      1. *-commutative 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-9} \lor \neg \left(z \leq 50000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27} \lor \neg \left(z \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+27) (not (<= z 2.5e+21)))
   (- (/ (- t a) (- b y)) (/ x z))
   (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+27) || !(z <= 2.5e+21)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d+27)) .or. (.not. (z <= 2.5d+21))) then
        tmp = ((t - a) / (b - y)) - (x / z)
    else
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+27) || !(z <= 2.5e+21)) {
		tmp = ((t - a) / (b - y)) - (x / z);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e+27) or not (z <= 2.5e+21):
		tmp = ((t - a) / (b - y)) - (x / z)
	else:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+27) || !(z <= 2.5e+21))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(x / z));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e+27) || ~((z <= 2.5e+21)))
		tmp = ((t - a) / (b - y)) - (x / z);
	else
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+27], N[Not[LessEqual[z, 2.5e+21]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999989e27 or 2.5e21 < z

   1. Initial program 51.1%

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

   3. Taylor expanded in z around -inf 73.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.3%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 73.3%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 73.3%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 74.2%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 86.4%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 87.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 87.3%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in y around inf 88.6%

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

      1. mul-1-neg 88.6%

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

   8. Simplified 88.6%

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

   if -4.19999999999999989e27 < z < 2.5e21

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+27} \lor \neg \left(z \leq 2.5 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-94} \lor \neg \left(z \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85e-94) (not (<= z 4.2e+15)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e-94) || !(z <= 4.2e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.85d-94)) .or. (.not. (z <= 4.2d+15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e-94) || !(z <= 4.2e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e-94) or not (z <= 4.2e+15):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85e-94) || !(z <= 4.2e+15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.85e-94) || ~((z <= 4.2e+15)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85e-94], N[Not[LessEqual[z, 4.2e+15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8499999999999999e-94 or 4.2e15 < z

   1. Initial program 59.2%

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

   3. Taylor expanded in z around inf 75.3%

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

   if -1.8499999999999999e-94 < z < 4.2e15

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

   5. Simplified 52.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-94} \lor \neg \left(z \leq 4.2 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-27} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.65e-27) (not (<= y 2.8e+34))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.65e-27) || !(y <= 2.8e+34)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.65d-27)) .or. (.not. (y <= 2.8d+34))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.65e-27) || !(y <= 2.8e+34)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.65e-27) or not (y <= 2.8e+34):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.65e-27) || !(y <= 2.8e+34))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.65e-27) || ~((y <= 2.8e+34)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.65e-27], N[Not[LessEqual[y, 2.8e+34]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999999e-27 or 2.80000000000000008e34 < y

   1. Initial program 54.1%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. unsub-neg 58.9%

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

   5. Simplified 58.9%

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

   if -1.64999999999999999e-27 < y < 2.80000000000000008e34

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 55.2%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-27} \lor \neg \left(y \leq 2.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-5} \lor \neg \left(y \leq 1.45 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.1e-5) (not (<= y 1.45e+40))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.1e-5) || !(y <= 1.45e+40)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.1d-5)) .or. (.not. (y <= 1.45d+40))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.1e-5) || !(y <= 1.45e+40)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.1e-5) or not (y <= 1.45e+40):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.1e-5) || !(y <= 1.45e+40))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.1e-5) || ~((y <= 1.45e+40)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.1e-5], N[Not[LessEqual[y, 1.45e+40]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000014e-5 or 1.45000000000000009e40 < y

   1. Initial program 53.8%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   if -3.10000000000000014e-5 < y < 1.45000000000000009e40

   1. Initial program 85.5%

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

   3. Taylor expanded in z around -inf 71.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 71.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 71.6%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 71.6%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 67.9%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 64.3%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 65.0%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 65.0%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 78.6%

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

      1. times-frac 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in t around inf 43.1%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-5} \lor \neg \left(y \leq 1.45 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-86} \lor \neg \left(z \leq 4 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.2e-86) (not (<= z 4e-42))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.2e-86) || !(z <= 4e-42)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.2d-86)) .or. (.not. (z <= 4d-42))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.2e-86) || !(z <= 4e-42)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.2e-86) or not (z <= 4e-42):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.2e-86) || !(z <= 4e-42))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.2e-86) || ~((z <= 4e-42)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.2e-86], N[Not[LessEqual[z, 4e-42]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999932e-86 or 4.00000000000000015e-42 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in z around -inf 70.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ 70.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. mul-1-neg 70.6%

         \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      3. distribute-lft-out-- 70.6%

         \[\leadsto \left(-\frac{\color{blue}{-1 \cdot \left(\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      4. associate-/l* 70.7%

         \[\leadsto \left(-\frac{-1 \cdot \left(\color{blue}{x \cdot \frac{y}{b - y}} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      5. associate-/l* 81.2%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - \color{blue}{y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}\right)}{z}\right) + \left(\frac{t}{b - y} - \frac{a}{b - y}\right) \]

      6. div-sub 81.8%

         \[\leadsto \left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \color{blue}{\frac{t - a}{b - y}} \]

   5. Simplified 81.8%

      \[\leadsto \color{blue}{\left(-\frac{-1 \cdot \left(x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}{z}\right) + \frac{t - a}{b - y}} \]

   6. Taylor expanded in x around inf 80.6%

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

      1. times-frac 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in t around inf 45.5%

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

   if -7.19999999999999932e-86 < z < 4.00000000000000015e-42

   1. Initial program 82.9%

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

   3. Taylor expanded in z around 0 55.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-86} \lor \neg \left(z \leq 4 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e-49) x (if (<= y 1.3e+38) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e-49) {
		tmp = x;
	} else if (y <= 1.3e+38) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7d-49)) then
        tmp = x
    else if (y <= 1.3d+38) then
        tmp = t / b
    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 b) {
	double tmp;
	if (y <= -7e-49) {
		tmp = x;
	} else if (y <= 1.3e+38) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e-49:
		tmp = x
	elif y <= 1.3e+38:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e-49)
		tmp = x;
	elseif (y <= 1.3e+38)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7e-49)
		tmp = x;
	elseif (y <= 1.3e+38)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e-49], x, If[LessEqual[y, 1.3e+38], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000012e-49 or 1.3e38 < y

   1. Initial program 55.5%

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

   3. Taylor expanded in z around 0 43.9%

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

   if -7.00000000000000012e-49 < y < 1.3e38

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 83.9%

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

      1. associate--l+ 83.9%

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

      2. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in b around inf 67.6%

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

   7. Taylor expanded in t around inf 35.4%

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

Alternative 15: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.4%

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

3. Taylor expanded in z around 0 25.9%

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

Developer Target 1: 73.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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