Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.7% → 90.4%

Time: 16.1s

Alternatives: 18

Speedup: 1.5×

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: 66.7% 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: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00039 \lor \neg \left(z \leq 200000\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.00039) (not (<= z 200000.0)))
   (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.00039) || !(z <= 200000.0)) {
		tmp = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) + (z * (t - a))) / (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 <= (-0.00039d0)) .or. (.not. (z <= 200000.0d0))) then
        tmp = ((y / z) * (x / (b - y))) + ((t - a) / (b - y))
    else
        tmp = ((y * x) + (z * (t - a))) / (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 <= -0.00039) || !(z <= 200000.0)) {
		tmp = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.00039) or not (z <= 200000.0):
		tmp = ((y / z) * (x / (b - y))) + ((t - a) / (b - y))
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.00039) || !(z <= 200000.0))
		tmp = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / 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 <= -0.00039) || ~((z <= 200000.0)))
		tmp = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.00039], N[Not[LessEqual[z, 200000.0]], $MachinePrecision]], N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999993e-4 or 2e5 < z

   1. Initial program 39.4%

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

   2. Taylor expanded in z around -inf 65.1%

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

      1. +-commutative 65.1%

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

      2. associate--l+ 65.1%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in x around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. times-frac 91.6%

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

   7. Simplified 91.6%

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

   if -3.89999999999999993e-4 < z < 2e5

   1. Initial program 92.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00039 \lor \neg \left(z \leq 200000\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 2: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-93}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))))
   (if (<= z -1.1e-19)
     t_1
     (if (<= z 8e-93)
       (+ x (* (- t a) (/ z y)))
       (if (<= z 1.7e-70)
         (/ (+ (- t a) (* (/ y z) x)) b)
         (if (<= z 5.8e-46) (/ (+ (* y x) (* z (- t a))) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	double tmp;
	if (z <= -1.1e-19) {
		tmp = t_1;
	} else if (z <= 8e-93) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 1.7e-70) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 5.8e-46) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} 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 = ((y / z) * (x / (b - y))) + ((t - a) / (b - y))
    if (z <= (-1.1d-19)) then
        tmp = t_1
    else if (z <= 8d-93) then
        tmp = x + ((t - a) * (z / y))
    else if (z <= 1.7d-70) then
        tmp = ((t - a) + ((y / z) * x)) / b
    else if (z <= 5.8d-46) then
        tmp = ((y * x) + (z * (t - a))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	double tmp;
	if (z <= -1.1e-19) {
		tmp = t_1;
	} else if (z <= 8e-93) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 1.7e-70) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 5.8e-46) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y / z) * (x / (b - y))) + ((t - a) / (b - y))
	tmp = 0
	if z <= -1.1e-19:
		tmp = t_1
	elif z <= 8e-93:
		tmp = x + ((t - a) * (z / y))
	elif z <= 1.7e-70:
		tmp = ((t - a) + ((y / z) * x)) / b
	elif z <= 5.8e-46:
		tmp = ((y * x) + (z * (t - a))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -1.1e-19)
		tmp = t_1;
	elseif (z <= 8e-93)
		tmp = Float64(x + Float64(Float64(t - a) * Float64(z / y)));
	elseif (z <= 1.7e-70)
		tmp = Float64(Float64(Float64(t - a) + Float64(Float64(y / z) * x)) / b);
	elseif (z <= 5.8e-46)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y / z) * (x / (b - y))) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -1.1e-19)
		tmp = t_1;
	elseif (z <= 8e-93)
		tmp = x + ((t - a) * (z / y));
	elseif (z <= 1.7e-70)
		tmp = ((t - a) + ((y / z) * x)) / b;
	elseif (z <= 5.8e-46)
		tmp = ((y * x) + (z * (t - a))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-19], t$95$1, If[LessEqual[z, 8e-93], N[(x + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-70], N[(N[(N[(t - a), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 5.8e-46], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0999999999999999e-19 or 5.80000000000000009e-46 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in z around -inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate--l+ 63.5%

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

   4. Simplified 70.6%

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

   5. Taylor expanded in x around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. times-frac 87.4%

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

   7. Simplified 87.4%

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

   if -1.0999999999999999e-19 < z < 7.9999999999999992e-93

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 76.2%

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

   3. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

      1. div-inv 81.4%

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

      2. clear-num 81.4%

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

   7. Applied egg-rr 81.4%

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

   if 7.9999999999999992e-93 < z < 1.69999999999999998e-70

   1. Initial program 100.0%

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

   2. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. times-frac 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in b around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if 1.69999999999999998e-70 < z < 5.80000000000000009e-46

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-93}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-70}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+114}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.5e+144)
     t_1
     (if (<= z -6e+114)
       (- (/ (- a t) y) (/ x z))
       (if (<= z -3.7e-14)
         t_1
         (if (<= z 3.8e-92)
           (+ x (* (- t a) (/ z y)))
           (if (<= z 2.6e-68)
             (/ (+ (- t a) (* (/ y z) x)) b)
             (if (<= z 8.6e-18) (/ (+ (* y x) (* z (- t a))) y) 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 <= -2.5e+144) {
		tmp = t_1;
	} else if (z <= -6e+114) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= -3.7e-14) {
		tmp = t_1;
	} else if (z <= 3.8e-92) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 2.6e-68) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 8.6e-18) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} 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 <= (-2.5d+144)) then
        tmp = t_1
    else if (z <= (-6d+114)) then
        tmp = ((a - t) / y) - (x / z)
    else if (z <= (-3.7d-14)) then
        tmp = t_1
    else if (z <= 3.8d-92) then
        tmp = x + ((t - a) * (z / y))
    else if (z <= 2.6d-68) then
        tmp = ((t - a) + ((y / z) * x)) / b
    else if (z <= 8.6d-18) then
        tmp = ((y * x) + (z * (t - a))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.5e+144) {
		tmp = t_1;
	} else if (z <= -6e+114) {
		tmp = ((a - t) / y) - (x / z);
	} else if (z <= -3.7e-14) {
		tmp = t_1;
	} else if (z <= 3.8e-92) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 2.6e-68) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 8.6e-18) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} 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 <= -2.5e+144:
		tmp = t_1
	elif z <= -6e+114:
		tmp = ((a - t) / y) - (x / z)
	elif z <= -3.7e-14:
		tmp = t_1
	elif z <= 3.8e-92:
		tmp = x + ((t - a) * (z / y))
	elif z <= 2.6e-68:
		tmp = ((t - a) + ((y / z) * x)) / b
	elif z <= 8.6e-18:
		tmp = ((y * x) + (z * (t - a))) / y
	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 <= -2.5e+144)
		tmp = t_1;
	elseif (z <= -6e+114)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	elseif (z <= -3.7e-14)
		tmp = t_1;
	elseif (z <= 3.8e-92)
		tmp = Float64(x + Float64(Float64(t - a) * Float64(z / y)));
	elseif (z <= 2.6e-68)
		tmp = Float64(Float64(Float64(t - a) + Float64(Float64(y / z) * x)) / b);
	elseif (z <= 8.6e-18)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	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 <= -2.5e+144)
		tmp = t_1;
	elseif (z <= -6e+114)
		tmp = ((a - t) / y) - (x / z);
	elseif (z <= -3.7e-14)
		tmp = t_1;
	elseif (z <= 3.8e-92)
		tmp = x + ((t - a) * (z / y));
	elseif (z <= 2.6e-68)
		tmp = ((t - a) + ((y / z) * x)) / b;
	elseif (z <= 8.6e-18)
		tmp = ((y * x) + (z * (t - a))) / y;
	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, -2.5e+144], t$95$1, If[LessEqual[z, -6e+114], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-14], t$95$1, If[LessEqual[z, 3.8e-92], N[(x + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-68], N[(N[(N[(t - a), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 8.6e-18], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.5e144 or -6.0000000000000001e114 < z < -3.70000000000000001e-14 or 8.6000000000000005e-18 < z

   1. Initial program 42.6%

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

   2. Taylor expanded in z around inf 74.0%

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

   if -2.5e144 < z < -6.0000000000000001e114

   1. Initial program 39.8%

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

   2. Taylor expanded in z around -inf 30.8%

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

      1. +-commutative 30.8%

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

      2. associate--l+ 30.8%

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

   4. Simplified 32.0%

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

   5. Taylor expanded in x around inf 40.0%

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

      1. *-commutative 40.0%

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

      2. times-frac 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in b around 0 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. +-commutative 90.2%

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

      3. metadata-eval 90.2%

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

      4. *-lft-identity 90.2%

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

      5. associate-+l+ 90.2%

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

      6. associate-*r/ 90.2%

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

      7. mul-1-neg 90.2%

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

      8. mul-1-neg 90.2%

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

      9. remove-double-neg 90.2%

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

      10. mul-1-neg 90.2%

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

      11. distribute-neg-in 90.2%

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

      12. mul-1-neg 90.2%

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

      13. sub-neg 90.2%

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

      14. div-sub 90.2%

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

   10. Simplified 90.2%

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

   if -3.70000000000000001e-14 < z < 3.8000000000000001e-92

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 76.2%

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

   3. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

      2. associate-/l* 81.4%

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

   5. Simplified 81.4%

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

      1. div-inv 81.4%

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

      2. clear-num 81.4%

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

   7. Applied egg-rr 81.4%

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

   if 3.8000000000000001e-92 < z < 2.5999999999999998e-68

   1. Initial program 100.0%

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

   2. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. times-frac 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in b around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if 2.5999999999999998e-68 < z < 8.6000000000000005e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{\color{blue}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+114}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 69.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.055:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.055)
   (- (* (/ x z) (/ y (- b y))) (/ a (- b y)))
   (if (<= z 3.8e-92)
     (+ x (* (- t a) (/ z y)))
     (if (<= z 1.3e-67)
       (/ (+ (- t a) (* (/ y z) x)) b)
       (if (<= z 9.5e-18)
         (/ (+ (* y x) (* z (- t a))) y)
         (/ (- t a) (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.055) {
		tmp = ((x / z) * (y / (b - y))) - (a / (b - y));
	} else if (z <= 3.8e-92) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 1.3e-67) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 9.5e-18) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else {
		tmp = (t - a) / (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 <= (-0.055d0)) then
        tmp = ((x / z) * (y / (b - y))) - (a / (b - y))
    else if (z <= 3.8d-92) then
        tmp = x + ((t - a) * (z / y))
    else if (z <= 1.3d-67) then
        tmp = ((t - a) + ((y / z) * x)) / b
    else if (z <= 9.5d-18) then
        tmp = ((y * x) + (z * (t - a))) / y
    else
        tmp = (t - a) / (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 <= -0.055) {
		tmp = ((x / z) * (y / (b - y))) - (a / (b - y));
	} else if (z <= 3.8e-92) {
		tmp = x + ((t - a) * (z / y));
	} else if (z <= 1.3e-67) {
		tmp = ((t - a) + ((y / z) * x)) / b;
	} else if (z <= 9.5e-18) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.055:
		tmp = ((x / z) * (y / (b - y))) - (a / (b - y))
	elif z <= 3.8e-92:
		tmp = x + ((t - a) * (z / y))
	elif z <= 1.3e-67:
		tmp = ((t - a) + ((y / z) * x)) / b
	elif z <= 9.5e-18:
		tmp = ((y * x) + (z * (t - a))) / y
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.055)
		tmp = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) - Float64(a / Float64(b - y)));
	elseif (z <= 3.8e-92)
		tmp = Float64(x + Float64(Float64(t - a) * Float64(z / y)));
	elseif (z <= 1.3e-67)
		tmp = Float64(Float64(Float64(t - a) + Float64(Float64(y / z) * x)) / b);
	elseif (z <= 9.5e-18)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.055)
		tmp = ((x / z) * (y / (b - y))) - (a / (b - y));
	elseif (z <= 3.8e-92)
		tmp = x + ((t - a) * (z / y));
	elseif (z <= 1.3e-67)
		tmp = ((t - a) + ((y / z) * x)) / b;
	elseif (z <= 9.5e-18)
		tmp = ((y * x) + (z * (t - a))) / y;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.055], N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-92], N[(x + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-67], N[(N[(N[(t - a), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 9.5e-18], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.0550000000000000003

   1. Initial program 42.0%

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

   2. Taylor expanded in z around -inf 59.8%

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

      1. +-commutative 59.8%

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

      2. associate--l+ 59.8%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in x around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. times-frac 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 42.5%

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

      1. *-commutative 42.5%

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

      2. times-frac 72.3%

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

   10. Simplified 72.3%

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

   if -0.0550000000000000003 < z < 3.8000000000000001e-92

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 74.7%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/l* 80.0%

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

   5. Simplified 80.0%

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

      1. div-inv 79.9%

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

      2. clear-num 80.0%

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

   7. Applied egg-rr 80.0%

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

   if 3.8000000000000001e-92 < z < 1.2999999999999999e-67

   1. Initial program 100.0%

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

   2. Taylor expanded in z around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. times-frac 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in b around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if 1.2999999999999999e-67 < z < 9.5000000000000003e-18

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.6%

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

   if 9.5000000000000003e-18 < z

   1. Initial program 41.6%

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

   2. Taylor expanded in z around inf 73.1%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.055:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{y}{z} \cdot x}{b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 42.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -150000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)))
   (if (<= z -1.65e+223)
     t_2
     (if (<= z -1.85e+68)
       t_1
       (if (<= z -150000.0)
         t_2
         (if (<= z -2.95e-43)
           (/ t (/ y z))
           (if (<= z -2.2e-61)
             (/ t b)
             (if (<= z 1.25e-5) (+ x (* z x)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -1.65e+223) {
		tmp = t_2;
	} else if (z <= -1.85e+68) {
		tmp = t_1;
	} else if (z <= -150000.0) {
		tmp = t_2;
	} else if (z <= -2.95e-43) {
		tmp = t / (y / z);
	} else if (z <= -2.2e-61) {
		tmp = t / b;
	} else if (z <= 1.25e-5) {
		tmp = x + (z * x);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = -a / b
    if (z <= (-1.65d+223)) then
        tmp = t_2
    else if (z <= (-1.85d+68)) then
        tmp = t_1
    else if (z <= (-150000.0d0)) then
        tmp = t_2
    else if (z <= (-2.95d-43)) then
        tmp = t / (y / z)
    else if (z <= (-2.2d-61)) then
        tmp = t / b
    else if (z <= 1.25d-5) then
        tmp = x + (z * x)
    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 / (b - y);
	double t_2 = -a / b;
	double tmp;
	if (z <= -1.65e+223) {
		tmp = t_2;
	} else if (z <= -1.85e+68) {
		tmp = t_1;
	} else if (z <= -150000.0) {
		tmp = t_2;
	} else if (z <= -2.95e-43) {
		tmp = t / (y / z);
	} else if (z <= -2.2e-61) {
		tmp = t / b;
	} else if (z <= 1.25e-5) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	tmp = 0
	if z <= -1.65e+223:
		tmp = t_2
	elif z <= -1.85e+68:
		tmp = t_1
	elif z <= -150000.0:
		tmp = t_2
	elif z <= -2.95e-43:
		tmp = t / (y / z)
	elif z <= -2.2e-61:
		tmp = t / b
	elif z <= 1.25e-5:
		tmp = x + (z * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -1.65e+223)
		tmp = t_2;
	elseif (z <= -1.85e+68)
		tmp = t_1;
	elseif (z <= -150000.0)
		tmp = t_2;
	elseif (z <= -2.95e-43)
		tmp = Float64(t / Float64(y / z));
	elseif (z <= -2.2e-61)
		tmp = Float64(t / b);
	elseif (z <= 1.25e-5)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	tmp = 0.0;
	if (z <= -1.65e+223)
		tmp = t_2;
	elseif (z <= -1.85e+68)
		tmp = t_1;
	elseif (z <= -150000.0)
		tmp = t_2;
	elseif (z <= -2.95e-43)
		tmp = t / (y / z);
	elseif (z <= -2.2e-61)
		tmp = t / b;
	elseif (z <= 1.25e-5)
		tmp = x + (z * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -1.65e+223], t$95$2, If[LessEqual[z, -1.85e+68], t$95$1, If[LessEqual[z, -150000.0], t$95$2, If[LessEqual[z, -2.95e-43], N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-61], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.25e-5], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.65e223 or -1.84999999999999999e68 < z < -1.5e5

   1. Initial program 40.3%

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

   2. Taylor expanded in z around -inf 67.8%

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

      1. +-commutative 67.8%

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

      2. associate--l+ 67.8%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. times-frac 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in a around inf 57.0%

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

      1. associate-*r/ 57.0%

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

      2. neg-mul-1 57.0%

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

   10. Simplified 57.0%

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

   11. Taylor expanded in b around inf 43.5%

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

       1. associate-*r/ 43.5%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 43.5%

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

   13. Simplified 43.5%

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

   if -1.65e223 < z < -1.84999999999999999e68 or 1.25000000000000006e-5 < z

   1. Initial program 40.5%

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

      1. div-inv 40.5%

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

      2. fma-def 40.5%

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

      3. +-commutative 40.5%

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

      4. fma-def 40.5%

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

   3. Applied egg-rr 40.5%

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

   4. Taylor expanded in t around inf 24.5%

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

   5. Taylor expanded in z around inf 40.3%

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

   if -1.5e5 < z < -2.94999999999999988e-43

   1. Initial program 81.0%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in t around inf 41.9%

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

      1. associate-/l* 41.7%

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

   5. Simplified 41.7%

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

   if -2.94999999999999988e-43 < z < -2.20000000000000009e-61

   1. Initial program 99.7%

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

      1. div-inv 99.7%

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

      2. fma-def 99.7%

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

      3. +-commutative 99.7%

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

      4. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in t around inf 42.0%

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

   5. Taylor expanded in b around inf 43.1%

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

   if -2.20000000000000009e-61 < z < 1.25000000000000006e-5

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in z around 0 55.0%

      \[\leadsto \color{blue}{z \cdot x + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+223}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -150000:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-43}:\\ \;\;\;\;\frac{t}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 6: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-14} \lor \neg \left(z \leq 1.6 \cdot 10^{-18}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.5e+144)
     t_1
     (if (<= z -8.8e+114)
       (- (/ (- a t) y) (/ x z))
       (if (or (<= z -1.36e-14) (not (<= z 1.6e-18)))
         t_1
         (+ x (* (- t a) (/ z y))))))))

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 <= -2.5e+144) {
		tmp = t_1;
	} else if (z <= -8.8e+114) {
		tmp = ((a - t) / y) - (x / z);
	} else if ((z <= -1.36e-14) || !(z <= 1.6e-18)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - a) * (z / 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) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.5d+144)) then
        tmp = t_1
    else if (z <= (-8.8d+114)) then
        tmp = ((a - t) / y) - (x / z)
    else if ((z <= (-1.36d-14)) .or. (.not. (z <= 1.6d-18))) then
        tmp = t_1
    else
        tmp = x + ((t - a) * (z / 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 tmp;
	if (z <= -2.5e+144) {
		tmp = t_1;
	} else if (z <= -8.8e+114) {
		tmp = ((a - t) / y) - (x / z);
	} else if ((z <= -1.36e-14) || !(z <= 1.6e-18)) {
		tmp = t_1;
	} else {
		tmp = x + ((t - a) * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.5e+144:
		tmp = t_1
	elif z <= -8.8e+114:
		tmp = ((a - t) / y) - (x / z)
	elif (z <= -1.36e-14) or not (z <= 1.6e-18):
		tmp = t_1
	else:
		tmp = x + ((t - a) * (z / y))
	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 <= -2.5e+144)
		tmp = t_1;
	elseif (z <= -8.8e+114)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	elseif ((z <= -1.36e-14) || !(z <= 1.6e-18))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(t - a) * Float64(z / y)));
	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 <= -2.5e+144)
		tmp = t_1;
	elseif (z <= -8.8e+114)
		tmp = ((a - t) / y) - (x / z);
	elseif ((z <= -1.36e-14) || ~((z <= 1.6e-18)))
		tmp = t_1;
	else
		tmp = x + ((t - a) * (z / 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]}, If[LessEqual[z, -2.5e+144], t$95$1, If[LessEqual[z, -8.8e+114], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.36e-14], N[Not[LessEqual[z, 1.6e-18]], $MachinePrecision]], t$95$1, N[(x + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e144 or -8.8000000000000001e114 < z < -1.36e-14 or 1.6e-18 < z

   1. Initial program 42.6%

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

   2. Taylor expanded in z around inf 74.0%

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

   if -2.5e144 < z < -8.8000000000000001e114

   1. Initial program 39.8%

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

   2. Taylor expanded in z around -inf 30.8%

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

      1. +-commutative 30.8%

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

      2. associate--l+ 30.8%

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

   4. Simplified 32.0%

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

   5. Taylor expanded in x around inf 40.0%

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

      1. *-commutative 40.0%

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

      2. times-frac 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in b around 0 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. +-commutative 90.2%

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

      3. metadata-eval 90.2%

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

      4. *-lft-identity 90.2%

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

      5. associate-+l+ 90.2%

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

      6. associate-*r/ 90.2%

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

      7. mul-1-neg 90.2%

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

      8. mul-1-neg 90.2%

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

      9. remove-double-neg 90.2%

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

      10. mul-1-neg 90.2%

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

      11. distribute-neg-in 90.2%

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

      12. mul-1-neg 90.2%

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

      13. sub-neg 90.2%

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

      14. div-sub 90.2%

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

   10. Simplified 90.2%

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

   if -1.36e-14 < z < 1.6e-18

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 73.1%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

      1. div-inv 76.1%

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

      2. clear-num 76.1%

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

   7. Applied egg-rr 76.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-14} \lor \neg \left(z \leq 1.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \]

Alternative 7: 69.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-62}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e-19)
     t_1
     (if (<= z -1.25e-62)
       (/ (- t a) (/ y z))
       (if (<= z 1.4e-47) (+ x (/ (* z t) y)) 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 <= -4e-19) {
		tmp = t_1;
	} else if (z <= -1.25e-62) {
		tmp = (t - a) / (y / z);
	} else if (z <= 1.4e-47) {
		tmp = x + ((z * t) / y);
	} 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 <= (-4d-19)) then
        tmp = t_1
    else if (z <= (-1.25d-62)) then
        tmp = (t - a) / (y / z)
    else if (z <= 1.4d-47) then
        tmp = x + ((z * t) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e-19) {
		tmp = t_1;
	} else if (z <= -1.25e-62) {
		tmp = (t - a) / (y / z);
	} else if (z <= 1.4e-47) {
		tmp = x + ((z * t) / y);
	} 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 <= -4e-19:
		tmp = t_1
	elif z <= -1.25e-62:
		tmp = (t - a) / (y / z)
	elif z <= 1.4e-47:
		tmp = x + ((z * t) / y)
	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 <= -4e-19)
		tmp = t_1;
	elseif (z <= -1.25e-62)
		tmp = Float64(Float64(t - a) / Float64(y / z));
	elseif (z <= 1.4e-47)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	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 <= -4e-19)
		tmp = t_1;
	elseif (z <= -1.25e-62)
		tmp = (t - a) / (y / z);
	elseif (z <= 1.4e-47)
		tmp = x + ((z * t) / y);
	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, -4e-19], t$95$1, If[LessEqual[z, -1.25e-62], N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-47], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999999e-19 or 1.39999999999999996e-47 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 70.4%

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

   if -3.9999999999999999e-19 < z < -1.25e-62

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 83.7%

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

   3. Taylor expanded in x around 0 83.7%

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

      1. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

   if -1.25e-62 < z < 1.39999999999999996e-47

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 73.4%

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

   3. Taylor expanded in x around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-/l* 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in a around 0 73.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-62}:\\ \;\;\;\;\frac{t - a}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 74.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.85 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.4e-13) (not (<= z 1.85e-17)))
   (/ (- t a) (- b y))
   (+ x (* (- t a) (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.4e-13) || !(z <= 1.85e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) * (z / 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 <= (-8.4d-13)) .or. (.not. (z <= 1.85d-17))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((t - a) * (z / 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 <= -8.4e-13) || !(z <= 1.85e-17)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.4e-13) or not (z <= 1.85e-17):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((t - a) * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.4e-13) || !(z <= 1.85e-17))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(t - a) * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.4e-13) || ~((z <= 1.85e-17)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((t - a) * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.4e-13], N[Not[LessEqual[z, 1.85e-17]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.39999999999999955e-13 or 1.8499999999999999e-17 < z

   1. Initial program 42.4%

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

   2. Taylor expanded in z around inf 71.6%

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

   if -8.39999999999999955e-13 < z < 1.8499999999999999e-17

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 73.1%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. +-commutative 79.8%

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

      2. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

      1. div-inv 76.1%

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

      2. clear-num 76.1%

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

   7. Applied egg-rr 76.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.85 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \]

Alternative 9: 43.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+222}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-61} \lor \neg \left(z \leq 0.0006\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.32e+222)
   (/ (- a) b)
   (if (or (<= z -2.2e-61) (not (<= z 0.0006))) (/ t (- b y)) (+ x (* z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.32e+222) {
		tmp = -a / b;
	} else if ((z <= -2.2e-61) || !(z <= 0.0006)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * 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 <= (-1.32d+222)) then
        tmp = -a / b
    else if ((z <= (-2.2d-61)) .or. (.not. (z <= 0.0006d0))) then
        tmp = t / (b - y)
    else
        tmp = x + (z * 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 <= -1.32e+222) {
		tmp = -a / b;
	} else if ((z <= -2.2e-61) || !(z <= 0.0006)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.32e+222:
		tmp = -a / b
	elif (z <= -2.2e-61) or not (z <= 0.0006):
		tmp = t / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.32e+222)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -2.2e-61) || !(z <= 0.0006))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.32e+222)
		tmp = -a / b;
	elseif ((z <= -2.2e-61) || ~((z <= 0.0006)))
		tmp = t / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.32e+222], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -2.2e-61], N[Not[LessEqual[z, 0.0006]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999997e222

   1. Initial program 23.6%

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

   2. Taylor expanded in z around -inf 72.5%

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

      1. +-commutative 72.5%

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

      2. associate--l+ 72.5%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in x around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. times-frac 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in a around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   10. Simplified 62.9%

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

   11. Taylor expanded in b around inf 50.5%

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

       1. associate-*r/ 50.5%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 50.5%

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

   13. Simplified 50.5%

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

   if -1.31999999999999997e222 < z < -2.20000000000000009e-61 or 5.99999999999999947e-4 < z

   1. Initial program 49.0%

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

      1. div-inv 48.9%

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

      2. fma-def 48.9%

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

      3. +-commutative 48.9%

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

      4. fma-def 48.9%

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

   3. Applied egg-rr 48.9%

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

   4. Taylor expanded in t around inf 26.1%

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

   5. Taylor expanded in z around inf 36.0%

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

   if -2.20000000000000009e-61 < z < 5.99999999999999947e-4

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in z around 0 55.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+222}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-61} \lor \neg \left(z \leq 0.0006\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 10: 36.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+152}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+152)
   (/ (- a) b)
   (if (<= z -0.75) (/ (- x) z) (if (<= z 21.0) (+ x (* z x)) (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+152) {
		tmp = -a / b;
	} else if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 21.0) {
		tmp = x + (z * x);
	} else {
		tmp = t / 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 (z <= (-5.6d+152)) then
        tmp = -a / b
    else if (z <= (-0.75d0)) then
        tmp = -x / z
    else if (z <= 21.0d0) then
        tmp = x + (z * x)
    else
        tmp = t / 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 (z <= -5.6e+152) {
		tmp = -a / b;
	} else if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 21.0) {
		tmp = x + (z * x);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.6e+152:
		tmp = -a / b
	elif z <= -0.75:
		tmp = -x / z
	elif z <= 21.0:
		tmp = x + (z * x)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+152)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= -0.75)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 21.0)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.6e+152)
		tmp = -a / b;
	elseif (z <= -0.75)
		tmp = -x / z;
	elseif (z <= 21.0)
		tmp = x + (z * x);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+152], N[((-a) / b), $MachinePrecision], If[LessEqual[z, -0.75], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 21.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6000000000000004e152

   1. Initial program 34.9%

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

   2. Taylor expanded in z around -inf 69.9%

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

      1. +-commutative 69.9%

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

      2. associate--l+ 69.9%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. times-frac 94.3%

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

   7. Simplified 94.3%

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

   8. Taylor expanded in a around inf 53.9%

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

      1. associate-*r/ 53.9%

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

      2. neg-mul-1 53.9%

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

   10. Simplified 53.9%

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

   11. Taylor expanded in b around inf 40.9%

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

       1. associate-*r/ 40.9%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 40.9%

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

   13. Simplified 40.9%

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

   if -5.6000000000000004e152 < z < -0.75

   1. Initial program 49.5%

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

   2. Taylor expanded in y around inf 38.1%

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

      1. +-commutative 38.1%

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

      2. mul-1-neg 38.1%

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

      3. unsub-neg 38.1%

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

   4. Simplified 38.1%

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

   5. Taylor expanded in z around inf 36.3%

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

      1. associate-*r/ 36.3%

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

      2. mul-1-neg 36.3%

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

   7. Simplified 36.3%

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

   if -0.75 < z < 21

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   4. Simplified 50.7%

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

   5. Taylor expanded in z around 0 49.7%

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

   if 21 < z

   1. Initial program 37.1%

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

      1. div-inv 37.1%

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

      2. fma-def 37.1%

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

      3. +-commutative 37.1%

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

      4. fma-def 37.1%

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

   3. Applied egg-rr 37.1%

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

   4. Taylor expanded in t around inf 23.9%

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

   5. Taylor expanded in b around inf 31.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+152}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 11: 69.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-61} \lor \neg \left(z \leq 7 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e-61) (not (<= z 7e-48)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e-61) || !(z <= 7e-48)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / 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 <= (-1.9d-61)) .or. (.not. (z <= 7d-48))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / 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 <= -1.9e-61) || !(z <= 7e-48)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e-61) or not (z <= 7e-48):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e-61) || !(z <= 7e-48))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e-61) || ~((z <= 7e-48)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e-61], N[Not[LessEqual[z, 7e-48]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e-61 or 6.99999999999999982e-48 < z

   1. Initial program 48.7%

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

   2. Taylor expanded in z around inf 68.3%

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

   if -1.8999999999999999e-61 < z < 6.99999999999999982e-48

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 73.6%

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

   3. Taylor expanded in x around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in a around 0 72.7%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-61} \lor \neg \left(z \leq 7 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 12: 36.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e+149)
   (/ (- a) b)
   (if (<= z -1.0) (/ (- x) z) (if (<= z 21.0) x (/ t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+149) {
		tmp = -a / b;
	} else if (z <= -1.0) {
		tmp = -x / z;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / 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 (z <= (-5.5d+149)) then
        tmp = -a / b
    else if (z <= (-1.0d0)) then
        tmp = -x / z
    else if (z <= 21.0d0) then
        tmp = x
    else
        tmp = t / 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 (z <= -5.5e+149) {
		tmp = -a / b;
	} else if (z <= -1.0) {
		tmp = -x / z;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.5e+149:
		tmp = -a / b
	elif z <= -1.0:
		tmp = -x / z
	elif z <= 21.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e+149)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= -1.0)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.5e+149)
		tmp = -a / b;
	elseif (z <= -1.0)
		tmp = -x / z;
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e+149], N[((-a) / b), $MachinePrecision], If[LessEqual[z, -1.0], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 21.0], x, N[(t / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999999e149

   1. Initial program 34.9%

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

   2. Taylor expanded in z around -inf 69.9%

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

      1. +-commutative 69.9%

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

      2. associate--l+ 69.9%

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

   4. Simplified 76.4%

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

   5. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. times-frac 94.3%

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

   7. Simplified 94.3%

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

   8. Taylor expanded in a around inf 53.9%

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

      1. associate-*r/ 53.9%

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

      2. neg-mul-1 53.9%

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

   10. Simplified 53.9%

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

   11. Taylor expanded in b around inf 40.9%

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

       1. associate-*r/ 40.9%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 40.9%

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

   13. Simplified 40.9%

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

   if -5.49999999999999999e149 < z < -1

   1. Initial program 49.5%

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

   2. Taylor expanded in y around inf 38.1%

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

      1. +-commutative 38.1%

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

      2. mul-1-neg 38.1%

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

      3. unsub-neg 38.1%

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

   4. Simplified 38.1%

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

   5. Taylor expanded in z around inf 36.3%

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

      1. associate-*r/ 36.3%

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

      2. mul-1-neg 36.3%

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

   7. Simplified 36.3%

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

   if -1 < z < 21

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 49.0%

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

   if 21 < z

   1. Initial program 37.1%

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

      1. div-inv 37.1%

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

      2. fma-def 37.1%

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

      3. +-commutative 37.1%

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

      4. fma-def 37.1%

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

   3. Applied egg-rr 37.1%

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

   4. Taylor expanded in t around inf 23.9%

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

   5. Taylor expanded in b around inf 31.9%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 13: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-55} \lor \neg \left(y \leq 2.5 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e-55) (not (<= y 2.5e-125))) (/ x (- 1.0 z)) (/ (- a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e-55) || !(y <= 2.5e-125)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -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 <= (-1.45d-55)) .or. (.not. (y <= 2.5d-125))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = -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 <= -1.45e-55) || !(y <= 2.5e-125)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e-55) or not (y <= 2.5e-125):
		tmp = x / (1.0 - z)
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e-55) || !(y <= 2.5e-125))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e-55) || ~((y <= 2.5e-125)))
		tmp = x / (1.0 - z);
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e-55], N[Not[LessEqual[y, 2.5e-125]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[((-a) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e-55 or 2.49999999999999983e-125 < y

   1. Initial program 58.8%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   4. Simplified 53.0%

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

   if -1.45e-55 < y < 2.49999999999999983e-125

   1. Initial program 84.2%

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

   2. Taylor expanded in z around -inf 65.1%

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

      1. +-commutative 65.1%

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

      2. associate--l+ 65.1%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. times-frac 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in a around inf 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   10. Simplified 48.6%

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

   11. Taylor expanded in b around inf 40.7%

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

       1. associate-*r/ 40.7%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 40.7%

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

   13. Simplified 40.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-55} \lor \neg \left(y \leq 2.5 \cdot 10^{-125}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 54.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-56} \lor \neg \left(y \leq 4 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e-56) (not (<= y 4e-48))) (/ 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 <= -5.4e-56) || !(y <= 4e-48)) {
		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 <= (-5.4d-56)) .or. (.not. (y <= 4d-48))) 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 <= -5.4e-56) || !(y <= 4e-48)) {
		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 <= -5.4e-56) or not (y <= 4e-48):
		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 <= -5.4e-56) || !(y <= 4e-48))
		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 <= -5.4e-56) || ~((y <= 4e-48)))
		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, -5.4e-56], N[Not[LessEqual[y, 4e-48]], $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 < -5.3999999999999999e-56 or 3.9999999999999999e-48 < y

   1. Initial program 57.4%

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

   2. Taylor expanded in y around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

   4. Simplified 56.0%

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

   if -5.3999999999999999e-56 < y < 3.9999999999999999e-48

   1. Initial program 82.0%

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

   2. Taylor expanded in y around 0 64.9%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-56} \lor \neg \left(y \leq 4 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 34.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.2e-50) (/ a y) (if (<= z 1.0) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.2e-50) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = a / 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 <= (-8.2d-50)) then
        tmp = a / y
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = a / 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 <= -8.2e-50) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.2e-50:
		tmp = a / y
	elif z <= 1.0:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.2e-50)
		tmp = Float64(a / y);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.2e-50)
		tmp = a / y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.2e-50], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999971e-50 or 1 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in z around -inf 61.0%

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

      1. +-commutative 61.0%

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

      2. associate--l+ 61.0%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in x around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. times-frac 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in a around inf 41.4%

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

      1. associate-*r/ 41.4%

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

      2. neg-mul-1 41.4%

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

   10. Simplified 41.4%

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

   11. Taylor expanded in b around 0 20.1%

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

   if -8.19999999999999971e-50 < z < 1

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 53.7%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 16: 37.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.1e-62) (/ t b) (if (<= z 21.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.1e-62) {
		tmp = t / b;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / 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 (z <= (-2.1d-62)) then
        tmp = t / b
    else if (z <= 21.0d0) then
        tmp = x
    else
        tmp = t / 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 (z <= -2.1e-62) {
		tmp = t / b;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.1e-62:
		tmp = t / b
	elif z <= 21.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.1e-62)
		tmp = Float64(t / b);
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.1e-62)
		tmp = t / b;
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.1e-62], N[(t / b), $MachinePrecision], If[LessEqual[z, 21.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e-62 or 21 < z

   1. Initial program 45.2%

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

      1. div-inv 45.2%

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

      2. fma-def 45.2%

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

      3. +-commutative 45.2%

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

      4. fma-def 45.2%

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

   3. Applied egg-rr 45.2%

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

   4. Taylor expanded in t around inf 23.9%

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

   5. Taylor expanded in b around inf 25.1%

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

   if -2.0999999999999999e-62 < z < 21

   1. Initial program 92.0%

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

   2. Taylor expanded in z around 0 54.0%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 17: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+24) (/ (- a) b) (if (<= z 21.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+24) {
		tmp = -a / b;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / 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 (z <= (-1.9d+24)) then
        tmp = -a / b
    else if (z <= 21.0d0) then
        tmp = x
    else
        tmp = t / 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 (z <= -1.9e+24) {
		tmp = -a / b;
	} else if (z <= 21.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9e+24:
		tmp = -a / b
	elif z <= 21.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+24)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9e+24)
		tmp = -a / b;
	elseif (z <= 21.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+24], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 21.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000008e24

   1. Initial program 41.6%

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

   2. Taylor expanded in z around -inf 60.0%

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

      1. +-commutative 60.0%

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

      2. associate--l+ 60.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in x around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. times-frac 90.8%

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

   7. Simplified 90.8%

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

   8. Taylor expanded in a around inf 46.2%

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

      1. associate-*r/ 46.2%

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

      2. neg-mul-1 46.2%

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

   10. Simplified 46.2%

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

   11. Taylor expanded in b around inf 32.8%

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

       1. associate-*r/ 32.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. neg-mul-1 32.8%

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

   13. Simplified 32.8%

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

   if -1.90000000000000008e24 < z < 21

   1. Initial program 91.5%

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

   2. Taylor expanded in z around 0 48.5%

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

   if 21 < z

   1. Initial program 37.1%

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

      1. div-inv 37.1%

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

      2. fma-def 37.1%

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

      3. +-commutative 37.1%

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

      4. fma-def 37.1%

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

   3. Applied egg-rr 37.1%

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

   4. Taylor expanded in t around inf 23.9%

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

   5. Taylor expanded in b around inf 31.9%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 21:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 18: 25.8% 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 67.3%

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

2. Taylor expanded in z around 0 27.5%

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

3. Final simplification 27.5%

   \[\leadsto x \]

Developer target: 74.1% 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 2023240 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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