Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 89.7%

Time: 23.0s

Alternatives: 19

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := \frac{a}{b - y}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(t_1 + \left(\frac{y}{t_2} \cdot \frac{a - t}{z} - t_3\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{t_2}{y}}}{z} - t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (pow (- b y) 2.0)) (t_3 (/ a (- b y))))
   (if (<= z -1.85e+59)
     (+ (* (/ y (- b y)) (/ x z)) (+ t_1 (- (* (/ y t_2) (/ (- a t) z)) t_3)))
     (if (<= z 1.5e+35)
       (/ (+ (* y x) (- (* z t) (* z a))) (+ y (* z (- b y))))
       (+ t_1 (- (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ t_2 y))) z) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = pow((b - y), 2.0);
	double t_3 = a / (b - y);
	double tmp;
	if (z <= -1.85e+59) {
		tmp = ((y / (b - y)) * (x / z)) + (t_1 + (((y / t_2) * ((a - t) / z)) - t_3));
	} else if (z <= 1.5e+35) {
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	} else {
		tmp = t_1 + ((((y / ((b - y) / x)) + ((a - t) / (t_2 / y))) / z) - t_3);
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = (b - y) ** 2.0d0
    t_3 = a / (b - y)
    if (z <= (-1.85d+59)) then
        tmp = ((y / (b - y)) * (x / z)) + (t_1 + (((y / t_2) * ((a - t) / z)) - t_3))
    else if (z <= 1.5d+35) then
        tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    else
        tmp = t_1 + ((((y / ((b - y) / x)) + ((a - t) / (t_2 / y))) / z) - t_3)
    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 = Math.pow((b - y), 2.0);
	double t_3 = a / (b - y);
	double tmp;
	if (z <= -1.85e+59) {
		tmp = ((y / (b - y)) * (x / z)) + (t_1 + (((y / t_2) * ((a - t) / z)) - t_3));
	} else if (z <= 1.5e+35) {
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	} else {
		tmp = t_1 + ((((y / ((b - y) / x)) + ((a - t) / (t_2 / y))) / z) - t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = math.pow((b - y), 2.0)
	t_3 = a / (b - y)
	tmp = 0
	if z <= -1.85e+59:
		tmp = ((y / (b - y)) * (x / z)) + (t_1 + (((y / t_2) * ((a - t) / z)) - t_3))
	elif z <= 1.5e+35:
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	else:
		tmp = t_1 + ((((y / ((b - y) / x)) + ((a - t) / (t_2 / y))) / z) - t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(b - y) ^ 2.0
	t_3 = Float64(a / Float64(b - y))
	tmp = 0.0
	if (z <= -1.85e+59)
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(t_1 + Float64(Float64(Float64(y / t_2) * Float64(Float64(a - t) / z)) - t_3)));
	elseif (z <= 1.5e+35)
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64(t_2 / y))) / z) - t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = (b - y) ^ 2.0;
	t_3 = a / (b - y);
	tmp = 0.0;
	if (z <= -1.85e+59)
		tmp = ((y / (b - y)) * (x / z)) + (t_1 + (((y / t_2) * ((a - t) / z)) - t_3));
	elseif (z <= 1.5e+35)
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	else
		tmp = t_1 + ((((y / ((b - y) / x)) + ((a - t) / (t_2 / y))) / z) - t_3);
	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[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+59], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(N[(N[(y / t$95$2), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+35], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.84999999999999999e59

   1. Initial program 27.6%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. *-commutative 65.0%

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

      3. times-frac 71.9%

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

      4. +-commutative 71.9%

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

      5. times-frac 98.2%

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

   4. Simplified 98.2%

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

   if -1.84999999999999999e59 < z < 1.49999999999999995e35

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. distribute-lft-in 89.8%

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

   3. Applied egg-rr 89.8%

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

   if 1.49999999999999995e35 < z

   1. Initial program 32.6%

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

   2. Taylor expanded in z around -inf 75.4%

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

      1. associate--l+ 75.4%

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

      2. mul-1-neg 75.4%

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

      3. distribute-lft-out-- 75.4%

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

      4. associate-/l* 84.0%

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

      5. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} + \left(\frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternative 2: 88.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* y x) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -1e-294)
       t_2
       (if (<= t_2 0.0)
         (+
          (/ (+ (/ (* y x) (- b y)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
          t_3)
         (if (<= t_2 2e+270) (/ (+ (* y x) (- (* z t) (* z a))) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((y * x) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((y * x) / (b - y)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + t_3;
	} else if (t_2 <= 2e+270) {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((y * x) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((y * x) / (b - y)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z) + t_3;
	} else if (t_2 <= 2e+270) {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((y * x) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif t_2 <= -1e-294:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((((y * x) / (b - y)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z) + t_3
	elif t_2 <= 2e+270:
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + t_3);
	elseif (t_2 <= 2e+270)
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((y * x) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((((y * x) / (b - y)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z) + t_3;
	elseif (t_2 <= 2e+270)
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-294], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 2e+270], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 20.7%

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

   2. Taylor expanded in y around -inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

      3. mul-1-neg 55.0%

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

      4. distribute-neg-frac 55.0%

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

      5. cancel-sign-sub-inv 55.0%

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

      6. associate-/l* 62.4%

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

      7. metadata-eval 62.4%

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

      8. *-lft-identity 62.4%

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

      9. associate-/l* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around inf 77.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000002e-294

   1. Initial program 99.6%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 18.7%

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

   2. Taylor expanded in z around -inf 85.7%

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

      1. +-commutative 85.7%

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

      2. associate--l+ 85.7%

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

   4. Simplified 100.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e270

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   3. Applied egg-rr 99.4%

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

   if 2.0000000000000001e270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.6%

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

   2. Taylor expanded in z around inf 78.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 90.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+59} \lor \neg \left(z \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} + \left(\frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85e+59) (not (<= z 5.5e+32)))
   (+
    (* (/ y (- b y)) (/ x z))
    (+
     (/ t (- b y))
     (- (* (/ y (pow (- b y) 2.0)) (/ (- a t) z)) (/ a (- b y)))))
   (/ (+ (* y x) (- (* z t) (* z a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85e+59) || !(z <= 5.5e+32)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t / (b - y)) + (((y / pow((b - y), 2.0)) * ((a - t) / z)) - (a / (b - y))));
	} else {
		tmp = ((y * x) + ((z * t) - (z * 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 <= (-1.85d+59)) .or. (.not. (z <= 5.5d+32))) then
        tmp = ((y / (b - y)) * (x / z)) + ((t / (b - y)) + (((y / ((b - y) ** 2.0d0)) * ((a - t) / z)) - (a / (b - y))))
    else
        tmp = ((y * x) + ((z * t) - (z * 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 <= -1.85e+59) || !(z <= 5.5e+32)) {
		tmp = ((y / (b - y)) * (x / z)) + ((t / (b - y)) + (((y / Math.pow((b - y), 2.0)) * ((a - t) / z)) - (a / (b - y))));
	} else {
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e+59) or not (z <= 5.5e+32):
		tmp = ((y / (b - y)) * (x / z)) + ((t / (b - y)) + (((y / math.pow((b - y), 2.0)) * ((a - t) / z)) - (a / (b - y))))
	else:
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85e+59) || !(z <= 5.5e+32))
		tmp = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(Float64(a - t) / z)) - Float64(a / Float64(b - y)))));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * 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 <= -1.85e+59) || ~((z <= 5.5e+32)))
		tmp = ((y / (b - y)) * (x / z)) + ((t / (b - y)) + (((y / ((b - y) ^ 2.0)) * ((a - t) / z)) - (a / (b - y))));
	else
		tmp = ((y * x) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85e+59], N[Not[LessEqual[z, 5.5e+32]], $MachinePrecision]], N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * 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 < -1.84999999999999999e59 or 5.49999999999999984e32 < z

   1. Initial program 31.3%

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

   2. Taylor expanded in z around inf 69.0%

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

      1. associate--l+ 69.0%

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

      2. *-commutative 69.0%

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

      3. times-frac 78.3%

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

      4. +-commutative 78.3%

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

      5. times-frac 99.1%

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

   4. Simplified 99.1%

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

   if -1.84999999999999999e59 < z < 5.49999999999999984e32

   1. Initial program 89.6%

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

      1. sub-neg 89.6%

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

      2. distribute-lft-in 89.6%

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

   3. Applied egg-rr 89.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+59} \lor \neg \left(z \leq 5.5 \cdot 10^{+32}\right):\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} + \left(\frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 4: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2 \cdot 10^{+270}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (+ (* y x) (* z (- t a))) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_2 -1e-294)
       t_2
       (if (or (<= t_2 0.0) (not (<= t_2 2e+270)))
         (/ (- t a) (- b y))
         (/ (+ (* y x) (- (* z t) (* z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((y * x) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+270)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((y * x) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_2 <= -1e-294) {
		tmp = t_2;
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+270)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((y * x) + (z * (t - a))) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif t_2 <= -1e-294:
		tmp = t_2
	elif (t_2 <= 0.0) or not (t_2 <= 2e+270):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif ((t_2 <= 0.0) || !(t_2 <= 2e+270))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((y * x) + (z * (t - a))) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (t_2 <= -1e-294)
		tmp = t_2;
	elseif ((t_2 <= 0.0) || ~((t_2 <= 2e+270)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-294], t$95$2, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2e+270]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 20.7%

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

   2. Taylor expanded in y around -inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

      3. mul-1-neg 55.0%

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

      4. distribute-neg-frac 55.0%

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

      5. cancel-sign-sub-inv 55.0%

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

      6. associate-/l* 62.4%

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

      7. metadata-eval 62.4%

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

      8. *-lft-identity 62.4%

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

      9. associate-/l* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around inf 77.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000002e-294

   1. Initial program 99.6%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.0000000000000001e270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.9%

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

   2. Taylor expanded in z around inf 80.1%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e270

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   3. Applied egg-rr 99.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-294}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+270}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 5: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-294} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (or (<= t_1 -1e-294) (and (not (<= t_1 0.0)) (<= t_1 2e+270)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -1e-294) || (!(t_1 <= 0.0) && (t_1 <= 2e+270))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -1e-294) || (!(t_1 <= 0.0) && (t_1 <= 2e+270))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif (t_1 <= -1e-294) or (not (t_1 <= 0.0) and (t_1 <= 2e+270)):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -1e-294) || (!(t_1 <= 0.0) && (t_1 <= 2e+270)))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -1e-294) || (~((t_1 <= 0.0)) && (t_1 <= 2e+270)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-294], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+270]]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0

   1. Initial program 20.7%

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

   2. Taylor expanded in y around -inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

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

      3. mul-1-neg 55.0%

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

      4. distribute-neg-frac 55.0%

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

      5. cancel-sign-sub-inv 55.0%

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

      6. associate-/l* 62.4%

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

      7. metadata-eval 62.4%

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

      8. *-lft-identity 62.4%

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

      9. associate-/l* 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in z around inf 77.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000002e-294 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e270

   1. Initial program 99.5%

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

   if -1.00000000000000002e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.0000000000000001e270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.9%

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

   2. Taylor expanded in z around inf 80.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-294} \lor \neg \left(\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 0.26:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.6e-15)
     t_1
     (if (<= z -3.8e-80)
       (+ x (* z (- x (/ a y))))
       (if (<= z -2.7e-122)
         (/ (- (/ (* y x) z) a) b)
         (if (<= z 0.26) (/ (+ (* y x) (- (* z t) (* z 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 <= -1.6e-15) {
		tmp = t_1;
	} else if (z <= -3.8e-80) {
		tmp = x + (z * (x - (a / y)));
	} else if (z <= -2.7e-122) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 0.26) {
		tmp = ((y * x) + ((z * t) - (z * 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 <= (-1.6d-15)) then
        tmp = t_1
    else if (z <= (-3.8d-80)) then
        tmp = x + (z * (x - (a / y)))
    else if (z <= (-2.7d-122)) then
        tmp = (((y * x) / z) - a) / b
    else if (z <= 0.26d0) then
        tmp = ((y * x) + ((z * t) - (z * 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 <= -1.6e-15) {
		tmp = t_1;
	} else if (z <= -3.8e-80) {
		tmp = x + (z * (x - (a / y)));
	} else if (z <= -2.7e-122) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 0.26) {
		tmp = ((y * x) + ((z * t) - (z * 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 <= -1.6e-15:
		tmp = t_1
	elif z <= -3.8e-80:
		tmp = x + (z * (x - (a / y)))
	elif z <= -2.7e-122:
		tmp = (((y * x) / z) - a) / b
	elif z <= 0.26:
		tmp = ((y * x) + ((z * t) - (z * 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 <= -1.6e-15)
		tmp = t_1;
	elseif (z <= -3.8e-80)
		tmp = Float64(x + Float64(z * Float64(x - Float64(a / y))));
	elseif (z <= -2.7e-122)
		tmp = Float64(Float64(Float64(Float64(y * x) / z) - a) / b);
	elseif (z <= 0.26)
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * 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 <= -1.6e-15)
		tmp = t_1;
	elseif (z <= -3.8e-80)
		tmp = x + (z * (x - (a / y)));
	elseif (z <= -2.7e-122)
		tmp = (((y * x) / z) - a) / b;
	elseif (z <= 0.26)
		tmp = ((y * x) + ((z * t) - (z * 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, -1.6e-15], t$95$1, If[LessEqual[z, -3.8e-80], N[(x + N[(z * N[(x - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-122], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 0.26], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e-15 or 0.26000000000000001 < z

   1. Initial program 38.5%

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

   2. Taylor expanded in z around inf 82.9%

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

   if -1.6e-15 < z < -3.79999999999999967e-80

   1. Initial program 64.3%

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

   2. Taylor expanded in y around -inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

      3. mul-1-neg 87.7%

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

      4. distribute-neg-frac 87.7%

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

      5. cancel-sign-sub-inv 87.7%

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

      6. associate-/l* 87.7%

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

      7. metadata-eval 87.7%

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

      8. *-lft-identity 87.7%

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

      9. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in a around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. associate-*r* 99.6%

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

      3. neg-mul-1 99.6%

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

      4. *-commutative 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 100.0%

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

   if -3.79999999999999967e-80 < z < -2.70000000000000009e-122

   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 inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. *-commutative 51.0%

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

      3. times-frac 22.4%

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

      4. +-commutative 22.4%

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

      5. times-frac 32.0%

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

   4. Simplified 32.0%

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

   5. Taylor expanded in b around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-*r/ 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in t around 0 70.7%

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

   if -2.70000000000000009e-122 < z < 0.26000000000000001

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. distribute-lft-in 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in z around 0 70.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 0.26:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-79}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{t}{z + -1} \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.1e-16)
     t_1
     (if (<= z -2.55e-79)
       (+ x (* z (- x (/ a y))))
       (if (<= z -8.6e-125)
         (/ (- (/ (* y x) z) a) b)
         (if (<= z 2.8e-17) (- x (* (/ t (+ z -1.0)) (/ z 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 <= -2.1e-16) {
		tmp = t_1;
	} else if (z <= -2.55e-79) {
		tmp = x + (z * (x - (a / y)));
	} else if (z <= -8.6e-125) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 2.8e-17) {
		tmp = x - ((t / (z + -1.0)) * (z / 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 <= (-2.1d-16)) then
        tmp = t_1
    else if (z <= (-2.55d-79)) then
        tmp = x + (z * (x - (a / y)))
    else if (z <= (-8.6d-125)) then
        tmp = (((y * x) / z) - a) / b
    else if (z <= 2.8d-17) then
        tmp = x - ((t / (z + (-1.0d0))) * (z / 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 <= -2.1e-16) {
		tmp = t_1;
	} else if (z <= -2.55e-79) {
		tmp = x + (z * (x - (a / y)));
	} else if (z <= -8.6e-125) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 2.8e-17) {
		tmp = x - ((t / (z + -1.0)) * (z / 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 <= -2.1e-16:
		tmp = t_1
	elif z <= -2.55e-79:
		tmp = x + (z * (x - (a / y)))
	elif z <= -8.6e-125:
		tmp = (((y * x) / z) - a) / b
	elif z <= 2.8e-17:
		tmp = x - ((t / (z + -1.0)) * (z / 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 <= -2.1e-16)
		tmp = t_1;
	elseif (z <= -2.55e-79)
		tmp = Float64(x + Float64(z * Float64(x - Float64(a / y))));
	elseif (z <= -8.6e-125)
		tmp = Float64(Float64(Float64(Float64(y * x) / z) - a) / b);
	elseif (z <= 2.8e-17)
		tmp = Float64(x - Float64(Float64(t / Float64(z + -1.0)) * Float64(z / 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 <= -2.1e-16)
		tmp = t_1;
	elseif (z <= -2.55e-79)
		tmp = x + (z * (x - (a / y)));
	elseif (z <= -8.6e-125)
		tmp = (((y * x) / z) - a) / b;
	elseif (z <= 2.8e-17)
		tmp = x - ((t / (z + -1.0)) * (z / 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, -2.1e-16], t$95$1, If[LessEqual[z, -2.55e-79], N[(x + N[(z * N[(x - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-125], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.8e-17], N[(x - N[(N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1000000000000001e-16 or 2.7999999999999999e-17 < z

   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 81.2%

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

   if -2.1000000000000001e-16 < z < -2.55e-79

   1. Initial program 64.3%

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

   2. Taylor expanded in y around -inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

      3. mul-1-neg 87.7%

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

      4. distribute-neg-frac 87.7%

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

      5. cancel-sign-sub-inv 87.7%

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

      6. associate-/l* 87.7%

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

      7. metadata-eval 87.7%

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

      8. *-lft-identity 87.7%

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

      9. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in a around inf 99.6%

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

      1. associate-*r/ 99.6%

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

      2. associate-*r* 99.6%

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

      3. neg-mul-1 99.6%

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

      4. *-commutative 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 100.0%

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

   if -2.55e-79 < z < -8.6000000000000004e-125

   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 inf 46.3%

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

      1. associate--l+ 46.3%

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

      2. *-commutative 46.3%

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

      3. times-frac 20.3%

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

      4. +-commutative 20.3%

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

      5. times-frac 29.1%

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

   4. Simplified 29.1%

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

   5. Taylor expanded in b around inf 64.9%

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

      1. associate--l+ 64.9%

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

      2. associate-*r/ 47.7%

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

   7. Simplified 47.7%

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

   8. Taylor expanded in t around 0 64.9%

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

   if -8.6000000000000004e-125 < z < 2.7999999999999999e-17

   1. Initial program 89.6%

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

   2. Taylor expanded in y around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. unsub-neg 77.1%

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

      3. mul-1-neg 77.1%

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

      4. distribute-neg-frac 77.1%

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

      5. cancel-sign-sub-inv 77.1%

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

      6. associate-/l* 77.1%

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

      7. metadata-eval 77.1%

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

      8. *-lft-identity 77.1%

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

      9. associate-/l* 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. times-frac 64.2%

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

      2. sub-neg 64.2%

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

      3. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around 0 64.2%

      \[\leadsto \color{blue}{x} - \frac{t}{z + -1} \cdot \frac{z}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-79}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{t}{z + -1} \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+16} \lor \neg \left(z \leq 44000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.52e+16) (not (<= z 44000000.0)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.52e+16) || !(z <= 44000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * 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 <= (-1.52d+16)) .or. (.not. (z <= 44000000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * 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 <= -1.52e+16) || !(z <= 44000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.52e+16) or not (z <= 44000000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.52e+16) || !(z <= 44000000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.52e+16) || ~((z <= 44000000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.52e+16], N[Not[LessEqual[z, 44000000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.52e16 or 4.4e7 < z

   1. Initial program 36.8%

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

   2. Taylor expanded in z around inf 84.5%

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

   if -1.52e16 < z < 4.4e7

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 88.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+16} \lor \neg \left(z \leq 44000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]

Alternative 9: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(x - \frac{a}{y}\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 0.054:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- x (/ a y))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3e-16)
     t_2
     (if (<= z -3.7e-80)
       t_1
       (if (<= z -1.3e-122)
         (/ (- (/ (* y x) z) a) b)
         (if (<= z 0.054) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (x - (a / y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3e-16) {
		tmp = t_2;
	} else if (z <= -3.7e-80) {
		tmp = t_1;
	} else if (z <= -1.3e-122) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 0.054) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (x - (a / y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-3d-16)) then
        tmp = t_2
    else if (z <= (-3.7d-80)) then
        tmp = t_1
    else if (z <= (-1.3d-122)) then
        tmp = (((y * x) / z) - a) / b
    else if (z <= 0.054d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (x - (a / y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3e-16) {
		tmp = t_2;
	} else if (z <= -3.7e-80) {
		tmp = t_1;
	} else if (z <= -1.3e-122) {
		tmp = (((y * x) / z) - a) / b;
	} else if (z <= 0.054) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (x - (a / y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3e-16:
		tmp = t_2
	elif z <= -3.7e-80:
		tmp = t_1
	elif z <= -1.3e-122:
		tmp = (((y * x) / z) - a) / b
	elif z <= 0.054:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(x - Float64(a / y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3e-16)
		tmp = t_2;
	elseif (z <= -3.7e-80)
		tmp = t_1;
	elseif (z <= -1.3e-122)
		tmp = Float64(Float64(Float64(Float64(y * x) / z) - a) / b);
	elseif (z <= 0.054)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (x - (a / y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3e-16)
		tmp = t_2;
	elseif (z <= -3.7e-80)
		tmp = t_1;
	elseif (z <= -1.3e-122)
		tmp = (((y * x) / z) - a) / b;
	elseif (z <= 0.054)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(x - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-16], t$95$2, If[LessEqual[z, -3.7e-80], t$95$1, If[LessEqual[z, -1.3e-122], N[(N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 0.054], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999994e-16 or 0.0539999999999999994 < z

   1. Initial program 38.5%

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

   2. Taylor expanded in z around inf 82.9%

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

   if -2.99999999999999994e-16 < z < -3.70000000000000033e-80 or -1.29999999999999988e-122 < z < 0.0539999999999999994

   1. Initial program 88.3%

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

   2. Taylor expanded in y around -inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

      3. mul-1-neg 77.9%

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

      4. distribute-neg-frac 77.9%

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

      5. cancel-sign-sub-inv 77.9%

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

      6. associate-/l* 77.9%

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

      7. metadata-eval 77.9%

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

      8. *-lft-identity 77.9%

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

      9. associate-/l* 77.9%

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

   4. Simplified 77.9%

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

   5. Taylor expanded in a around inf 66.8%

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

      1. associate-*r/ 66.8%

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

      2. associate-*r* 66.8%

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

      3. neg-mul-1 66.8%

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

      4. *-commutative 66.8%

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

      5. sub-neg 66.8%

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

      6. metadata-eval 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in z around 0 59.5%

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

   if -3.70000000000000033e-80 < z < -1.29999999999999988e-122

   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 inf 51.0%

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

      1. associate--l+ 51.0%

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

      2. *-commutative 51.0%

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

      3. times-frac 22.4%

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

      4. +-commutative 22.4%

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

      5. times-frac 32.0%

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

   4. Simplified 32.0%

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

   5. Taylor expanded in b around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-*r/ 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in t around 0 70.7%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{y \cdot x}{z} - a}{b}\\ \mathbf{elif}\;z \leq 0.054:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 34.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{y}\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+245}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -820:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.95:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t) y)))
   (if (<= z -6.1e+286)
     t_1
     (if (<= z -9.5e+245)
       (/ a y)
       (if (<= z -820.0)
         t_1
         (if (<= z 0.95) x (if (<= z 7e+212) t_1 (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t / y;
	double tmp;
	if (z <= -6.1e+286) {
		tmp = t_1;
	} else if (z <= -9.5e+245) {
		tmp = a / y;
	} else if (z <= -820.0) {
		tmp = t_1;
	} else if (z <= 0.95) {
		tmp = x;
	} else if (z <= 7e+212) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -t / y
    if (z <= (-6.1d+286)) then
        tmp = t_1
    else if (z <= (-9.5d+245)) then
        tmp = a / y
    else if (z <= (-820.0d0)) then
        tmp = t_1
    else if (z <= 0.95d0) then
        tmp = x
    else if (z <= 7d+212) then
        tmp = t_1
    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 t_1 = -t / y;
	double tmp;
	if (z <= -6.1e+286) {
		tmp = t_1;
	} else if (z <= -9.5e+245) {
		tmp = a / y;
	} else if (z <= -820.0) {
		tmp = t_1;
	} else if (z <= 0.95) {
		tmp = x;
	} else if (z <= 7e+212) {
		tmp = t_1;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t / y
	tmp = 0
	if z <= -6.1e+286:
		tmp = t_1
	elif z <= -9.5e+245:
		tmp = a / y
	elif z <= -820.0:
		tmp = t_1
	elif z <= 0.95:
		tmp = x
	elif z <= 7e+212:
		tmp = t_1
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) / y)
	tmp = 0.0
	if (z <= -6.1e+286)
		tmp = t_1;
	elseif (z <= -9.5e+245)
		tmp = Float64(a / y);
	elseif (z <= -820.0)
		tmp = t_1;
	elseif (z <= 0.95)
		tmp = x;
	elseif (z <= 7e+212)
		tmp = t_1;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t / y;
	tmp = 0.0;
	if (z <= -6.1e+286)
		tmp = t_1;
	elseif (z <= -9.5e+245)
		tmp = a / y;
	elseif (z <= -820.0)
		tmp = t_1;
	elseif (z <= 0.95)
		tmp = x;
	elseif (z <= 7e+212)
		tmp = t_1;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) / y), $MachinePrecision]}, If[LessEqual[z, -6.1e+286], t$95$1, If[LessEqual[z, -9.5e+245], N[(a / y), $MachinePrecision], If[LessEqual[z, -820.0], t$95$1, If[LessEqual[z, 0.95], x, If[LessEqual[z, 7e+212], t$95$1, N[(t / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1000000000000002e286 or -9.49999999999999939e245 < z < -820 or 0.94999999999999996 < z < 6.99999999999999974e212

   1. Initial program 50.0%

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

   2. Taylor expanded in y around -inf 38.3%

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

      1. mul-1-neg 38.3%

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

      2. unsub-neg 38.3%

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

      3. mul-1-neg 38.3%

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

      4. distribute-neg-frac 38.3%

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

      5. cancel-sign-sub-inv 38.3%

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

      6. associate-/l* 53.0%

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

      7. metadata-eval 53.0%

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

      8. *-lft-identity 53.0%

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

      9. associate-/l* 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in t around inf 33.4%

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

      1. times-frac 50.2%

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

      2. sub-neg 50.2%

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

      3. metadata-eval 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in z around inf 41.0%

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

      1. associate-*r/ 41.0%

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

      2. neg-mul-1 41.0%

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

   10. Simplified 41.0%

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

   if -6.1000000000000002e286 < z < -9.49999999999999939e245

   1. Initial program 13.4%

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

   2. Taylor expanded in y around -inf 23.1%

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

      1. mul-1-neg 23.1%

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

      2. unsub-neg 23.1%

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

      3. mul-1-neg 23.1%

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

      4. distribute-neg-frac 23.1%

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

      5. cancel-sign-sub-inv 23.1%

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

      6. associate-/l* 28.6%

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

      7. metadata-eval 28.6%

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

      8. *-lft-identity 28.6%

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

      9. associate-/l* 45.4%

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

   4. Simplified 45.4%

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

   5. Taylor expanded in a around inf 13.9%

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

      1. associate-*r/ 13.9%

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

      2. associate-*r* 13.9%

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

      3. neg-mul-1 13.9%

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

      4. *-commutative 13.9%

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

      5. sub-neg 13.9%

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

      6. metadata-eval 13.9%

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

   7. Simplified 13.9%

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

   8. Taylor expanded in z around inf 37.2%

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

   if -820 < z < 0.94999999999999996

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 49.1%

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

   if 6.99999999999999974e212 < z

   1. Initial program 14.8%

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

   2. Taylor expanded in z around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. *-commutative 79.2%

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

      3. times-frac 87.4%

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

      4. +-commutative 87.4%

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

      5. times-frac 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around inf 61.8%

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

      1. associate--l+ 61.8%

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

      2. associate-*r/ 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in t around inf 37.9%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+286}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+245}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -820:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{elif}\;z \leq 0.95:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+212}:\\ \;\;\;\;\frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 11: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-16} \lor \neg \left(z \leq 0.054\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.9e-16) (not (<= z 0.054)))
   (/ (- t a) (- b y))
   (+ x (* z (- x (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-16) || !(z <= 0.054)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x - (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 <= (-3.9d-16)) .or. (.not. (z <= 0.054d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (x - (a / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-16) || !(z <= 0.054)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (x - (a / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.9e-16) or not (z <= 0.054):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (x - (a / y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.9e-16) || !(z <= 0.054))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(x - Float64(a / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.9e-16) || ~((z <= 0.054)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (x - (a / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.9e-16], N[Not[LessEqual[z, 0.054]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999977e-16 or 0.0539999999999999994 < z

   1. Initial program 38.5%

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

   2. Taylor expanded in z around inf 82.9%

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

   if -3.89999999999999977e-16 < z < 0.0539999999999999994

   1. Initial program 89.2%

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

   2. Taylor expanded in y around -inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. unsub-neg 74.3%

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

      3. mul-1-neg 74.3%

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

      4. distribute-neg-frac 74.3%

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

      5. cancel-sign-sub-inv 74.3%

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

      6. associate-/l* 74.2%

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

      7. metadata-eval 74.2%

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

      8. *-lft-identity 74.2%

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

      9. associate-/l* 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in a around inf 64.1%

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

      1. associate-*r/ 64.1%

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

      2. associate-*r* 64.1%

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

      3. neg-mul-1 64.1%

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

      4. *-commutative 64.1%

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

      5. sub-neg 64.1%

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

      6. metadata-eval 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in z around 0 56.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-16} \lor \neg \left(z \leq 0.054\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - \frac{a}{y}\right)\\ \end{array} \]

Alternative 12: 64.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-16} \lor \neg \left(z \leq 1.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e-16) (not (<= z 1.6e-48)))
   (/ (- t a) (- b y))
   (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e-16) || !(z <= 1.6e-48)) {
		tmp = (t - a) / (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 <= (-1.95d-16)) .or. (.not. (z <= 1.6d-48))) then
        tmp = (t - a) / (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 <= -1.95e-16) || !(z <= 1.6e-48)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e-16) or not (z <= 1.6e-48):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e-16) || !(z <= 1.6e-48))
		tmp = Float64(Float64(t - a) / 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 <= -1.95e-16) || ~((z <= 1.6e-48)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e-16], N[Not[LessEqual[z, 1.6e-48]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999989e-16 or 1.5999999999999999e-48 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in z around inf 79.8%

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

   if -1.94999999999999989e-16 < z < 1.5999999999999999e-48

   1. Initial program 89.2%

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

   2. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 51.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-16} \lor \neg \left(z \leq 1.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 13: 45.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \lor \neg \left(z \leq 2.45 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.12) (not (<= z 2.45e-48))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12) || !(z <= 2.45e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.12d0)) .or. (.not. (z <= 2.45d-48))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12) || !(z <= 2.45e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.12) or not (z <= 2.45e-48):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.12) || !(z <= 2.45e-48))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.12) || ~((z <= 2.45e-48)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.12], N[Not[LessEqual[z, 2.45e-48]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.1200000000000001 or 2.4500000000000001e-48 < 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 80.2%

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

   3. Taylor expanded in t around inf 49.5%

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

   if -1.1200000000000001 < z < 2.4500000000000001e-48

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 50.9%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \lor \neg \left(z \leq 2.45 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 45.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \lor \neg \left(z \leq 2.45 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.46) (not (<= z 2.45e-48))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.46) || !(z <= 2.45e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.46d0)) .or. (.not. (z <= 2.45d-48))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.46) || !(z <= 2.45e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.46) or not (z <= 2.45e-48):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.46) || !(z <= 2.45e-48))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.46) || ~((z <= 2.45e-48)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.46], N[Not[LessEqual[z, 2.45e-48]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.46 or 2.4500000000000001e-48 < 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 80.2%

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

   3. Taylor expanded in t around inf 49.5%

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

   if -1.46 < z < 2.4500000000000001e-48

   1. Initial program 88.6%

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

   2. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

   4. Simplified 51.6%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \lor \neg \left(z \leq 2.45 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 15: 46.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -730:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -730.0)
   (/ t (- b y))
   (if (<= z 6e+22) (/ 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 (z <= -730.0) {
		tmp = t / (b - y);
	} else if (z <= 6e+22) {
		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 (z <= (-730.0d0)) then
        tmp = t / (b - y)
    else if (z <= 6d+22) 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 (z <= -730.0) {
		tmp = t / (b - y);
	} else if (z <= 6e+22) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -730.0:
		tmp = t / (b - y)
	elif z <= 6e+22:
		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 (z <= -730.0)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= 6e+22)
		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 (z <= -730.0)
		tmp = t / (b - y);
	elseif (z <= 6e+22)
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -730.0], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+22], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -730

   1. Initial program 36.5%

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

   2. Taylor expanded in z around inf 88.1%

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

   3. Taylor expanded in t around inf 55.7%

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

   if -730 < z < 6e22

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

   4. Simplified 49.3%

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

   if 6e22 < z

   1. Initial program 37.1%

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

   2. Taylor expanded in y around 0 50.2%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -730:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 16: 33.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -62000000000.0) (/ a y) (if (<= z 2.9e+33) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -62000000000.0) {
		tmp = a / y;
	} else if (z <= 2.9e+33) {
		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 <= (-62000000000.0d0)) then
        tmp = a / y
    else if (z <= 2.9d+33) 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 <= -62000000000.0) {
		tmp = a / y;
	} else if (z <= 2.9e+33) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -62000000000.0:
		tmp = a / y
	elif z <= 2.9e+33:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -62000000000.0)
		tmp = Float64(a / y);
	elseif (z <= 2.9e+33)
		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 <= -62000000000.0)
		tmp = a / y;
	elseif (z <= 2.9e+33)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -62000000000.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 2.9e+33], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e10 or 2.90000000000000025e33 < z

   1. Initial program 34.1%

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

   2. Taylor expanded in y around -inf 31.1%

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

      1. mul-1-neg 31.1%

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

      2. unsub-neg 31.1%

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

      3. mul-1-neg 31.1%

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

      4. distribute-neg-frac 31.1%

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

      5. cancel-sign-sub-inv 31.1%

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

      6. associate-/l* 44.9%

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

      7. metadata-eval 44.9%

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

      8. *-lft-identity 44.9%

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

      9. associate-/l* 52.5%

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

   4. Simplified 52.5%

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

   5. Taylor expanded in a around inf 17.8%

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

      1. associate-*r/ 17.8%

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

      2. associate-*r* 17.8%

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

      3. neg-mul-1 17.8%

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

      4. *-commutative 17.8%

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

      5. sub-neg 17.8%

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

      6. metadata-eval 17.8%

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

   7. Simplified 17.8%

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

   8. Taylor expanded in z around inf 19.1%

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

   if -6.2e10 < z < 2.90000000000000025e33

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 46.4%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -62000000000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 17: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.12) (/ t b) (if (<= z 2.4e-48) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.12) {
		tmp = t / b;
	} else if (z <= 2.4e-48) {
		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 <= (-1.12d0)) then
        tmp = t / b
    else if (z <= 2.4d-48) 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 <= -1.12) {
		tmp = t / b;
	} else if (z <= 2.4e-48) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.12:
		tmp = t / b
	elif z <= 2.4e-48:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.12)
		tmp = Float64(t / b);
	elseif (z <= 2.4e-48)
		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 <= -1.12)
		tmp = t / b;
	elseif (z <= 2.4e-48)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.12], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.4e-48], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1200000000000001 or 2.4e-48 < 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 65.9%

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

      1. associate--l+ 65.9%

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

      2. *-commutative 65.9%

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

      3. times-frac 73.7%

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

      4. +-commutative 73.7%

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

      5. times-frac 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in b around inf 46.7%

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

      1. associate--l+ 46.7%

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

      2. associate-*r/ 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in t around inf 25.7%

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

   if -1.1200000000000001 < z < 2.4e-48

   1. Initial program 88.6%

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

   2. Taylor expanded in z around 0 50.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 18: 36.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.2e-16) (/ (- a) b) (if (<= z 1.8e-48) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.2e-16) {
		tmp = -a / b;
	} else if (z <= 1.8e-48) {
		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 <= (-7.2d-16)) then
        tmp = -a / b
    else if (z <= 1.8d-48) 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 <= -7.2e-16) {
		tmp = -a / b;
	} else if (z <= 1.8e-48) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.2e-16:
		tmp = -a / b
	elif z <= 1.8e-48:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.2e-16)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.8e-48)
		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 <= -7.2e-16)
		tmp = -a / b;
	elseif (z <= 1.8e-48)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.2e-16], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.8e-48], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999965e-16

   1. Initial program 36.9%

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

   2. Taylor expanded in a around inf 18.3%

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

      1. mul-1-neg 18.3%

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

      2. distribute-lft-neg-out 18.3%

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

      3. *-commutative 18.3%

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

   4. Simplified 18.3%

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

   5. Taylor expanded in y around 0 25.9%

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

      1. associate-*r/ 25.9%

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

      2. neg-mul-1 25.9%

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

   7. Simplified 25.9%

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

   if -7.19999999999999965e-16 < z < 1.8000000000000001e-48

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 51.6%

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

   if 1.8000000000000001e-48 < z

   1. Initial program 46.2%

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

   2. Taylor expanded in z around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. *-commutative 68.4%

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

      3. times-frac 77.8%

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

      4. +-commutative 77.8%

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

      5. times-frac 88.8%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in b around inf 52.2%

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

      1. associate--l+ 52.2%

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

      2. associate-*r/ 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in t around inf 26.9%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 19: 25.2% 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 63.4%

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

2. Taylor expanded in z around 0 26.1%

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

3. Final simplification 26.1%

   \[\leadsto x \]

Developer target: 73.4% 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 2023274 
(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)))))