Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 92.0%

Time: 14.7s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% 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: 92.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t\_3 + x \cdot y}{t\_1}\\ t_5 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (+ (* x (/ y (- b y))) (* y (/ (- a t) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ t_3 (* x y)) t_1))
        (t_5 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-299)
       t_4
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 2e+306) t_4 (if (<= t_4 INFINITY) t_5 t_2)))))))

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 = (((x * (y / (b - y))) + (y * ((a - t) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (x * y)) / t_1;
	double t_5 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-299) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+306) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	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 = (((x * (y / (b - y))) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (x * y)) / t_1;
	double t_5 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-299) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+306) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (((x * (y / (b - y))) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z) + ((t - a) / (b - y))
	t_3 = z * (t - a)
	t_4 = (t_3 + (x * y)) / t_1
	t_5 = x * ((y / t_1) + (t_3 / (x * t_1)))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-299:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = t_2
	elif t_4 <= 2e+306:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_2
	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(Float64(x * Float64(y / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_5 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-299)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+306)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (((x * (y / (b - y))) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z) + ((t - a) / (b - y));
	t_3 = z * (t - a);
	t_4 = (t_3 + (x * y)) / t_1;
	t_5 = x * ((y / t_1) + (t_3 / (x * t_1)));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-299)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+306)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	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[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-299], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 2e+306], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$2]]]]]]]]]]

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 or 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.9%

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

   3. Taylor expanded in x around inf 75.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999998e-299 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.9%

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

   3. Taylor expanded in z around -inf 60.6%

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

      1. associate--l+ 60.6%

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

      2. mul-1-neg 60.6%

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

      3. distribute-lft-out-- 60.6%

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

      4. associate-/l* 70.5%

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

      5. associate-/l* 99.8%

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

      6. div-sub 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-299}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{y - b}{y} - \frac{a}{y}\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-299} \lor \neg \left(t\_1 \leq 0\right) \land t\_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))))
   (if (<= t_1 (- INFINITY))
     (+ x (* z (- (* x (/ (- y b) y)) (/ a y))))
     (if (or (<= t_1 -2e-299) (and (not (<= t_1 0.0)) (<= t_1 2e+306)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (z * ((x * ((y - b) / y)) - (a / y)));
	} else if ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+306))) {
		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 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * ((x * ((y - b) / y)) - (a / y)));
	} else if ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+306))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (z * ((x * ((y - b) / y)) - (a / y)))
	elif (t_1 <= -2e-299) or (not (t_1 <= 0.0) and (t_1 <= 2e+306)):
		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(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(x * Float64(Float64(y - b) / y)) - Float64(a / y))));
	elseif ((t_1 <= -2e-299) || (!(t_1 <= 0.0) && (t_1 <= 2e+306)))
		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 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (z * ((x * ((y - b) / y)) - (a / y)));
	elseif ((t_1 <= -2e-299) || (~((t_1 <= 0.0)) && (t_1 <= 2e+306)))
		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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(z * N[(N[(x * N[(N[(y - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-299], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+306]]], 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 27.6%

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

   3. Taylor expanded in t around 0 20.8%

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

      1. +-commutative 20.8%

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

      2. mul-1-neg 20.8%

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

      3. unsub-neg 20.8%

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

      4. *-commutative 20.8%

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

      5. *-commutative 20.8%

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

   5. Simplified 20.8%

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

   6. Taylor expanded in z around 0 12.1%

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

      1. associate-*r/ 12.1%

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

      2. neg-mul-1 12.1%

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

      3. associate-/l* 60.7%

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

   8. Simplified 60.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999998e-299 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf 76.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{y - b}{y} - \frac{a}{y}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-299} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t\_2 + x \cdot y}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{t\_2}{x \cdot t\_1} + 1\right)\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-299} \lor \neg \left(t\_3 \leq 0\right) \land t\_3 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* x y)) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ t_2 (* x t_1)) 1.0))
     (if (or (<= t_3 -2e-299) (and (not (<= t_3 0.0)) (<= t_3 2e+306)))
       t_3
       (/ (- t a) (- b y))))))

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 = z * (t - a);
	double t_3 = (t_2 + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	} else if ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306))) {
		tmp = t_3;
	} 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 + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	} else if ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (t_2 + (x * y)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((t_2 / (x * t_1)) + 1.0)
	elif (t_3 <= -2e-299) or (not (t_3 <= 0.0) and (t_3 <= 2e+306)):
		tmp = t_3
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(t_2 / Float64(x * t_1)) + 1.0));
	elseif ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306)))
		tmp = t_3;
	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 + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (t_2 + (x * y)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	elseif ((t_3 <= -2e-299) || (~((t_3 <= 0.0)) && (t_3 <= 2e+306)))
		tmp = t_3;
	else
		tmp = (t - a) / (b - y);
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(t$95$2 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$3, -2e-299], And[N[Not[LessEqual[t$95$3, 0.0]], $MachinePrecision], LessEqual[t$95$3, 2e+306]]], t$95$3, 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 27.6%

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

   3. Taylor expanded in x around inf 77.5%

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

   4. Taylor expanded in z around 0 74.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999998e-299 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf 76.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)} + 1\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-299} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t\_2 + x \cdot y}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t\_2}{x \cdot t\_1}\right)\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-299} \lor \neg \left(t\_3 \leq 0\right) \land t\_3 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* x y)) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ y t_1) (/ t_2 (* x t_1))))
     (if (or (<= t_3 -2e-299) (and (not (<= t_3 0.0)) (<= t_3 2e+306)))
       t_3
       (/ (- t a) (- b y))))))

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 = z * (t - a);
	double t_3 = (t_2 + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306))) {
		tmp = t_3;
	} 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 + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (x * y)) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	} else if ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (t_2 + (x * y)) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)))
	elif (t_3 <= -2e-299) or (not (t_3 <= 0.0) and (t_3 <= 2e+306)):
		tmp = t_3
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(x * y)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(t_2 / Float64(x * t_1))));
	elseif ((t_3 <= -2e-299) || (!(t_3 <= 0.0) && (t_3 <= 2e+306)))
		tmp = t_3;
	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 + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (t_2 + (x * y)) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((y / t_1) + (t_2 / (x * t_1)));
	elseif ((t_3 <= -2e-299) || (~((t_3 <= 0.0)) && (t_3 <= 2e+306)))
		tmp = t_3;
	else
		tmp = (t - a) / (b - y);
	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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$2 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$3, -2e-299], And[N[Not[LessEqual[t$95$3, 0.0]], $MachinePrecision], LessEqual[t$95$3, 2e+306]]], t$95$3, 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 27.6%

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

   3. Taylor expanded in x around inf 77.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999998e-299 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -1.99999999999999998e-299 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf 76.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-299} \lor \neg \left(\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-78}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -8.2e-58)
     t_1
     (if (<= z -6.4e-75)
       (* a (- (/ x a) (/ z y)))
       (if (<= z -1.25e-78)
         (/ (* z a) (- (* z (- y b)) y))
         (if (<= z 6e-25) x 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 <= -8.2e-58) {
		tmp = t_1;
	} else if (z <= -6.4e-75) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= -1.25e-78) {
		tmp = (z * a) / ((z * (y - b)) - y);
	} else if (z <= 6e-25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-8.2d-58)) then
        tmp = t_1
    else if (z <= (-6.4d-75)) then
        tmp = a * ((x / a) - (z / y))
    else if (z <= (-1.25d-78)) then
        tmp = (z * a) / ((z * (y - b)) - y)
    else if (z <= 6d-25) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.2e-58) {
		tmp = t_1;
	} else if (z <= -6.4e-75) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= -1.25e-78) {
		tmp = (z * a) / ((z * (y - b)) - y);
	} else if (z <= 6e-25) {
		tmp = x;
	} 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 <= -8.2e-58:
		tmp = t_1
	elif z <= -6.4e-75:
		tmp = a * ((x / a) - (z / y))
	elif z <= -1.25e-78:
		tmp = (z * a) / ((z * (y - b)) - y)
	elif z <= 6e-25:
		tmp = x
	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 <= -8.2e-58)
		tmp = t_1;
	elseif (z <= -6.4e-75)
		tmp = Float64(a * Float64(Float64(x / a) - Float64(z / y)));
	elseif (z <= -1.25e-78)
		tmp = Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y));
	elseif (z <= 6e-25)
		tmp = x;
	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 <= -8.2e-58)
		tmp = t_1;
	elseif (z <= -6.4e-75)
		tmp = a * ((x / a) - (z / y));
	elseif (z <= -1.25e-78)
		tmp = (z * a) / ((z * (y - b)) - y);
	elseif (z <= 6e-25)
		tmp = x;
	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, -8.2e-58], t$95$1, If[LessEqual[z, -6.4e-75], N[(a * N[(N[(x / a), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-78], N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-25], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.20000000000000056e-58 or 5.9999999999999995e-25 < z

   1. Initial program 54.6%

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

   3. Taylor expanded in z around inf 80.4%

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

   if -8.20000000000000056e-58 < z < -6.39999999999999953e-75

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 86.5%

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

      1. +-commutative 86.5%

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

      2. mul-1-neg 86.5%

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

      3. unsub-neg 86.5%

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

      4. *-commutative 86.5%

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

      5. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in z around 0 73.4%

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

   7. Taylor expanded in a around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

   9. Simplified 86.7%

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

   if -6.39999999999999953e-75 < z < -1.2499999999999999e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.2499999999999999e-78 < z < 5.9999999999999995e-25

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 63.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-78}:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-17} \lor \neg \left(z \leq 0.0085\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.45e-17) (not (<= z 0.0085)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* 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 <= -2.45e-17) || !(z <= 0.0085)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (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 <= (-2.45d-17)) .or. (.not. (z <= 0.0085d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (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 <= -2.45e-17) || !(z <= 0.0085)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.45e-17) or not (z <= 0.0085):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.45e-17) || !(z <= 0.0085))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - 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 <= -2.45e-17) || ~((z <= 0.0085)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.45e-17], N[Not[LessEqual[z, 0.0085]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000006e-17 or 0.0085000000000000006 < z

   1. Initial program 51.0%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -2.45000000000000006e-17 < z < 0.0085000000000000006

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

   5. Simplified 70.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-17} \lor \neg \left(z \leq 0.0085\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 44.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+227}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3.9e-32)
     t_1
     (if (<= z 3.6e-25) x (if (<= z 1.55e+227) t_1 (/ a (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.9e-32) {
		tmp = t_1;
	} else if (z <= 3.6e-25) {
		tmp = x;
	} else if (z <= 1.55e+227) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-3.9d-32)) then
        tmp = t_1
    else if (z <= 3.6d-25) then
        tmp = x
    else if (z <= 1.55d+227) then
        tmp = t_1
    else
        tmp = a / -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.9e-32) {
		tmp = t_1;
	} else if (z <= 3.6e-25) {
		tmp = x;
	} else if (z <= 1.55e+227) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3.9e-32:
		tmp = t_1
	elif z <= 3.6e-25:
		tmp = x
	elif z <= 1.55e+227:
		tmp = t_1
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3.9e-32)
		tmp = t_1;
	elseif (z <= 3.6e-25)
		tmp = x;
	elseif (z <= 1.55e+227)
		tmp = t_1;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3.9e-32)
		tmp = t_1;
	elseif (z <= 3.6e-25)
		tmp = x;
	elseif (z <= 1.55e+227)
		tmp = t_1;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-32], t$95$1, If[LessEqual[z, 3.6e-25], x, If[LessEqual[z, 1.55e+227], t$95$1, N[(a / (-b)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000001e-32 or 3.5999999999999999e-25 < z < 1.5499999999999999e227

   1. Initial program 55.4%

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

   3. Taylor expanded in t around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

   6. Taylor expanded in z around inf 49.4%

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

   if -3.9000000000000001e-32 < z < 3.5999999999999999e-25

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 60.4%

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

   if 1.5499999999999999e227 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in t around 0 43.2%

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

      1. +-commutative 43.2%

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

      2. mul-1-neg 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in y around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

   8. Simplified 69.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+227}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+229}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.35e-19)
     t_1
     (if (<= z 3.9e+69)
       (/ x (- 1.0 z))
       (if (<= z 1.25e+229) t_1 (/ a (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.35e-19) {
		tmp = t_1;
	} else if (z <= 3.9e+69) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e+229) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-1.35d-19)) then
        tmp = t_1
    else if (z <= 3.9d+69) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.25d+229) then
        tmp = t_1
    else
        tmp = a / -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.35e-19) {
		tmp = t_1;
	} else if (z <= 3.9e+69) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e+229) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1.35e-19:
		tmp = t_1
	elif z <= 3.9e+69:
		tmp = x / (1.0 - z)
	elif z <= 1.25e+229:
		tmp = t_1
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.35e-19)
		tmp = t_1;
	elseif (z <= 3.9e+69)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.25e+229)
		tmp = t_1;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.35e-19)
		tmp = t_1;
	elseif (z <= 3.9e+69)
		tmp = x / (1.0 - z);
	elseif (z <= 1.25e+229)
		tmp = t_1;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-19], t$95$1, If[LessEqual[z, 3.9e+69], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+229], t$95$1, N[(a / (-b)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e-19 or 3.8999999999999999e69 < z < 1.25000000000000012e229

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf 30.2%

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

      1. *-commutative 30.2%

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

   5. Simplified 30.2%

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

   6. Taylor expanded in z around inf 54.4%

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

   if -1.35e-19 < z < 3.8999999999999999e69

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

   5. Simplified 56.4%

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

   if 1.25000000000000012e229 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in t around 0 43.2%

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

      1. +-commutative 43.2%

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

      2. mul-1-neg 43.2%

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

      3. unsub-neg 43.2%

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

      4. *-commutative 43.2%

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

      5. *-commutative 43.2%

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

   5. Simplified 43.2%

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

   6. Taylor expanded in y around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

   8. Simplified 69.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+229}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+196}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.9e+196)
   (/ a y)
   (if (<= z -2.65e-17) (/ t b) (if (<= z 5.1e-21) x (/ a (- b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e+196) {
		tmp = a / y;
	} else if (z <= -2.65e-17) {
		tmp = t / b;
	} else if (z <= 5.1e-21) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.9d+196)) then
        tmp = a / y
    else if (z <= (-2.65d-17)) then
        tmp = t / b
    else if (z <= 5.1d-21) then
        tmp = x
    else
        tmp = a / -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.9e+196) {
		tmp = a / y;
	} else if (z <= -2.65e-17) {
		tmp = t / b;
	} else if (z <= 5.1e-21) {
		tmp = x;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.9e+196:
		tmp = a / y
	elif z <= -2.65e-17:
		tmp = t / b
	elif z <= 5.1e-21:
		tmp = x
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.9e+196)
		tmp = Float64(a / y);
	elseif (z <= -2.65e-17)
		tmp = Float64(t / b);
	elseif (z <= 5.1e-21)
		tmp = x;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.9e+196)
		tmp = a / y;
	elseif (z <= -2.65e-17)
		tmp = t / b;
	elseif (z <= 5.1e-21)
		tmp = x;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.9e+196], N[(a / y), $MachinePrecision], If[LessEqual[z, -2.65e-17], N[(t / b), $MachinePrecision], If[LessEqual[z, 5.1e-21], x, N[(a / (-b)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9e196

   1. Initial program 27.4%

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

   3. Taylor expanded in t around 0 17.3%

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

      1. +-commutative 17.3%

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

      2. mul-1-neg 17.3%

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

      3. unsub-neg 17.3%

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

      4. *-commutative 17.3%

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

      5. *-commutative 17.3%

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

   5. Simplified 17.3%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in b around 0 39.5%

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

   if -3.9e196 < z < -2.6499999999999999e-17

   1. Initial program 59.0%

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

   3. Taylor expanded in x around inf 43.6%

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

   4. Taylor expanded in b around inf 49.9%

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

      1. associate-/l* 47.5%

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

      2. associate--l+ 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in t around inf 38.2%

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

   if -2.6499999999999999e-17 < z < 5.10000000000000004e-21

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 60.0%

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

   if 5.10000000000000004e-21 < z

   1. Initial program 56.9%

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

   3. Taylor expanded in t around 0 43.7%

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

      1. +-commutative 43.7%

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

      2. mul-1-neg 43.7%

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

      3. unsub-neg 43.7%

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

      4. *-commutative 43.7%

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

      5. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in y around 0 38.9%

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

      1. associate-*r/ 38.9%

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

      2. neg-mul-1 38.9%

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

   8. Simplified 38.9%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+196}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-17}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+197}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-17} \lor \neg \left(z \leq 3.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.8e+197)
   (/ a y)
   (if (or (<= z -2.55e-17) (not (<= z 3.4e-25))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+197) {
		tmp = a / y;
	} else if ((z <= -2.55e-17) || !(z <= 3.4e-25)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.8d+197)) then
        tmp = a / y
    else if ((z <= (-2.55d-17)) .or. (.not. (z <= 3.4d-25))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.8e+197) {
		tmp = a / y;
	} else if ((z <= -2.55e-17) || !(z <= 3.4e-25)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.8e+197:
		tmp = a / y
	elif (z <= -2.55e-17) or not (z <= 3.4e-25):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.8e+197)
		tmp = Float64(a / y);
	elseif ((z <= -2.55e-17) || !(z <= 3.4e-25))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.8e+197)
		tmp = a / y;
	elseif ((z <= -2.55e-17) || ~((z <= 3.4e-25)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.8e+197], N[(a / y), $MachinePrecision], If[Or[LessEqual[z, -2.55e-17], N[Not[LessEqual[z, 3.4e-25]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999991e197

   1. Initial program 27.4%

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

   3. Taylor expanded in t around 0 17.3%

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

      1. +-commutative 17.3%

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

      2. mul-1-neg 17.3%

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

      3. unsub-neg 17.3%

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

      4. *-commutative 17.3%

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

      5. *-commutative 17.3%

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

   5. Simplified 17.3%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. associate-*r/ 49.5%

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

      2. neg-mul-1 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in b around 0 39.5%

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

   if -1.79999999999999991e197 < z < -2.5500000000000001e-17 or 3.40000000000000002e-25 < z

   1. Initial program 58.1%

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

   3. Taylor expanded in x around inf 46.7%

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

   4. Taylor expanded in b around inf 45.0%

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

      1. associate-/l* 42.6%

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

      2. associate--l+ 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in t around inf 32.9%

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

   if -2.5500000000000001e-17 < z < 3.40000000000000002e-25

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 60.4%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+197}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-17} \lor \neg \left(z \leq 3.4 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-63} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e-63) (not (<= z 5e-24))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e-63) || !(z <= 5e-24)) {
		tmp = (t - a) / (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 <= (-2.4d-63)) .or. (.not. (z <= 5d-24))) then
        tmp = (t - a) / (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 <= -2.4e-63) || !(z <= 5e-24)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e-63) or not (z <= 5e-24):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e-63) || !(z <= 5e-24))
		tmp = Float64(Float64(t - a) / 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 <= -2.4e-63) || ~((z <= 5e-24)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e-63], N[Not[LessEqual[z, 5e-24]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e-63 or 4.9999999999999998e-24 < z

   1. Initial program 54.6%

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

   3. Taylor expanded in z around inf 80.4%

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

   if -2.4000000000000001e-63 < z < 4.9999999999999998e-24

   1. Initial program 82.1%

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

   3. Taylor expanded in z around 0 61.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-63} \lor \neg \left(z \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-71} \lor \neg \left(y \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e-71) (not (<= y 6.5e+16))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-71) || !(y <= 6.5e+16)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d-71)) .or. (.not. (y <= 6.5d+16))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e-71) || !(y <= 6.5e+16)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e-71) or not (y <= 6.5e+16):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e-71) || !(y <= 6.5e+16))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e-71) || ~((y <= 6.5e+16)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e-71], N[Not[LessEqual[y, 6.5e+16]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999996e-71 or 6.5e16 < y

   1. Initial program 57.3%

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

   3. Taylor expanded in y around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   if -1.89999999999999996e-71 < y < 6.5e16

   1. Initial program 81.3%

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

   3. Taylor expanded in y around 0 62.8%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-71} \lor \neg \left(y \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.35 \lor \neg \left(z \leq 118000000000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.35) (not (<= z 118000000000.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.35) || !(z <= 118000000000.0)) {
		tmp = a / 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 <= (-0.35d0)) .or. (.not. (z <= 118000000000.0d0))) then
        tmp = a / 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 <= -0.35) || !(z <= 118000000000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.35) or not (z <= 118000000000.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.35) || !(z <= 118000000000.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.35) || ~((z <= 118000000000.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.35], N[Not[LessEqual[z, 118000000000.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.34999999999999998 or 1.18e11 < z

   1. Initial program 50.5%

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

   3. Taylor expanded in t around 0 32.2%

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

      1. +-commutative 32.2%

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

      2. mul-1-neg 32.2%

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

      3. unsub-neg 32.2%

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

      4. *-commutative 32.2%

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

      5. *-commutative 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in z around inf 44.7%

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

      1. associate-*r/ 44.7%

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

      2. neg-mul-1 44.7%

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

   8. Simplified 44.7%

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

   9. Taylor expanded in b around 0 19.4%

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

   if -0.34999999999999998 < z < 1.18e11

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 56.0%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.35 \lor \neg \left(z \leq 118000000000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.7%

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

3. Taylor expanded in z around 0 31.8%

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

4. Final simplification 31.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.5% 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 2024115 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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