Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.3% → 93.2%

Time: 20.6s

Alternatives: 23

Speedup: 0.8×

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: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y - b\right)\\ t_2 := y - t\_1\\ t_3 := \left(\frac{t - a}{b - y} - \frac{y}{z} \cdot \frac{x}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ t_4 := \frac{z \cdot \left(t - a\right) + y \cdot x}{t\_2}\\ t_5 := x \cdot \left(\frac{y}{t\_2} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot t\_2} + \frac{z}{t\_1 - y}\right)}{x}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-238}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y b)))
        (t_2 (- y t_1))
        (t_3
         (+
          (- (/ (- t a) (- b y)) (* (/ y z) (/ x (- y b))))
          (* y (/ (- a t) (* z (pow (- b y) 2.0))))))
        (t_4 (/ (+ (* z (- t a)) (* y x)) t_2))
        (t_5
         (*
          x
          (+
           (/ y t_2)
           (/ (* a (+ (/ (* z t) (* a t_2)) (/ z (- t_1 y)))) x)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-238)
       t_4
       (if (<= t_4 0.0)
         t_3
         (if (<= t_4 2e+292) t_4 (if (<= t_4 INFINITY) t_5 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y - b);
	double t_2 = y - t_1;
	double t_3 = (((t - a) / (b - y)) - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	double t_4 = ((z * (t - a)) + (y * x)) / t_2;
	double t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-238) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_3;
	} else if (t_4 <= 2e+292) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = z * (y - b);
	double t_2 = y - t_1;
	double t_3 = (((t - a) / (b - y)) - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	double t_4 = ((z * (t - a)) + (y * x)) / t_2;
	double t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-238) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_3;
	} else if (t_4 <= 2e+292) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y - b)
	t_2 = y - t_1
	t_3 = (((t - a) / (b - y)) - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	t_4 = ((z * (t - a)) + (y * x)) / t_2
	t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-238:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = t_3
	elif t_4 <= 2e+292:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y - b))
	t_2 = Float64(y - t_1)
	t_3 = Float64(Float64(Float64(Float64(t - a) / Float64(b - y)) - Float64(Float64(y / z) * Float64(x / Float64(y - b)))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))))
	t_4 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / t_2)
	t_5 = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(a * Float64(Float64(Float64(z * t) / Float64(a * t_2)) + Float64(z / Float64(t_1 - y)))) / x)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-238)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_3;
	elseif (t_4 <= 2e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y - b);
	t_2 = y - t_1;
	t_3 = (((t - a) / (b - y)) - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	t_4 = ((z * (t - a)) + (y * x)) / t_2;
	t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-238)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_3;
	elseif (t_4 <= 2e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(x / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(N[(z * t), $MachinePrecision] / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-238], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$3, If[LessEqual[t$95$4, 2e+292], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$3]]]]]]]]]]

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 2e292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.9%

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

   3. Taylor expanded in a around -inf 40.9%

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

      1. associate-*r* 40.9%

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

      2. neg-mul-1 40.9%

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

      3. fma-define 40.9%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-238 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e292

   1. Initial program 99.5%

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

   if -2e-238 < (/.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 10.9%

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

   3. Taylor expanded in z around inf 47.6%

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

      1. associate--r+ 47.6%

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

      2. +-commutative 47.6%

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

      3. associate--l+ 47.6%

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

      4. *-commutative 47.6%

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

      5. times-frac 63.9%

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

      6. div-sub 63.9%

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

      7. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -2 \cdot 10^{-238}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} - \frac{y}{z} \cdot \frac{x}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} - \frac{y}{z} \cdot \frac{x}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y - b\right)\\ t_2 := y - t\_1\\ t_3 := \frac{z \cdot \left(t - a\right) + y \cdot x}{t\_2}\\ t_4 := x \cdot \left(\frac{y}{t\_2} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot t\_2} + \frac{z}{t\_1 - y}\right)}{x}\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{t}{b - y} + \frac{\frac{y \cdot x}{b - y} - \frac{t \cdot y}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y b)))
        (t_2 (- y t_1))
        (t_3 (/ (+ (* z (- t a)) (* y x)) t_2))
        (t_4
         (*
          x
          (+
           (/ y t_2)
           (/ (* a (+ (/ (* z t) (* a t_2)) (/ z (- t_1 y)))) x)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -2e-301)
       t_3
       (if (<= t_3 0.0)
         (+
          (/ t (- b y))
          (/ (- (/ (* y x) (- b y)) (/ (* t y) (pow (- b y) 2.0))) z))
         (if (<= t_3 2e+292)
           t_3
           (if (<= t_3 INFINITY) t_4 (/ (- t a) (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y - b);
	double t_2 = y - t_1;
	double t_3 = ((z * (t - a)) + (y * x)) / t_2;
	double t_4 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -2e-301) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t / (b - y)) + ((((y * x) / (b - y)) - ((t * y) / pow((b - y), 2.0))) / z);
	} else if (t_3 <= 2e+292) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 * (y - b);
	double t_2 = y - t_1;
	double t_3 = ((z * (t - a)) + (y * x)) / t_2;
	double t_4 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -2e-301) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t / (b - y)) + ((((y * x) / (b - y)) - ((t * y) / Math.pow((b - y), 2.0))) / z);
	} else if (t_3 <= 2e+292) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y - b)
	t_2 = y - t_1
	t_3 = ((z * (t - a)) + (y * x)) / t_2
	t_4 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -2e-301:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (t / (b - y)) + ((((y * x) / (b - y)) - ((t * y) / math.pow((b - y), 2.0))) / z)
	elif t_3 <= 2e+292:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_4
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y - b))
	t_2 = Float64(y - t_1)
	t_3 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / t_2)
	t_4 = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(a * Float64(Float64(Float64(z * t) / Float64(a * t_2)) + Float64(z / Float64(t_1 - y)))) / x)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -2e-301)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) - Float64(Float64(t * y) / (Float64(b - y) ^ 2.0))) / z));
	elseif (t_3 <= 2e+292)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	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 * (y - b);
	t_2 = y - t_1;
	t_3 = ((z * (t - a)) + (y * x)) / t_2;
	t_4 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -2e-301)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (t / (b - y)) + ((((y * x) / (b - y)) - ((t * y) / ((b - y) ^ 2.0))) / z);
	elseif (t_3 <= 2e+292)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(N[(z * t), $MachinePrecision] / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -2e-301], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(t * y), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+292], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$4, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $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 or 2e292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.9%

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

   3. Taylor expanded in a around -inf 40.9%

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

      1. associate-*r* 40.9%

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

      2. neg-mul-1 40.9%

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

      3. fma-define 40.9%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000013e-301 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e292

   1. Initial program 99.5%

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

   if -2.00000000000000013e-301 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 26.5%

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

   3. Taylor expanded in t around inf 26.5%

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

   4. Taylor expanded in z around -inf 84.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 77.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\frac{t}{b - y} + \frac{\frac{y \cdot x}{b - y} - \frac{t \cdot y}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y - b\right)\\ t_2 := y - t\_1\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{z \cdot \left(t - a\right) + y \cdot x}{t\_2}\\ t_5 := x \cdot \left(\frac{y}{t\_2} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot t\_2} + \frac{z}{t\_1 - y}\right)}{x}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-238}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y b)))
        (t_2 (- y t_1))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ (+ (* z (- t a)) (* y x)) t_2))
        (t_5
         (*
          x
          (+
           (/ y t_2)
           (/ (* a (+ (/ (* z t) (* a t_2)) (/ z (- t_1 y)))) x)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-238)
       t_4
       (if (<= t_4 0.0)
         t_3
         (if (<= t_4 2e+292) t_4 (if (<= t_4 INFINITY) t_5 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (y - b);
	double t_2 = y - t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = ((z * (t - a)) + (y * x)) / t_2;
	double t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-238) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_3;
	} else if (t_4 <= 2e+292) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = z * (y - b);
	double t_2 = y - t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = ((z * (t - a)) + (y * x)) / t_2;
	double t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-238) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_3;
	} else if (t_4 <= 2e+292) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (y - b)
	t_2 = y - t_1
	t_3 = (t - a) / (b - y)
	t_4 = ((z * (t - a)) + (y * x)) / t_2
	t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-238:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = t_3
	elif t_4 <= 2e+292:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(y - b))
	t_2 = Float64(y - t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / t_2)
	t_5 = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(a * Float64(Float64(Float64(z * t) / Float64(a * t_2)) + Float64(z / Float64(t_1 - y)))) / x)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-238)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_3;
	elseif (t_4 <= 2e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (y - b);
	t_2 = y - t_1;
	t_3 = (t - a) / (b - y);
	t_4 = ((z * (t - a)) + (y * x)) / t_2;
	t_5 = x * ((y / t_2) + ((a * (((z * t) / (a * t_2)) + (z / (t_1 - y)))) / x));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-238)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_3;
	elseif (t_4 <= 2e+292)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(a * N[(N[(N[(z * t), $MachinePrecision] / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-238], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$3, If[LessEqual[t$95$4, 2e+292], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$3]]]]]]]]]]

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 2e292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.9%

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

   3. Taylor expanded in a around -inf 40.9%

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

      1. associate-*r* 40.9%

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

      2. neg-mul-1 40.9%

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

      3. fma-define 40.9%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in x around inf 80.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-238 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e292

   1. Initial program 99.5%

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

   if -2e-238 < (/.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 10.9%

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

   3. Taylor expanded in z around inf 78.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -2 \cdot 10^{-238}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{a \cdot \left(\frac{z \cdot t}{a \cdot \left(y - z \cdot \left(y - b\right)\right)} + \frac{z}{z \cdot \left(y - b\right) - y}\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -320000000 \lor \neg \left(z \leq 1.6 \cdot 10^{-6}\right):\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} - \frac{z \cdot \left(a - t\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))))
   (if (or (<= z -320000000.0) (not (<= z 1.6e-6)))
     (+
      (+ (/ t (- b y)) (* (/ x z) (/ y (- b y))))
      (+ (* y (/ (- a t) (* z (pow (- b y) 2.0)))) (/ a (- y b))))
     (* x (- (/ y t_1) (/ (* z (- a t)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -320000000.0) || !(z <= 1.6e-6)) {
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((y * ((a - t) / (z * pow((b - y), 2.0)))) + (a / (y - b)));
	} else {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    if ((z <= (-320000000.0d0)) .or. (.not. (z <= 1.6d-6))) then
        tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((y * ((a - t) / (z * ((b - y) ** 2.0d0)))) + (a / (y - b)))
    else
        tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -320000000.0) || !(z <= 1.6e-6)) {
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((y * ((a - t) / (z * Math.pow((b - y), 2.0)))) + (a / (y - b)));
	} else {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	tmp = 0
	if (z <= -320000000.0) or not (z <= 1.6e-6):
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((y * ((a - t) / (z * math.pow((b - y), 2.0)))) + (a / (y - b)))
	else:
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	tmp = 0.0
	if ((z <= -320000000.0) || !(z <= 1.6e-6))
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) + Float64(Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))) + Float64(a / Float64(y - b))));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) - Float64(Float64(z * Float64(a - t)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	tmp = 0.0;
	if ((z <= -320000000.0) || ~((z <= 1.6e-6)))
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((y * ((a - t) / (z * ((b - y) ^ 2.0)))) + (a / (y - b)));
	else
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -320000000.0], N[Not[LessEqual[z, 1.6e-6]], $MachinePrecision]], N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e8 or 1.5999999999999999e-6 < z

   1. Initial program 41.3%

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

   3. Taylor expanded in z around inf 66.7%

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

      1. times-frac 75.9%

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

      2. associate-/l* 95.8%

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

   5. Simplified 95.8%

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

   if -3.2e8 < z < 1.5999999999999999e-6

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 89.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000 \lor \neg \left(z \leq 1.6 \cdot 10^{-6}\right):\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}} + \frac{a}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} - \frac{z \cdot \left(a - t\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := {\left(b - y\right)}^{2}\\ \mathbf{if}\;z \leq -4200000000:\\ \;\;\;\;\left(t\_2 - \frac{y}{z} \cdot \frac{x}{y - b}\right) + y \cdot \frac{a - t}{z \cdot t\_3}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} - \frac{z \cdot \left(a - t\right)}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - \frac{x \cdot \frac{y}{y - b} - y \cdot \frac{a - t}{t\_3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (pow (- b y) 2.0)))
   (if (<= z -4200000000.0)
     (+ (- t_2 (* (/ y z) (/ x (- y b)))) (* y (/ (- a t) (* z t_3))))
     (if (<= z 1.6e-6)
       (* x (- (/ y t_1) (/ (* z (- a t)) (* x t_1))))
       (- t_2 (/ (- (* x (/ y (- y b))) (* y (/ (- a t) t_3))) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double t_3 = pow((b - y), 2.0);
	double tmp;
	if (z <= -4200000000.0) {
		tmp = (t_2 - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * t_3)));
	} else if (z <= 1.6e-6) {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	} else {
		tmp = t_2 - (((x * (y / (y - b))) - (y * ((a - t) / t_3))) / 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    t_3 = (b - y) ** 2.0d0
    if (z <= (-4200000000.0d0)) then
        tmp = (t_2 - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * t_3)))
    else if (z <= 1.6d-6) then
        tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
    else
        tmp = t_2 - (((x * (y / (y - b))) - (y * ((a - t) / t_3))) / 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 t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double t_3 = Math.pow((b - y), 2.0);
	double tmp;
	if (z <= -4200000000.0) {
		tmp = (t_2 - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * t_3)));
	} else if (z <= 1.6e-6) {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	} else {
		tmp = t_2 - (((x * (y / (y - b))) - (y * ((a - t) / t_3))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (t - a) / (b - y)
	t_3 = math.pow((b - y), 2.0)
	tmp = 0
	if z <= -4200000000.0:
		tmp = (t_2 - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * t_3)))
	elif z <= 1.6e-6:
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
	else:
		tmp = t_2 - (((x * (y / (y - b))) - (y * ((a - t) / t_3))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(b - y) ^ 2.0
	tmp = 0.0
	if (z <= -4200000000.0)
		tmp = Float64(Float64(t_2 - Float64(Float64(y / z) * Float64(x / Float64(y - b)))) + Float64(y * Float64(Float64(a - t) / Float64(z * t_3))));
	elseif (z <= 1.6e-6)
		tmp = Float64(x * Float64(Float64(y / t_1) - Float64(Float64(z * Float64(a - t)) / Float64(x * t_1))));
	else
		tmp = Float64(t_2 - Float64(Float64(Float64(x * Float64(y / Float64(y - b))) - Float64(y * Float64(Float64(a - t) / t_3))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (t - a) / (b - y);
	t_3 = (b - y) ^ 2.0;
	tmp = 0.0;
	if (z <= -4200000000.0)
		tmp = (t_2 - ((y / z) * (x / (y - b)))) + (y * ((a - t) / (z * t_3)));
	elseif (z <= 1.6e-6)
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	else
		tmp = t_2 - (((x * (y / (y - b))) - (y * ((a - t) / t_3))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[z, -4200000000.0], N[(N[(t$95$2 - N[(N[(y / z), $MachinePrecision] * N[(x / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-6], N[(x * N[(N[(y / t$95$1), $MachinePrecision] - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - N[(N[(N[(x * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(a - t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e9

   1. Initial program 38.1%

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

   3. Taylor expanded in z around inf 66.3%

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

      1. associate--r+ 66.3%

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

      2. +-commutative 66.3%

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

      3. associate--l+ 66.3%

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

      4. *-commutative 66.3%

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

      5. times-frac 78.6%

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

      6. div-sub 78.6%

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

      7. associate-/l* 93.5%

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

   5. Simplified 93.5%

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

   if -4.2e9 < z < 1.5999999999999999e-6

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf 89.4%

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

   if 1.5999999999999999e-6 < z

   1. Initial program 43.4%

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

   3. Taylor expanded in z around -inf 70.1%

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

      1. associate--l+ 70.1%

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

      2. mul-1-neg 70.1%

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

      3. distribute-lft-out-- 70.1%

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

      4. associate-/l* 74.3%

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

      5. associate-/l* 93.2%

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

      6. div-sub 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4200000000:\\ \;\;\;\;\left(\frac{t - a}{b - y} - \frac{y}{z} \cdot \frac{x}{y - b}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} - \frac{z \cdot \left(a - t\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x \cdot \frac{y}{y - b} - y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+48} \lor \neg \left(z \leq 5.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} - \frac{z \cdot \left(a - t\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))))
   (if (or (<= z -3.2e+48) (not (<= z 5.6e+63)))
     (/ (- t a) (- b y))
     (* x (- (/ y t_1) (/ (* z (- a t)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -3.2e+48) || !(z <= 5.6e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    if ((z <= (-3.2d+48)) .or. (.not. (z <= 5.6d+63))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double tmp;
	if ((z <= -3.2e+48) || !(z <= 5.6e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	tmp = 0
	if (z <= -3.2e+48) or not (z <= 5.6e+63):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	tmp = 0.0
	if ((z <= -3.2e+48) || !(z <= 5.6e+63))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) - Float64(Float64(z * Float64(a - t)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	tmp = 0.0;
	if ((z <= -3.2e+48) || ~((z <= 5.6e+63)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) - ((z * (a - t)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.2e+48], N[Not[LessEqual[z, 5.6e+63]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000001e48 or 5.59999999999999974e63 < z

   1. Initial program 32.1%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -3.2000000000000001e48 < z < 5.59999999999999974e63

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf 87.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+48} \lor \neg \left(z \leq 5.6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} - \frac{z \cdot \left(a - t\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -78000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;x \cdot \left(1 - \frac{z \cdot a}{y \cdot x}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (- y (* z (- y b))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -78000000.0)
     t_2
     (if (<= z -8.2e-169)
       t_1
       (if (<= z 6.5e-136)
         (* x (- 1.0 (/ (* z a) (* y x))))
         (if (<= z 2.2e+29) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -78000000.0) {
		tmp = t_2;
	} else if (z <= -8.2e-169) {
		tmp = t_1;
	} else if (z <= 6.5e-136) {
		tmp = x * (1.0 - ((z * a) / (y * x)));
	} else if (z <= 2.2e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y - (z * (y - b)))
    t_2 = (t - a) / (b - y)
    if (z <= (-78000000.0d0)) then
        tmp = t_2
    else if (z <= (-8.2d-169)) then
        tmp = t_1
    else if (z <= 6.5d-136) then
        tmp = x * (1.0d0 - ((z * a) / (y * x)))
    else if (z <= 2.2d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -78000000.0) {
		tmp = t_2;
	} else if (z <= -8.2e-169) {
		tmp = t_1;
	} else if (z <= 6.5e-136) {
		tmp = x * (1.0 - ((z * a) / (y * x)));
	} else if (z <= 2.2e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y - (z * (y - b)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -78000000.0:
		tmp = t_2
	elif z <= -8.2e-169:
		tmp = t_1
	elif z <= 6.5e-136:
		tmp = x * (1.0 - ((z * a) / (y * x)))
	elif z <= 2.2e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y - Float64(z * Float64(y - b))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -78000000.0)
		tmp = t_2;
	elseif (z <= -8.2e-169)
		tmp = t_1;
	elseif (z <= 6.5e-136)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(z * a) / Float64(y * x))));
	elseif (z <= 2.2e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y - (z * (y - b)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -78000000.0)
		tmp = t_2;
	elseif (z <= -8.2e-169)
		tmp = t_1;
	elseif (z <= 6.5e-136)
		tmp = x * (1.0 - ((z * a) / (y * x)));
	elseif (z <= 2.2e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -78000000.0], t$95$2, If[LessEqual[z, -8.2e-169], t$95$1, If[LessEqual[z, 6.5e-136], N[(x * N[(1.0 - N[(N[(z * a), $MachinePrecision] / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8e7 or 2.2000000000000001e29 < z

   1. Initial program 37.2%

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

   3. Taylor expanded in z around inf 78.8%

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

   if -7.8e7 < z < -8.1999999999999996e-169 or 6.50000000000000011e-136 < z < 2.2000000000000001e29

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 65.8%

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

   if -8.1999999999999996e-169 < z < 6.50000000000000011e-136

   1. Initial program 82.8%

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

   3. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in z around 0 58.8%

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

   7. Taylor expanded in x around -inf 68.4%

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

      1. associate-*r* 68.4%

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

      2. mul-1-neg 68.4%

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

      3. sub-neg 68.4%

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

      4. *-commutative 68.4%

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

      5. *-commutative 68.4%

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

      6. metadata-eval 68.4%

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

   9. Simplified 68.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -78000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;x \cdot \left(1 - \frac{z \cdot a}{y \cdot x}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5e-64)
     t_1
     (if (<= z -2.3e-215)
       (/ (* y x) (- y (* z (- y b))))
       (if (<= z 9e-169)
         (* a (- (/ x a) (/ z y)))
         (if (<= z 7.5) (/ (- (+ t (/ (* y x) z)) a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e-64) {
		tmp = t_1;
	} else if (z <= -2.3e-215) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 9e-169) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= 7.5) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-5d-64)) then
        tmp = t_1
    else if (z <= (-2.3d-215)) then
        tmp = (y * x) / (y - (z * (y - b)))
    else if (z <= 9d-169) then
        tmp = a * ((x / a) - (z / y))
    else if (z <= 7.5d0) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e-64) {
		tmp = t_1;
	} else if (z <= -2.3e-215) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 9e-169) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= 7.5) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -5e-64:
		tmp = t_1
	elif z <= -2.3e-215:
		tmp = (y * x) / (y - (z * (y - b)))
	elif z <= 9e-169:
		tmp = a * ((x / a) - (z / y))
	elif z <= 7.5:
		tmp = ((t + ((y * x) / z)) - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5e-64)
		tmp = t_1;
	elseif (z <= -2.3e-215)
		tmp = Float64(Float64(y * x) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 9e-169)
		tmp = Float64(a * Float64(Float64(x / a) - Float64(z / y)));
	elseif (z <= 7.5)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5e-64)
		tmp = t_1;
	elseif (z <= -2.3e-215)
		tmp = (y * x) / (y - (z * (y - b)));
	elseif (z <= 9e-169)
		tmp = a * ((x / a) - (z / y));
	elseif (z <= 7.5)
		tmp = ((t + ((y * x) / z)) - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-64], t$95$1, If[LessEqual[z, -2.3e-215], N[(N[(y * x), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-169], N[(a * N[(N[(x / a), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.00000000000000033e-64 or 7.5 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in z around inf 77.5%

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

   if -5.00000000000000033e-64 < z < -2.2999999999999999e-215

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 46.4%

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

      1. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   if -2.2999999999999999e-215 < z < 8.9999999999999997e-169

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around 0 66.2%

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

   7. Taylor expanded in a around inf 67.5%

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

   if 8.9999999999999997e-169 < z < 7.5

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. associate--r+ 46.7%

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

      2. +-commutative 46.7%

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

      3. associate--l+ 46.7%

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

      4. *-commutative 46.7%

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

      5. times-frac 46.7%

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

      6. div-sub 46.7%

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

      7. associate-/l* 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in b around inf 50.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;\frac{t - \left(a - x \cdot \frac{y}{z}\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e-64)
     t_1
     (if (<= z -1.12e-216)
       (/ (* y x) (- y (* z (- y b))))
       (if (<= z 1.48e-167)
         (* a (- (/ x a) (/ z y)))
         (if (<= z 6.5) (/ (- t (- a (* x (/ y z)))) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e-64) {
		tmp = t_1;
	} else if (z <= -1.12e-216) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.48e-167) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= 6.5) {
		tmp = (t - (a - (x * (y / z)))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-4d-64)) then
        tmp = t_1
    else if (z <= (-1.12d-216)) then
        tmp = (y * x) / (y - (z * (y - b)))
    else if (z <= 1.48d-167) then
        tmp = a * ((x / a) - (z / y))
    else if (z <= 6.5d0) then
        tmp = (t - (a - (x * (y / z)))) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -4e-64) {
		tmp = t_1;
	} else if (z <= -1.12e-216) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.48e-167) {
		tmp = a * ((x / a) - (z / y));
	} else if (z <= 6.5) {
		tmp = (t - (a - (x * (y / z)))) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -4e-64:
		tmp = t_1
	elif z <= -1.12e-216:
		tmp = (y * x) / (y - (z * (y - b)))
	elif z <= 1.48e-167:
		tmp = a * ((x / a) - (z / y))
	elif z <= 6.5:
		tmp = (t - (a - (x * (y / z)))) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4e-64)
		tmp = t_1;
	elseif (z <= -1.12e-216)
		tmp = Float64(Float64(y * x) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 1.48e-167)
		tmp = Float64(a * Float64(Float64(x / a) - Float64(z / y)));
	elseif (z <= 6.5)
		tmp = Float64(Float64(t - Float64(a - Float64(x * Float64(y / z)))) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4e-64)
		tmp = t_1;
	elseif (z <= -1.12e-216)
		tmp = (y * x) / (y - (z * (y - b)));
	elseif (z <= 1.48e-167)
		tmp = a * ((x / a) - (z / y));
	elseif (z <= 6.5)
		tmp = (t - (a - (x * (y / z)))) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e-64], t$95$1, If[LessEqual[z, -1.12e-216], N[(N[(y * x), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.48e-167], N[(a * N[(N[(x / a), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5], N[(N[(t - N[(a - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.99999999999999986e-64 or 6.5 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in z around inf 77.5%

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

   if -3.99999999999999986e-64 < z < -1.12e-216

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 46.4%

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

      1. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   if -1.12e-216 < z < 1.47999999999999999e-167

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around 0 66.2%

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

   7. Taylor expanded in a around inf 67.5%

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

   if 1.47999999999999999e-167 < z < 6.5

   1. Initial program 90.4%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. associate--r+ 46.7%

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

      2. +-commutative 46.7%

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

      3. associate--l+ 46.7%

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

      4. *-commutative 46.7%

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

      5. times-frac 46.7%

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

      6. div-sub 46.7%

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

      7. associate-/l* 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in b around inf 50.7%

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

      1. associate--l+ 50.7%

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

      2. associate-/l* 50.5%

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

   8. Simplified 50.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;\frac{t - \left(a - x \cdot \frac{y}{z}\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{t\_1}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.6e-64)
     t_2
     (if (<= z 1.6e-138)
       (/ (- (* y x) (* z a)) t_1)
       (if (<= z 2.2e+29) (/ (* z (- t a)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.6e-64) {
		tmp = t_2;
	} else if (z <= 1.6e-138) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (z <= 2.2e+29) {
		tmp = (z * (t - a)) / 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 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    if (z <= (-4.6d-64)) then
        tmp = t_2
    else if (z <= 1.6d-138) then
        tmp = ((y * x) - (z * a)) / t_1
    else if (z <= 2.2d+29) then
        tmp = (z * (t - a)) / 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 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.6e-64) {
		tmp = t_2;
	} else if (z <= 1.6e-138) {
		tmp = ((y * x) - (z * a)) / t_1;
	} else if (z <= 2.2e+29) {
		tmp = (z * (t - a)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.6e-64:
		tmp = t_2
	elif z <= 1.6e-138:
		tmp = ((y * x) - (z * a)) / t_1
	elif z <= 2.2e+29:
		tmp = (z * (t - a)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.6e-64)
		tmp = t_2;
	elseif (z <= 1.6e-138)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / t_1);
	elseif (z <= 2.2e+29)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.6e-64)
		tmp = t_2;
	elseif (z <= 1.6e-138)
		tmp = ((y * x) - (z * a)) / t_1;
	elseif (z <= 2.2e+29)
		tmp = (z * (t - a)) / t_1;
	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[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-64], t$95$2, If[LessEqual[z, 1.6e-138], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.2e+29], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000003e-64 or 2.2000000000000001e29 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in z around inf 77.6%

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

   if -4.6000000000000003e-64 < z < 1.60000000000000005e-138

   1. Initial program 84.7%

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

   3. Taylor expanded in t around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if 1.60000000000000005e-138 < z < 2.2000000000000001e29

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 70.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-138}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42} \lor \neg \left(z \leq 4.4 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e+42) (not (<= z 4.4e+63)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e+42) || !(z <= 4.4e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.5d+42)) .or. (.not. (z <= 4.4d+63))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e+42) || !(z <= 4.4e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e+42) or not (z <= 4.4e+63):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.5e+42) || !(z <= 4.4e+63))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y - Float64(z * Float64(y - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.5e+42) || ~((z <= 4.4e+63)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.5e+42], N[Not[LessEqual[z, 4.4e+63]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000003e42 or 4.3999999999999997e63 < z

   1. Initial program 32.1%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -2.50000000000000003e42 < z < 4.3999999999999997e63

   1. Initial program 86.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42} \lor \neg \left(z \leq 4.4 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.55 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-64) (not (<= z 1.55e-6)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z t)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-64) || !(z <= 1.55e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * t)) / (y - (z * (y - 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 <= (-6d-64)) .or. (.not. (z <= 1.55d-6))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * t)) / (y - (z * (y - 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 <= -6e-64) || !(z <= 1.55e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-64) or not (z <= 1.55e-6):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-64) || !(z <= 1.55e-6))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y - Float64(z * Float64(y - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-64) || ~((z <= 1.55e-6)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * t)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-64], N[Not[LessEqual[z, 1.55e-6]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000001e-64 or 1.55e-6 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in z around inf 77.1%

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

   if -6.0000000000000001e-64 < z < 1.55e-6

   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 inf 64.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.55 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5e-64)
     t_1
     (if (<= z -3.1e-216)
       (/ (* y x) (- y (* z (- y b))))
       (if (<= z 1.38e-167) (* a (- (/ x a) (/ 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 <= -5e-64) {
		tmp = t_1;
	} else if (z <= -3.1e-216) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.38e-167) {
		tmp = a * ((x / a) - (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 <= (-5d-64)) then
        tmp = t_1
    else if (z <= (-3.1d-216)) then
        tmp = (y * x) / (y - (z * (y - b)))
    else if (z <= 1.38d-167) then
        tmp = a * ((x / a) - (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 <= -5e-64) {
		tmp = t_1;
	} else if (z <= -3.1e-216) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.38e-167) {
		tmp = a * ((x / a) - (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 <= -5e-64:
		tmp = t_1
	elif z <= -3.1e-216:
		tmp = (y * x) / (y - (z * (y - b)))
	elif z <= 1.38e-167:
		tmp = a * ((x / a) - (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 <= -5e-64)
		tmp = t_1;
	elseif (z <= -3.1e-216)
		tmp = Float64(Float64(y * x) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 1.38e-167)
		tmp = Float64(a * Float64(Float64(x / a) - 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 <= -5e-64)
		tmp = t_1;
	elseif (z <= -3.1e-216)
		tmp = (y * x) / (y - (z * (y - b)));
	elseif (z <= 1.38e-167)
		tmp = a * ((x / a) - (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, -5e-64], t$95$1, If[LessEqual[z, -3.1e-216], N[(N[(y * x), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-167], N[(a * N[(N[(x / a), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000033e-64 or 1.38e-167 < z

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -5.00000000000000033e-64 < z < -3.1000000000000002e-216

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 46.4%

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

      1. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   if -3.1000000000000002e-216 < z < 1.38e-167

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around 0 66.2%

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

   7. Taylor expanded in a around inf 67.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.6e-64)
     t_1
     (if (<= z -6.2e-216)
       (/ (+ (* y x) (* z t)) y)
       (if (<= z 4.45e-169) (* a (- (/ x a) (/ 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 <= -5.6e-64) {
		tmp = t_1;
	} else if (z <= -6.2e-216) {
		tmp = ((y * x) + (z * t)) / y;
	} else if (z <= 4.45e-169) {
		tmp = a * ((x / a) - (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 <= (-5.6d-64)) then
        tmp = t_1
    else if (z <= (-6.2d-216)) then
        tmp = ((y * x) + (z * t)) / y
    else if (z <= 4.45d-169) then
        tmp = a * ((x / a) - (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 <= -5.6e-64) {
		tmp = t_1;
	} else if (z <= -6.2e-216) {
		tmp = ((y * x) + (z * t)) / y;
	} else if (z <= 4.45e-169) {
		tmp = a * ((x / a) - (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 <= -5.6e-64:
		tmp = t_1
	elif z <= -6.2e-216:
		tmp = ((y * x) + (z * t)) / y
	elif z <= 4.45e-169:
		tmp = a * ((x / a) - (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 <= -5.6e-64)
		tmp = t_1;
	elseif (z <= -6.2e-216)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / y);
	elseif (z <= 4.45e-169)
		tmp = Float64(a * Float64(Float64(x / a) - 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 <= -5.6e-64)
		tmp = t_1;
	elseif (z <= -6.2e-216)
		tmp = ((y * x) + (z * t)) / y;
	elseif (z <= 4.45e-169)
		tmp = a * ((x / a) - (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, -5.6e-64], t$95$1, If[LessEqual[z, -6.2e-216], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.45e-169], N[(a * N[(N[(x / a), $MachinePrecision] - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000008e-64 or 4.44999999999999971e-169 < z

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -5.60000000000000008e-64 < z < -6.2000000000000004e-216

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf 70.9%

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

   4. Taylor expanded in z around 0 44.6%

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

   if -6.2000000000000004e-216 < z < 4.44999999999999971e-169

   1. Initial program 83.6%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

      5. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in z around 0 66.2%

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

   7. Taylor expanded in a around inf 67.5%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-216}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(\frac{x}{a} - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-199}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-167}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.6e-64)
     t_1
     (if (<= z -7e-199)
       (/ (+ (* y x) (* z t)) y)
       (if (<= z 1.38e-167) (/ (- (* y x) (* 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 <= -5.6e-64) {
		tmp = t_1;
	} else if (z <= -7e-199) {
		tmp = ((y * x) + (z * t)) / y;
	} else if (z <= 1.38e-167) {
		tmp = ((y * x) - (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 <= (-5.6d-64)) then
        tmp = t_1
    else if (z <= (-7d-199)) then
        tmp = ((y * x) + (z * t)) / y
    else if (z <= 1.38d-167) then
        tmp = ((y * x) - (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 <= -5.6e-64) {
		tmp = t_1;
	} else if (z <= -7e-199) {
		tmp = ((y * x) + (z * t)) / y;
	} else if (z <= 1.38e-167) {
		tmp = ((y * x) - (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 <= -5.6e-64:
		tmp = t_1
	elif z <= -7e-199:
		tmp = ((y * x) + (z * t)) / y
	elif z <= 1.38e-167:
		tmp = ((y * x) - (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 <= -5.6e-64)
		tmp = t_1;
	elseif (z <= -7e-199)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * t)) / y);
	elseif (z <= 1.38e-167)
		tmp = Float64(Float64(Float64(y * x) - 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 <= -5.6e-64)
		tmp = t_1;
	elseif (z <= -7e-199)
		tmp = ((y * x) + (z * t)) / y;
	elseif (z <= 1.38e-167)
		tmp = ((y * x) - (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, -5.6e-64], t$95$1, If[LessEqual[z, -7e-199], N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.38e-167], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000008e-64 or 1.38e-167 < z

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -5.60000000000000008e-64 < z < -6.9999999999999998e-199

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 66.4%

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

   4. Taylor expanded in z around 0 42.0%

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

   if -6.9999999999999998e-199 < z < 1.38e-167

   1. Initial program 85.0%

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

   3. Taylor expanded in t around 0 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. *-commutative 74.3%

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

      5. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in z around 0 65.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-199}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-167}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-64} \lor \neg \left(z \leq 1.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z \cdot a}{y \cdot x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e-64) (not (<= z 1.2e-43)))
   (/ (- t a) (- b y))
   (* x (- 1.0 (/ (* z a) (* y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-64) || !(z <= 1.2e-43)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (1.0 - ((z * a) / (y * 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 <= (-2.8d-64)) .or. (.not. (z <= 1.2d-43))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * (1.0d0 - ((z * a) / (y * 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 <= -2.8e-64) || !(z <= 1.2e-43)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (1.0 - ((z * a) / (y * x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e-64) or not (z <= 1.2e-43):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * (1.0 - ((z * a) / (y * x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e-64) || !(z <= 1.2e-43))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(1.0 - Float64(Float64(z * a) / Float64(y * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e-64) || ~((z <= 1.2e-43)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * (1.0 - ((z * a) / (y * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e-64], N[Not[LessEqual[z, 1.2e-43]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(N[(z * a), $MachinePrecision] / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000004e-64 or 1.2000000000000001e-43 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in z around inf 75.5%

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

   if -2.80000000000000004e-64 < z < 1.2000000000000001e-43

   1. Initial program 85.8%

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

   3. Taylor expanded in t around 0 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

      5. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in z around 0 46.9%

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

   7. Taylor expanded in x around -inf 56.7%

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

      1. associate-*r* 56.7%

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

      2. mul-1-neg 56.7%

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

      3. sub-neg 56.7%

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

      4. *-commutative 56.7%

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

      5. *-commutative 56.7%

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

      6. metadata-eval 56.7%

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

   9. Simplified 56.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-64} \lor \neg \left(z \leq 1.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z \cdot a}{y \cdot x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 0.000215:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e-32)
   x
   (if (<= y 8.8e-196) (/ t b) (if (<= y 0.000215) (/ a (- b)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-32) {
		tmp = x;
	} else if (y <= 8.8e-196) {
		tmp = t / b;
	} else if (y <= 0.000215) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.8d-32)) then
        tmp = x
    else if (y <= 8.8d-196) then
        tmp = t / b
    else if (y <= 0.000215d0) then
        tmp = a / -b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e-32) {
		tmp = x;
	} else if (y <= 8.8e-196) {
		tmp = t / b;
	} else if (y <= 0.000215) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e-32:
		tmp = x
	elif y <= 8.8e-196:
		tmp = t / b
	elif y <= 0.000215:
		tmp = a / -b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e-32)
		tmp = x;
	elseif (y <= 8.8e-196)
		tmp = Float64(t / b);
	elseif (y <= 0.000215)
		tmp = Float64(a / Float64(-b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e-32)
		tmp = x;
	elseif (y <= 8.8e-196)
		tmp = t / b;
	elseif (y <= 0.000215)
		tmp = a / -b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e-32], x, If[LessEqual[y, 8.8e-196], N[(t / b), $MachinePrecision], If[LessEqual[y, 0.000215], N[(a / (-b)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999996e-32 or 2.14999999999999995e-4 < y

   1. Initial program 53.4%

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

   3. Taylor expanded in z around 0 37.8%

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

   if -1.79999999999999996e-32 < y < 8.8000000000000006e-196

   1. Initial program 80.2%

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

   3. Taylor expanded in t around inf 53.7%

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

   4. Taylor expanded in y around 0 43.8%

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

   if 8.8000000000000006e-196 < y < 2.14999999999999995e-4

   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 t around 0 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

      4. *-commutative 57.5%

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

      5. *-commutative 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in y around 0 33.4%

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

      1. associate-*r/ 33.4%

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

      2. mul-1-neg 33.4%

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

   8. Simplified 33.4%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 0.000215:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8e-64) (not (<= z 8.5e-139)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-64) || !(z <= 8.5e-139)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.8d-64)) .or. (.not. (z <= 8.5d-139))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-64) || !(z <= 8.5e-139)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.8e-64) or not (z <= 8.5e-139):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.8e-64) || !(z <= 8.5e-139))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.8e-64) || ~((z <= 8.5e-139)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.8e-64], N[Not[LessEqual[z, 8.5e-139]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999998e-64 or 8.5000000000000003e-139 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 69.0%

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

   if -5.7999999999999998e-64 < z < 8.5000000000000003e-139

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-32} \lor \neg \left(y \leq 0.00035\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e-32) (not (<= y 0.00035))) (/ 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 <= -2e-32) || !(y <= 0.00035)) {
		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 <= (-2d-32)) .or. (.not. (y <= 0.00035d0))) 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 <= -2e-32) || !(y <= 0.00035)) {
		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 <= -2e-32) or not (y <= 0.00035):
		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 <= -2e-32) || !(y <= 0.00035))
		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 <= -2e-32) || ~((y <= 0.00035)))
		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, -2e-32], N[Not[LessEqual[y, 0.00035]], $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 < -2.00000000000000011e-32 or 3.49999999999999996e-4 < y

   1. Initial program 53.4%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   if -2.00000000000000011e-32 < y < 3.49999999999999996e-4

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 59.1%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-32} \lor \neg \left(y \leq 0.00035\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+38} \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.2e+38) (not (<= y 14000.0))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.2e+38) || !(y <= 14000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.2d+38)) .or. (.not. (y <= 14000.0d0))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.2e+38) || !(y <= 14000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.2e+38) or not (y <= 14000.0):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.2e+38) || !(y <= 14000.0))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.2e+38) || ~((y <= 14000.0)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.2e+38], N[Not[LessEqual[y, 14000.0]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e38 or 14000 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

   5. Simplified 54.7%

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

   if -5.1999999999999998e38 < y < 14000

   1. Initial program 77.7%

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

   3. Taylor expanded in t around inf 51.3%

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

   4. Taylor expanded in z around inf 39.5%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+38} \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 43.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.05 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-64) (not (<= z 1.05e-44))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-64) || !(z <= 1.05e-44)) {
		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 <= (-6d-64)) .or. (.not. (z <= 1.05d-44))) 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 <= -6e-64) || !(z <= 1.05e-44)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-64) or not (z <= 1.05e-44):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-64) || !(z <= 1.05e-44))
		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 <= -6e-64) || ~((z <= 1.05e-44)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-64], N[Not[LessEqual[z, 1.05e-44]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000001e-64 or 1.05000000000000001e-44 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in t around inf 33.9%

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

   4. Taylor expanded in z around inf 42.8%

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

   if -6.0000000000000001e-64 < z < 1.05000000000000001e-44

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 46.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.05 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 34.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e-32) x (if (<= y 4.4e-48) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-32) {
		tmp = x;
	} else if (y <= 4.4e-48) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d-32)) then
        tmp = x
    else if (y <= 4.4d-48) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e-32) {
		tmp = x;
	} else if (y <= 4.4e-48) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e-32:
		tmp = x
	elif y <= 4.4e-48:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e-32)
		tmp = x;
	elseif (y <= 4.4e-48)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e-32)
		tmp = x;
	elseif (y <= 4.4e-48)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e-32], x, If[LessEqual[y, 4.4e-48], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999989e-32 or 4.40000000000000025e-48 < y

   1. Initial program 54.4%

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

   3. Taylor expanded in z around 0 35.6%

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

   if -1.69999999999999989e-32 < y < 4.40000000000000025e-48

   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 t around inf 54.8%

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

   4. Taylor expanded in y around 0 39.5%

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

Alternative 23: 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 66.3%

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

3. Taylor expanded in z around 0 23.9%

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

Developer Target 1: 74.4% 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 2024137 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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