Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.6% → 96.8%

Time: 28.8s

Alternatives: 20

Speedup: 0.6×

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: 65.6% 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: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{x}{1 - z} + t_2\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -1e-288)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_4 0.0)
         (+
          t_2
          (/ (- (/ (* x y) (- b y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z))
         (if (<= t_4 2e+306) (+ (/ (* x y) t_1) (/ t_3 t_1)) t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -1e-288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((((x * y) / (b - y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z);
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -1e-288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((((x * y) / (b - y)) - (y / (Math.pow((b - y), 2.0) / (t - a)))) / z);
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -1e-288:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_4 <= 0.0:
		tmp = t_2 + ((((x * y) / (b - y)) - (y / (math.pow((b - y), 2.0) / (t - a)))) / z)
	elif t_4 <= 2e+306:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -1e-288)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z));
	elseif (t_4 <= 2e+306)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -1e-288)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_4 <= 0.0)
		tmp = t_2 + ((((x * y) / (b - y)) - (y / (((b - y) ^ 2.0) / (t - a)))) / z);
	elseif (t_4 <= 2e+306)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -1e-288], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+306], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]

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

   1. Initial program 18.8%

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

   3. Taylor expanded in x around 0 18.8%

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

   4. Taylor expanded in z around inf 59.1%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. unsub-neg 87.6%

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

   7. Simplified 87.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000006e-288

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   4. Applied egg-rr 99.4%

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

   if -1.00000000000000006e-288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 26.2%

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

   3. Taylor expanded in z around -inf 89.7%

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

      1. associate--l+ 89.7%

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

      2. mul-1-neg 89.7%

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

      3. distribute-lft-out-- 89.7%

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

      4. *-commutative 89.7%

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

      5. associate-/l* 95.0%

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

      6. div-sub 95.0%

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

   5. Simplified 95.0%

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

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

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{x}{1 - z} + t_2\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\left(t_2 + \frac{x}{\frac{z}{\frac{y}{b - y}}}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -1e-288)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_4 0.0)
         (-
          (+ t_2 (/ x (/ z (/ y (- b y)))))
          (* (/ y z) (/ (- t a) (pow (- b y) 2.0))))
         (if (<= t_4 2e+306) (+ (/ (* x y) t_1) (/ t_3 t_1)) t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -1e-288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = (t_2 + (x / (z / (y / (b - y))))) - ((y / z) * ((t - a) / pow((b - y), 2.0)));
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -1e-288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = (t_2 + (x / (z / (y / (b - y))))) - ((y / z) * ((t - a) / Math.pow((b - y), 2.0)));
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -1e-288:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_4 <= 0.0:
		tmp = (t_2 + (x / (z / (y / (b - y))))) - ((y / z) * ((t - a) / math.pow((b - y), 2.0)))
	elif t_4 <= 2e+306:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -1e-288)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(t_2 + Float64(x / Float64(z / Float64(y / Float64(b - y))))) - Float64(Float64(y / z) * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))));
	elseif (t_4 <= 2e+306)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -1e-288)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_4 <= 0.0)
		tmp = (t_2 + (x / (z / (y / (b - y))))) - ((y / z) * ((t - a) / ((b - y) ^ 2.0)));
	elseif (t_4 <= 2e+306)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -1e-288], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(t$95$2 + N[(x / N[(z / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+306], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]

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

   1. Initial program 18.8%

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

   3. Taylor expanded in x around 0 18.8%

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

   4. Taylor expanded in z around inf 59.1%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. unsub-neg 87.6%

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

   7. Simplified 87.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000006e-288

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   4. Applied egg-rr 99.4%

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

   if -1.00000000000000006e-288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 26.2%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate--r+ 70.8%

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

      2. +-commutative 70.8%

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

      3. associate--l+ 70.8%

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

      4. associate-/l* 74.2%

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

      5. associate-/l* 88.2%

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

      6. div-sub 88.2%

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

      7. times-frac 93.4%

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

   5. Simplified 93.4%

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

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

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{x}{\frac{z}{\frac{y}{b - y}}}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{x}{1 - z} + t_2\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-273)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_4 0.0)
         (+ t_2 (* (/ y z) (/ x b)))
         (if (<= t_4 2e+306) (+ (/ (* x y) t_1) (/ t_3 t_1)) t_5))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-273) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((y / z) * (x / b));
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-273) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + ((y / z) * (x / b));
	} else if (t_4 <= 2e+306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-273:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_4 <= 0.0:
		tmp = t_2 + ((y / z) * (x / b))
	elif t_4 <= 2e+306:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-273)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(y / z) * Float64(x / b)));
	elseif (t_4 <= 2e+306)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-273)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_4 <= 0.0)
		tmp = t_2 + ((y / z) * (x / b));
	elseif (t_4 <= 2e+306)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-273], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(y / z), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+306], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]]]

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

   1. Initial program 18.8%

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

   3. Taylor expanded in x around 0 18.8%

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

   4. Taylor expanded in z around inf 59.1%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. unsub-neg 87.6%

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

   7. Simplified 87.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-273

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   4. Applied egg-rr 99.4%

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

   if -2e-273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 29.9%

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

   3. Taylor expanded in x around 0 29.9%

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

   4. Taylor expanded in z around inf 77.3%

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

      1. div-inv 77.2%

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

      2. *-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. fma-def 77.2%

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

   6. Applied egg-rr 77.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. times-frac 79.9%

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

   9. Simplified 79.9%

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

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

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z} + t_1\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1 + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (+ (/ x (- 1.0 z)) t_1)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-273)
       t_2
       (if (<= t_2 0.0)
         (+ t_1 (* (/ y z) (/ x b)))
         (if (<= t_2 2e+306) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-273) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} 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 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-273) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1 + ((y / z) * (x / b));
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_3 = (x / (1.0 - z)) + t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-273:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1 + ((y / z) * (x / b))
	elif t_2 <= 2e+306:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-273)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 + Float64(Float64(y / z) * Float64(x / b)));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_3 = (x / (1.0 - z)) + t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-273)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1 + ((y / z) * (x / b));
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-273], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, 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 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.8%

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

   3. Taylor expanded in x around 0 18.8%

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

   4. Taylor expanded in z around inf 59.1%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. unsub-neg 87.6%

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

   7. Simplified 87.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-273 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.5%

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

   if -2e-273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 29.9%

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

   3. Taylor expanded in x around 0 29.9%

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

   4. Taylor expanded in z around inf 77.3%

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

      1. div-inv 77.2%

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

      2. *-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. fma-def 77.2%

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

   6. Applied egg-rr 77.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. times-frac 79.9%

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

   9. Simplified 79.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := \frac{x}{1 - z} + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2 + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -2e-273)
       (/ (+ (* x y) (- (* z t) (* z a))) t_1)
       (if (<= t_3 0.0)
         (+ t_2 (* (/ y z) (/ x b)))
         (if (<= t_3 2e+306) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -2e-273) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = t_2 + ((y / z) * (x / b));
	} else if (t_3 <= 2e+306) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -2e-273) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = t_2 + ((y / z) * (x / b));
	} else if (t_3 <= 2e+306) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -2e-273:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	elif t_3 <= 0.0:
		tmp = t_2 + ((y / z) * (x / b))
	elif t_3 <= 2e+306:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -2e-273)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(y / z) * Float64(x / b)));
	elseif (t_3 <= 2e+306)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -2e-273)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	elseif (t_3 <= 0.0)
		tmp = t_2 + ((y / z) * (x / b));
	elseif (t_3 <= 2e+306)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -2e-273], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$2 + N[(N[(y / z), $MachinePrecision] * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+306], t$95$3, t$95$4]]]]]]]]

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

   1. Initial program 18.8%

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

   3. Taylor expanded in x around 0 18.8%

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

   4. Taylor expanded in z around inf 59.1%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. neg-mul-1 87.6%

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

      2. unsub-neg 87.6%

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

   7. Simplified 87.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-273

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. distribute-lft-in 99.4%

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

   4. Applied egg-rr 99.4%

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

   if -2e-273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 29.9%

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

   3. Taylor expanded in x around 0 29.9%

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

   4. Taylor expanded in z around inf 77.3%

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

      1. div-inv 77.2%

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

      2. *-commutative 77.2%

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

      3. +-commutative 77.2%

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

      4. fma-def 77.2%

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

   6. Applied egg-rr 77.2%

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

   7. Taylor expanded in y around 0 67.4%

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

      1. times-frac 79.9%

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

   9. Simplified 79.9%

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

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

   1. Initial program 99.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-273}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= z -1.15e+143)
     t_2
     (if (<= z -2.6e+86)
       (/ (- (/ x (/ z y)) (- a t)) b)
       (if (<= z -3.2e-43)
         t_2
         (if (<= z 1.4e-133)
           (+ x (/ t_1 y))
           (if (<= z 1.56e-46)
             (/ (+ t (- (* y (/ x z)) a)) b)
             (if (<= z 7e+18) (+ x (/ t_1 (* y (- 1.0 z)))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -1.15e+143) {
		tmp = t_2;
	} else if (z <= -2.6e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -3.2e-43) {
		tmp = t_2;
	} else if (z <= 1.4e-133) {
		tmp = x + (t_1 / y);
	} else if (z <= 1.56e-46) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 7e+18) {
		tmp = x + (t_1 / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    if (z <= (-1.15d+143)) then
        tmp = t_2
    else if (z <= (-2.6d+86)) then
        tmp = ((x / (z / y)) - (a - t)) / b
    else if (z <= (-3.2d-43)) then
        tmp = t_2
    else if (z <= 1.4d-133) then
        tmp = x + (t_1 / y)
    else if (z <= 1.56d-46) then
        tmp = (t + ((y * (x / z)) - a)) / b
    else if (z <= 7d+18) then
        tmp = x + (t_1 / (y * (1.0d0 - z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -1.15e+143) {
		tmp = t_2;
	} else if (z <= -2.6e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -3.2e-43) {
		tmp = t_2;
	} else if (z <= 1.4e-133) {
		tmp = x + (t_1 / y);
	} else if (z <= 1.56e-46) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 7e+18) {
		tmp = x + (t_1 / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if z <= -1.15e+143:
		tmp = t_2
	elif z <= -2.6e+86:
		tmp = ((x / (z / y)) - (a - t)) / b
	elif z <= -3.2e-43:
		tmp = t_2
	elif z <= 1.4e-133:
		tmp = x + (t_1 / y)
	elif z <= 1.56e-46:
		tmp = (t + ((y * (x / z)) - a)) / b
	elif z <= 7e+18:
		tmp = x + (t_1 / (y * (1.0 - z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -1.15e+143)
		tmp = t_2;
	elseif (z <= -2.6e+86)
		tmp = Float64(Float64(Float64(x / Float64(z / y)) - Float64(a - t)) / b);
	elseif (z <= -3.2e-43)
		tmp = t_2;
	elseif (z <= 1.4e-133)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 1.56e-46)
		tmp = Float64(Float64(t + Float64(Float64(y * Float64(x / z)) - a)) / b);
	elseif (z <= 7e+18)
		tmp = Float64(x + Float64(t_1 / Float64(y * Float64(1.0 - z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -1.15e+143)
		tmp = t_2;
	elseif (z <= -2.6e+86)
		tmp = ((x / (z / y)) - (a - t)) / b;
	elseif (z <= -3.2e-43)
		tmp = t_2;
	elseif (z <= 1.4e-133)
		tmp = x + (t_1 / y);
	elseif (z <= 1.56e-46)
		tmp = (t + ((y * (x / z)) - a)) / b;
	elseif (z <= 7e+18)
		tmp = x + (t_1 / (y * (1.0 - z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+143], t$95$2, If[LessEqual[z, -2.6e+86], N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a - t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -3.2e-43], t$95$2, If[LessEqual[z, 1.4e-133], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e-46], N[(N[(t + N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 7e+18], N[(x + N[(t$95$1 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.15e143 or -2.5999999999999998e86 < z < -3.19999999999999985e-43 or 7e18 < z

   1. Initial program 43.3%

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

   3. Taylor expanded in x around 0 43.3%

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

   4. Taylor expanded in z around inf 83.5%

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

   5. Taylor expanded in y around inf 86.8%

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

      1. neg-mul-1 86.8%

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

      2. unsub-neg 86.8%

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

   7. Simplified 86.8%

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

   if -1.15e143 < z < -2.5999999999999998e86

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in b around inf 83.6%

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

      1. associate-+r+ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. sub-neg 83.6%

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

      4. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -3.19999999999999985e-43 < z < 1.3999999999999999e-133

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in z around 0 88.3%

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

   5. Taylor expanded in z around 0 79.8%

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

   if 1.3999999999999999e-133 < z < 1.55999999999999991e-46

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in z around inf 83.1%

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

      1. times-frac 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in b around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-*l/ 72.4%

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

      3. *-commutative 72.4%

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

   9. Simplified 72.4%

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

   if 1.55999999999999991e-46 < z < 7e18

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 92.9%

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

   4. Taylor expanded in z around 0 70.6%

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

   5. Taylor expanded in y around inf 59.6%

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

      1. neg-mul-1 59.6%

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

      2. unsub-neg 59.6%

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

   7. Simplified 59.6%

      \[\leadsto x + \frac{z \cdot \left(t - a\right)}{\color{blue}{y \cdot \left(1 - z\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{-46}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= z -2.1e+143)
     t_2
     (if (<= z -2.3e+86)
       (/ (- (/ x (/ z y)) (- a t)) b)
       (if (<= z -1.7e-38)
         t_2
         (if (<= z 2.55e-135)
           (+ x (/ t_1 y))
           (if (<= z 750000000.0) (/ t_1 (+ y (* z (- b y)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -2.1e+143) {
		tmp = t_2;
	} else if (z <= -2.3e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -1.7e-38) {
		tmp = t_2;
	} else if (z <= 2.55e-135) {
		tmp = x + (t_1 / y);
	} else if (z <= 750000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    if (z <= (-2.1d+143)) then
        tmp = t_2
    else if (z <= (-2.3d+86)) then
        tmp = ((x / (z / y)) - (a - t)) / b
    else if (z <= (-1.7d-38)) then
        tmp = t_2
    else if (z <= 2.55d-135) then
        tmp = x + (t_1 / y)
    else if (z <= 750000000.0d0) then
        tmp = t_1 / (y + (z * (b - y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -2.1e+143) {
		tmp = t_2;
	} else if (z <= -2.3e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -1.7e-38) {
		tmp = t_2;
	} else if (z <= 2.55e-135) {
		tmp = x + (t_1 / y);
	} else if (z <= 750000000.0) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if z <= -2.1e+143:
		tmp = t_2
	elif z <= -2.3e+86:
		tmp = ((x / (z / y)) - (a - t)) / b
	elif z <= -1.7e-38:
		tmp = t_2
	elif z <= 2.55e-135:
		tmp = x + (t_1 / y)
	elif z <= 750000000.0:
		tmp = t_1 / (y + (z * (b - y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -2.1e+143)
		tmp = t_2;
	elseif (z <= -2.3e+86)
		tmp = Float64(Float64(Float64(x / Float64(z / y)) - Float64(a - t)) / b);
	elseif (z <= -1.7e-38)
		tmp = t_2;
	elseif (z <= 2.55e-135)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 750000000.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -2.1e+143)
		tmp = t_2;
	elseif (z <= -2.3e+86)
		tmp = ((x / (z / y)) - (a - t)) / b;
	elseif (z <= -1.7e-38)
		tmp = t_2;
	elseif (z <= 2.55e-135)
		tmp = x + (t_1 / y);
	elseif (z <= 750000000.0)
		tmp = t_1 / (y + (z * (b - y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+143], t$95$2, If[LessEqual[z, -2.3e+86], N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a - t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -1.7e-38], t$95$2, If[LessEqual[z, 2.55e-135], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 750000000.0], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999988e143 or -2.2999999999999999e86 < z < -1.7000000000000001e-38 or 7.5e8 < z

   1. Initial program 43.5%

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

   3. Taylor expanded in x around 0 43.5%

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

   4. Taylor expanded in z around inf 83.0%

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

   5. Taylor expanded in y around inf 86.2%

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

      1. neg-mul-1 86.2%

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

      2. unsub-neg 86.2%

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

   7. Simplified 86.2%

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

   if -2.09999999999999988e143 < z < -2.2999999999999999e86

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in b around inf 83.6%

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

      1. associate-+r+ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. sub-neg 83.6%

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

      4. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -1.7000000000000001e-38 < z < 2.5500000000000001e-135

   1. Initial program 83.7%

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

   3. Taylor expanded in x around 0 83.8%

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

   4. Taylor expanded in z around 0 88.1%

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

   5. Taylor expanded in z around 0 79.6%

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

   if 2.5500000000000001e-135 < z < 7.5e8

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 75.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 750000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x}{1 - z} + t_1\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -35000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 140000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ (/ x (- 1.0 z)) t_1)))
   (if (<= z -1.15e+143)
     t_2
     (if (<= z -2.6e+86)
       (/ (- (/ x (/ z y)) (- a t)) b)
       (if (<= z -35000000.0)
         t_1
         (if (<= z 140000.0)
           (- x (/ (* z (- a t)) (+ y (* z (- b y)))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (z <= -1.15e+143) {
		tmp = t_2;
	} else if (z <= -2.6e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -35000000.0) {
		tmp = t_1;
	} else if (z <= 140000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = (x / (1.0d0 - z)) + t_1
    if (z <= (-1.15d+143)) then
        tmp = t_2
    else if (z <= (-2.6d+86)) then
        tmp = ((x / (z / y)) - (a - t)) / b
    else if (z <= (-35000000.0d0)) then
        tmp = t_1
    else if (z <= 140000.0d0) then
        tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (z <= -1.15e+143) {
		tmp = t_2;
	} else if (z <= -2.6e+86) {
		tmp = ((x / (z / y)) - (a - t)) / b;
	} else if (z <= -35000000.0) {
		tmp = t_1;
	} else if (z <= 140000.0) {
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = (x / (1.0 - z)) + t_1
	tmp = 0
	if z <= -1.15e+143:
		tmp = t_2
	elif z <= -2.6e+86:
		tmp = ((x / (z / y)) - (a - t)) / b
	elif z <= -35000000.0:
		tmp = t_1
	elif z <= 140000.0:
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + t_1)
	tmp = 0.0
	if (z <= -1.15e+143)
		tmp = t_2;
	elseif (z <= -2.6e+86)
		tmp = Float64(Float64(Float64(x / Float64(z / y)) - Float64(a - t)) / b);
	elseif (z <= -35000000.0)
		tmp = t_1;
	elseif (z <= 140000.0)
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = (x / (1.0 - z)) + t_1;
	tmp = 0.0;
	if (z <= -1.15e+143)
		tmp = t_2;
	elseif (z <= -2.6e+86)
		tmp = ((x / (z / y)) - (a - t)) / b;
	elseif (z <= -35000000.0)
		tmp = t_1;
	elseif (z <= 140000.0)
		tmp = x - ((z * (a - t)) / (y + (z * (b - y))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -1.15e+143], t$95$2, If[LessEqual[z, -2.6e+86], N[(N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(a - t), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -35000000.0], t$95$1, If[LessEqual[z, 140000.0], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e143 or 1.4e5 < z

   1. Initial program 37.0%

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

   3. Taylor expanded in x around 0 37.0%

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

   4. Taylor expanded in z around inf 81.8%

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

   5. Taylor expanded in y around inf 87.8%

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

      1. neg-mul-1 87.8%

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

      2. unsub-neg 87.8%

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

   7. Simplified 87.8%

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

   if -1.15e143 < z < -2.5999999999999998e86

   1. Initial program 83.0%

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

   3. Taylor expanded in t around 0 83.0%

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

   4. Taylor expanded in b around inf 83.6%

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

      1. associate-+r+ 83.6%

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

      2. mul-1-neg 83.6%

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

      3. sub-neg 83.6%

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

      4. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -2.5999999999999998e86 < z < -3.5e7

   1. Initial program 58.4%

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

   3. Taylor expanded in z around inf 92.7%

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

   if -3.5e7 < z < 1.4e5

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 87.2%

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

   4. Taylor expanded in z around 0 84.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}} - \left(a - t\right)}{b}\\ \mathbf{elif}\;z \leq -35000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 140000:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{t_1}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.25e-13)
     t_2
     (if (<= z 1.4e-133)
       (+ x (/ t_1 y))
       (if (<= z 3.8e-47)
         (/ (+ t (- (* y (/ x z)) a)) b)
         (if (<= z 7e+18) (+ x (/ t_1 (* y (- 1.0 z)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.25e-13) {
		tmp = t_2;
	} else if (z <= 1.4e-133) {
		tmp = x + (t_1 / y);
	} else if (z <= 3.8e-47) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 7e+18) {
		tmp = x + (t_1 / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-2.25d-13)) then
        tmp = t_2
    else if (z <= 1.4d-133) then
        tmp = x + (t_1 / y)
    else if (z <= 3.8d-47) then
        tmp = (t + ((y * (x / z)) - a)) / b
    else if (z <= 7d+18) then
        tmp = x + (t_1 / (y * (1.0d0 - z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.25e-13) {
		tmp = t_2;
	} else if (z <= 1.4e-133) {
		tmp = x + (t_1 / y);
	} else if (z <= 3.8e-47) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 7e+18) {
		tmp = x + (t_1 / (y * (1.0 - z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.25e-13:
		tmp = t_2
	elif z <= 1.4e-133:
		tmp = x + (t_1 / y)
	elif z <= 3.8e-47:
		tmp = (t + ((y * (x / z)) - a)) / b
	elif z <= 7e+18:
		tmp = x + (t_1 / (y * (1.0 - z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.25e-13)
		tmp = t_2;
	elseif (z <= 1.4e-133)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 3.8e-47)
		tmp = Float64(Float64(t + Float64(Float64(y * Float64(x / z)) - a)) / b);
	elseif (z <= 7e+18)
		tmp = Float64(x + Float64(t_1 / Float64(y * Float64(1.0 - z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.25e-13)
		tmp = t_2;
	elseif (z <= 1.4e-133)
		tmp = x + (t_1 / y);
	elseif (z <= 3.8e-47)
		tmp = (t + ((y * (x / z)) - a)) / b;
	elseif (z <= 7e+18)
		tmp = x + (t_1 / (y * (1.0 - z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-13], t$95$2, If[LessEqual[z, 1.4e-133], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-47], N[(N[(t + N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 7e+18], N[(x + N[(t$95$1 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25e-13 or 7e18 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf 80.6%

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

   if -2.25e-13 < z < 1.3999999999999999e-133

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in z around 0 88.1%

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

   5. Taylor expanded in z around 0 78.2%

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

   if 1.3999999999999999e-133 < z < 3.80000000000000015e-47

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in z around inf 83.1%

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

      1. times-frac 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in b around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-*l/ 72.4%

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

      3. *-commutative 72.4%

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

   9. Simplified 72.4%

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

   if 3.80000000000000015e-47 < z < 7e18

   1. Initial program 92.9%

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

   3. Taylor expanded in x around 0 92.9%

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

   4. Taylor expanded in z around 0 70.6%

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

   5. Taylor expanded in y around inf 59.6%

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

      1. neg-mul-1 59.6%

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

      2. unsub-neg 59.6%

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

   7. Simplified 59.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y \cdot \left(1 - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{-a}{b - y}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+240}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ (- a) (- b y))))
   (if (<= z -9e+149)
     t_2
     (if (<= z -4.6e-67)
       t_1
       (if (<= z 1.4e-133)
         x
         (if (<= z 6.2e+135) t_1 (if (<= z 3e+240) (/ t (- b y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = -a / (b - y);
	double tmp;
	if (z <= -9e+149) {
		tmp = t_2;
	} else if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.4e-133) {
		tmp = x;
	} else if (z <= 6.2e+135) {
		tmp = t_1;
	} else if (z <= 3e+240) {
		tmp = t / (b - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / b
    t_2 = -a / (b - y)
    if (z <= (-9d+149)) then
        tmp = t_2
    else if (z <= (-4.6d-67)) then
        tmp = t_1
    else if (z <= 1.4d-133) then
        tmp = x
    else if (z <= 6.2d+135) then
        tmp = t_1
    else if (z <= 3d+240) then
        tmp = t / (b - y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = -a / (b - y);
	double tmp;
	if (z <= -9e+149) {
		tmp = t_2;
	} else if (z <= -4.6e-67) {
		tmp = t_1;
	} else if (z <= 1.4e-133) {
		tmp = x;
	} else if (z <= 6.2e+135) {
		tmp = t_1;
	} else if (z <= 3e+240) {
		tmp = t / (b - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = -a / (b - y)
	tmp = 0
	if z <= -9e+149:
		tmp = t_2
	elif z <= -4.6e-67:
		tmp = t_1
	elif z <= 1.4e-133:
		tmp = x
	elif z <= 6.2e+135:
		tmp = t_1
	elif z <= 3e+240:
		tmp = t / (b - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(Float64(-a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9e+149)
		tmp = t_2;
	elseif (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.4e-133)
		tmp = x;
	elseif (z <= 6.2e+135)
		tmp = t_1;
	elseif (z <= 3e+240)
		tmp = Float64(t / Float64(b - y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = -a / (b - y);
	tmp = 0.0;
	if (z <= -9e+149)
		tmp = t_2;
	elseif (z <= -4.6e-67)
		tmp = t_1;
	elseif (z <= 1.4e-133)
		tmp = x;
	elseif (z <= 6.2e+135)
		tmp = t_1;
	elseif (z <= 3e+240)
		tmp = t / (b - y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+149], t$95$2, If[LessEqual[z, -4.6e-67], t$95$1, If[LessEqual[z, 1.4e-133], x, If[LessEqual[z, 6.2e+135], t$95$1, If[LessEqual[z, 3e+240], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999965e149 or 2.9999999999999999e240 < z

   1. Initial program 26.0%

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

   3. Taylor expanded in x around 0 26.0%

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

   4. Taylor expanded in z around inf 84.0%

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

      1. div-inv 84.0%

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

      2. *-commutative 84.0%

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

      3. +-commutative 84.0%

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

      4. fma-def 84.0%

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

   6. Applied egg-rr 84.0%

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

   7. Taylor expanded in a around inf 64.9%

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

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

   9. Simplified 64.9%

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

   if -8.99999999999999965e149 < z < -4.6000000000000001e-67 or 1.3999999999999999e-133 < z < 6.20000000000000044e135

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 50.0%

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

   if -4.6000000000000001e-67 < z < 1.3999999999999999e-133

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0 59.3%

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

   if 6.20000000000000044e135 < z < 2.9999999999999999e240

   1. Initial program 40.7%

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

   3. Taylor expanded in x around 0 40.7%

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

   4. Taylor expanded in z around inf 87.0%

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

      1. div-inv 87.0%

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

      2. *-commutative 87.0%

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

      3. +-commutative 87.0%

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

      4. fma-def 87.0%

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in t around inf 59.3%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+149}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+240}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{y}{t - a}}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-38}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ y (- t a))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -9.2e-21)
     t_2
     (if (<= z 6.1e-103)
       t_1
       (if (<= z 1.55e-38) (/ (- t a) b) (if (<= z 2e-10) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / (t - a)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.2e-21) {
		tmp = t_2;
	} else if (z <= 6.1e-103) {
		tmp = t_1;
	} else if (z <= 1.55e-38) {
		tmp = (t - a) / b;
	} else if (z <= 2e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z / (y / (t - a)))
    t_2 = (t - a) / (b - y)
    if (z <= (-9.2d-21)) then
        tmp = t_2
    else if (z <= 6.1d-103) then
        tmp = t_1
    else if (z <= 1.55d-38) then
        tmp = (t - a) / b
    else if (z <= 2d-10) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / (t - a)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.2e-21) {
		tmp = t_2;
	} else if (z <= 6.1e-103) {
		tmp = t_1;
	} else if (z <= 1.55e-38) {
		tmp = (t - a) / b;
	} else if (z <= 2e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z / (y / (t - a)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.2e-21:
		tmp = t_2
	elif z <= 6.1e-103:
		tmp = t_1
	elif z <= 1.55e-38:
		tmp = (t - a) / b
	elif z <= 2e-10:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z / Float64(y / Float64(t - a))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.2e-21)
		tmp = t_2;
	elseif (z <= 6.1e-103)
		tmp = t_1;
	elseif (z <= 1.55e-38)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z / (y / (t - a)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.2e-21)
		tmp = t_2;
	elseif (z <= 6.1e-103)
		tmp = t_1;
	elseif (z <= 1.55e-38)
		tmp = (t - a) / b;
	elseif (z <= 2e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e-21], t$95$2, If[LessEqual[z, 6.1e-103], t$95$1, If[LessEqual[z, 1.55e-38], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2e-10], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.19999999999999998e-21 or 2.00000000000000007e-10 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around inf 79.1%

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

   if -9.19999999999999998e-21 < z < 6.1000000000000001e-103 or 1.54999999999999991e-38 < z < 2.00000000000000007e-10

   1. Initial program 86.2%

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

   3. Taylor expanded in x around 0 86.2%

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

   4. Taylor expanded in z around 0 85.3%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. associate-/l* 69.4%

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

   7. Simplified 69.4%

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

   if 6.1000000000000001e-103 < z < 1.54999999999999991e-38

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 83.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-38}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -8.6e-13)
     t_1
     (if (<= z 6.1e-103)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 2.8e-47)
         (/ (- t a) b)
         (if (<= z 2.9e-8) (+ x (/ z (/ y (- t a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.6e-13) {
		tmp = t_1;
	} else if (z <= 6.1e-103) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 2.8e-47) {
		tmp = (t - a) / b;
	} else if (z <= 2.9e-8) {
		tmp = x + (z / (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-8.6d-13)) then
        tmp = t_1
    else if (z <= 6.1d-103) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 2.8d-47) then
        tmp = (t - a) / b
    else if (z <= 2.9d-8) then
        tmp = x + (z / (y / (t - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.6e-13) {
		tmp = t_1;
	} else if (z <= 6.1e-103) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 2.8e-47) {
		tmp = (t - a) / b;
	} else if (z <= 2.9e-8) {
		tmp = x + (z / (y / (t - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -8.6e-13:
		tmp = t_1
	elif z <= 6.1e-103:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 2.8e-47:
		tmp = (t - a) / b
	elif z <= 2.9e-8:
		tmp = x + (z / (y / (t - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -8.6e-13)
		tmp = t_1;
	elseif (z <= 6.1e-103)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 2.8e-47)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2.9e-8)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -8.6e-13)
		tmp = t_1;
	elseif (z <= 6.1e-103)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 2.8e-47)
		tmp = (t - a) / b;
	elseif (z <= 2.9e-8)
		tmp = x + (z / (y / (t - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e-13], t$95$1, If[LessEqual[z, 6.1e-103], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-47], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.9e-8], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.5999999999999997e-13 or 2.9000000000000002e-8 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around inf 79.1%

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

   if -8.5999999999999997e-13 < z < 6.1000000000000001e-103

   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 x around 0 85.0%

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

   4. Taylor expanded in z around 0 86.2%

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

   5. Taylor expanded in z around 0 76.0%

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

   if 6.1000000000000001e-103 < z < 2.79999999999999993e-47

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 83.0%

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

   if 2.79999999999999993e-47 < z < 2.9000000000000002e-8

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 99.1%

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

   4. Taylor expanded in z around 0 76.4%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. associate-/l* 67.8%

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

   7. Simplified 67.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-103}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.7e-19)
     t_1
     (if (<= z 1.4e-133)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 4.3e-41)
         (/ (+ t (- (* y (/ x z)) a)) b)
         (if (<= z 5e-11) (+ x (/ z (/ y (- t a)))) 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 <= -3.7e-19) {
		tmp = t_1;
	} else if (z <= 1.4e-133) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 4.3e-41) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 5e-11) {
		tmp = x + (z / (y / (t - a)));
	} 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 <= (-3.7d-19)) then
        tmp = t_1
    else if (z <= 1.4d-133) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 4.3d-41) then
        tmp = (t + ((y * (x / z)) - a)) / b
    else if (z <= 5d-11) then
        tmp = x + (z / (y / (t - a)))
    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 <= -3.7e-19) {
		tmp = t_1;
	} else if (z <= 1.4e-133) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 4.3e-41) {
		tmp = (t + ((y * (x / z)) - a)) / b;
	} else if (z <= 5e-11) {
		tmp = x + (z / (y / (t - a)));
	} 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 <= -3.7e-19:
		tmp = t_1
	elif z <= 1.4e-133:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 4.3e-41:
		tmp = (t + ((y * (x / z)) - a)) / b
	elif z <= 5e-11:
		tmp = x + (z / (y / (t - a)))
	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 <= -3.7e-19)
		tmp = t_1;
	elseif (z <= 1.4e-133)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 4.3e-41)
		tmp = Float64(Float64(t + Float64(Float64(y * Float64(x / z)) - a)) / b);
	elseif (z <= 5e-11)
		tmp = Float64(x + Float64(z / Float64(y / Float64(t - a))));
	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 <= -3.7e-19)
		tmp = t_1;
	elseif (z <= 1.4e-133)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 4.3e-41)
		tmp = (t + ((y * (x / z)) - a)) / b;
	elseif (z <= 5e-11)
		tmp = x + (z / (y / (t - a)));
	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, -3.7e-19], t$95$1, If[LessEqual[z, 1.4e-133], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-41], N[(N[(t + N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 5e-11], N[(x + N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.70000000000000005e-19 or 5.00000000000000018e-11 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around inf 79.1%

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

   if -3.70000000000000005e-19 < z < 1.3999999999999999e-133

   1. Initial program 83.9%

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

   3. Taylor expanded in x around 0 83.9%

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

   4. Taylor expanded in z around 0 88.1%

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

   5. Taylor expanded in z around 0 78.2%

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

   if 1.3999999999999999e-133 < z < 4.2999999999999999e-41

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 94.8%

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

   4. Taylor expanded in z around inf 83.1%

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

      1. times-frac 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in b around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. associate-*l/ 72.4%

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

      3. *-commutative 72.4%

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

   9. Simplified 72.4%

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

   if 4.2999999999999999e-41 < z < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 99.1%

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

   4. Taylor expanded in z around 0 76.4%

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

   5. Taylor expanded in z around 0 67.4%

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

      1. associate-/l* 67.8%

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

   7. Simplified 67.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-133}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{t + \left(y \cdot \frac{x}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+83} \lor \neg \left(y \leq -9.5 \cdot 10^{+16}\right) \land \left(y \leq -1.2 \cdot 10^{-31} \lor \neg \left(y \leq 9.2 \cdot 10^{-26}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.45e+83)
         (and (not (<= y -9.5e+16)) (or (<= y -1.2e-31) (not (<= y 9.2e-26)))))
   (/ x (- 1.0 z))
   (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+83) || (!(y <= -9.5e+16) && ((y <= -1.2e-31) || !(y <= 9.2e-26)))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.45d+83)) .or. (.not. (y <= (-9.5d+16))) .and. (y <= (-1.2d-31)) .or. (.not. (y <= 9.2d-26))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.45e+83) || (!(y <= -9.5e+16) && ((y <= -1.2e-31) || !(y <= 9.2e-26)))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.45e+83) or (not (y <= -9.5e+16) and ((y <= -1.2e-31) or not (y <= 9.2e-26))):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.45e+83) || (!(y <= -9.5e+16) && ((y <= -1.2e-31) || !(y <= 9.2e-26))))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.45e+83) || (~((y <= -9.5e+16)) && ((y <= -1.2e-31) || ~((y <= 9.2e-26)))))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.45e+83], And[N[Not[LessEqual[y, -9.5e+16]], $MachinePrecision], Or[LessEqual[y, -1.2e-31], N[Not[LessEqual[y, 9.2e-26]], $MachinePrecision]]]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e83 or -9.5e16 < y < -1.2e-31 or 9.20000000000000035e-26 < y

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if -1.45e83 < y < -9.5e16 or -1.2e-31 < y < 9.20000000000000035e-26

   1. Initial program 74.8%

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

   3. Taylor expanded in y around 0 60.2%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+83} \lor \neg \left(y \leq -9.5 \cdot 10^{+16}\right) \land \left(y \leq -1.2 \cdot 10^{-31} \lor \neg \left(y \leq 9.2 \cdot 10^{-26}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-56} \lor \neg \left(z \leq 2.6 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.6e+182)
   (/ a y)
   (if (or (<= z -1.8e-56) (not (<= z 2.6e-119))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.6e+182) {
		tmp = a / y;
	} else if ((z <= -1.8e-56) || !(z <= 2.6e-119)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.6d+182)) then
        tmp = a / y
    else if ((z <= (-1.8d-56)) .or. (.not. (z <= 2.6d-119))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.6e+182) {
		tmp = a / y;
	} else if ((z <= -1.8e-56) || !(z <= 2.6e-119)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.6e+182:
		tmp = a / y
	elif (z <= -1.8e-56) or not (z <= 2.6e-119):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.6e+182)
		tmp = Float64(a / y);
	elseif ((z <= -1.8e-56) || !(z <= 2.6e-119))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.6e+182)
		tmp = a / y;
	elseif ((z <= -1.8e-56) || ~((z <= 2.6e-119)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.6e+182], N[(a / y), $MachinePrecision], If[Or[LessEqual[z, -1.8e-56], N[Not[LessEqual[z, 2.6e-119]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000003e182

   1. Initial program 24.6%

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

   3. Taylor expanded in x around 0 24.6%

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

   4. Taylor expanded in y around inf 21.6%

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

      1. times-frac 43.7%

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

      2. neg-mul-1 43.7%

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

      3. unsub-neg 43.7%

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

   6. Simplified 43.7%

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

   7. Taylor expanded in t around 0 28.6%

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

      1. associate-*r/ 28.6%

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

      2. neg-mul-1 28.6%

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

   9. Simplified 28.6%

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

   10. Taylor expanded in z around inf 36.8%

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

   if -8.6000000000000003e182 < z < -1.79999999999999989e-56 or 2.60000000000000012e-119 < z

   1. Initial program 63.2%

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

   3. Taylor expanded in y around 0 49.3%

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

   4. Taylor expanded in t around inf 32.3%

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

   if -1.79999999999999989e-56 < z < 2.60000000000000012e-119

   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 z around 0 58.3%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+182}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-56} \lor \neg \left(z \leq 2.6 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+168}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-54} \lor \neg \left(z \leq 2.8 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.1e+168)
   (/ (- a) b)
   (if (or (<= z -1e-54) (not (<= z 2.8e-119))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e+168) {
		tmp = -a / b;
	} else if ((z <= -1e-54) || !(z <= 2.8e-119)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.1d+168)) then
        tmp = -a / b
    else if ((z <= (-1d-54)) .or. (.not. (z <= 2.8d-119))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.1e+168) {
		tmp = -a / b;
	} else if ((z <= -1e-54) || !(z <= 2.8e-119)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.1e+168:
		tmp = -a / b
	elif (z <= -1e-54) or not (z <= 2.8e-119):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.1e+168)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -1e-54) || !(z <= 2.8e-119))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.1e+168)
		tmp = -a / b;
	elseif ((z <= -1e-54) || ~((z <= 2.8e-119)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.1e+168], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -1e-54], N[Not[LessEqual[z, 2.8e-119]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e168

   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 y around 0 47.8%

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

   4. Taylor expanded in t around 0 39.6%

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

      1. mul-1-neg 39.6%

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

   6. Simplified 39.6%

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

   if -1.1000000000000001e168 < z < -1e-54 or 2.8e-119 < z

   1. Initial program 64.5%

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

   3. Taylor expanded in y around 0 48.5%

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

   4. Taylor expanded in t around inf 33.6%

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

   if -1e-54 < z < 2.8e-119

   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 z around 0 58.3%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+168}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-54} \lor \neg \left(z \leq 2.8 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.4 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.9e-57) (not (<= z 1.4e-133))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-57) || !(z <= 1.4e-133)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.9d-57)) .or. (.not. (z <= 1.4d-133))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.9e-57) || !(z <= 1.4e-133)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.9e-57) or not (z <= 1.4e-133):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.9e-57) || !(z <= 1.4e-133))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.9e-57) || ~((z <= 1.4e-133)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.9e-57], N[Not[LessEqual[z, 1.4e-133]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.90000000000000006e-57 or 1.3999999999999999e-133 < z

   1. Initial program 57.9%

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

   3. Taylor expanded in z around inf 71.8%

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

   if -3.90000000000000006e-57 < z < 1.3999999999999999e-133

   1. Initial program 83.0%

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

   3. Taylor expanded in z around 0 59.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-57} \lor \neg \left(z \leq 1.4 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-58} \lor \neg \left(z \leq 7.5 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.15e-58) (not (<= z 7.5e-124))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.15e-58) || !(z <= 7.5e-124)) {
		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 <= (-3.15d-58)) .or. (.not. (z <= 7.5d-124))) 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 <= -3.15e-58) || !(z <= 7.5e-124)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.15e-58) or not (z <= 7.5e-124):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.15e-58) || !(z <= 7.5e-124))
		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 <= -3.15e-58) || ~((z <= 7.5e-124)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.15e-58], N[Not[LessEqual[z, 7.5e-124]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.14999999999999999e-58 or 7.4999999999999996e-124 < z

   1. Initial program 57.1%

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

   3. Taylor expanded in x around 0 57.1%

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

   4. Taylor expanded in z around inf 79.9%

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

      1. div-inv 79.8%

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

      2. *-commutative 79.8%

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

      3. +-commutative 79.8%

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

      4. fma-def 79.8%

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

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in t around inf 39.4%

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

   if -3.14999999999999999e-58 < z < 7.4999999999999996e-124

   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 z around 0 58.3%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-58} \lor \neg \left(z \leq 7.5 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38} \lor \neg \left(z \leq 6600\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e+38) (not (<= z 6600.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+38) || !(z <= 6600.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.7d+38)) .or. (.not. (z <= 6600.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+38) || !(z <= 6600.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.7e+38) or not (z <= 6600.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e+38) || !(z <= 6600.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.7e+38) || ~((z <= 6600.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e+38], N[Not[LessEqual[z, 6600.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999996e38 or 6600 < z

   1. Initial program 42.8%

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

   3. Taylor expanded in x around 0 36.2%

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

   4. Taylor expanded in y around inf 21.7%

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

      1. times-frac 34.6%

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

      2. neg-mul-1 34.6%

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

      3. unsub-neg 34.6%

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

   6. Simplified 34.6%

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

   7. Taylor expanded in t around 0 19.9%

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

      1. associate-*r/ 19.9%

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

      2. neg-mul-1 19.9%

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

   9. Simplified 19.9%

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

   10. Taylor expanded in z around inf 22.1%

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

   if -2.69999999999999996e38 < z < 6600

   1. Initial program 86.4%

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

   3. Taylor expanded in z around 0 43.0%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38} \lor \neg \left(z \leq 6600\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.6%

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

3. Taylor expanded in z around 0 24.9%

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

4. Final simplification 24.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.3% 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 2024014 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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