Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.9% → 95.4%

Time: 17.6s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.9% 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: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_4 := \frac{t - a}{x \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + t\_4\right)\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-276}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+244}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;x \cdot \left(t\_4 + \frac{y}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
          (/ (- a t) (- y b))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (/ (- t a) (* x (- b y)))))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ -1.0 (+ z -1.0)) t_4))
     (if (<= t_3 -5e-276)
       t_3
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 2e+244)
           t_3
           (if (<= t_3 INFINITY) (* x (+ t_4 (/ y t_1))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = (t - a) / (x * (b - y));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((-1.0 / (z + -1.0)) + t_4);
	} else if (t_3 <= -5e-276) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+244) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x * (t_4 + (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x * (y / (b - y))) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b));
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = (t - a) / (x * (b - y));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((-1.0 / (z + -1.0)) + t_4);
	} else if (t_3 <= -5e-276) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+244) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = x * (t_4 + (y / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (((x * (y / (b - y))) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + ((a - t) / (y - b))
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = (t - a) / (x * (b - y))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((-1.0 / (z + -1.0)) + t_4)
	elif t_3 <= -5e-276:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 2e+244:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = x * (t_4 + (y / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + Float64(Float64(a - t) / Float64(y - b)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(Float64(t - a) / Float64(x * Float64(b - y)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(-1.0 / Float64(z + -1.0)) + t_4));
	elseif (t_3 <= -5e-276)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+244)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(x * Float64(t_4 + Float64(y / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (((x * (y / (b - y))) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + ((a - t) / (y - b));
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = (t - a) / (x * (b - y));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((-1.0 / (z + -1.0)) + t_4);
	elseif (t_3 <= -5e-276)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+244)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = x * (t_4 + (y / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $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[(t - a), $MachinePrecision] / N[(x * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(-1.0 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-276], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 2e+244], t$95$3, If[LessEqual[t$95$3, Infinity], N[(x * N[(t$95$4 + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 47.0%

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

   3. Taylor expanded in x around inf 79.5%

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

   4. Taylor expanded in z around inf 93.5%

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

   5. Taylor expanded in y around inf 93.9%

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

      1. neg-mul-1 93.9%

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

      2. sub-neg 93.9%

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

   7. Simplified 93.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999967e-276 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   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 -4.99999999999999967e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 7.1%

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

   3. Taylor expanded in z around -inf 59.7%

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

      1. associate--l+ 59.7%

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

      2. mul-1-neg 59.7%

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

      3. distribute-lft-out-- 59.7%

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

      4. associate-/l* 67.3%

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

      5. associate-/l* 99.9%

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

      6. div-sub 99.9%

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

   5. Simplified 99.9%

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

   if 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 20.9%

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

   3. Taylor expanded in x around inf 65.4%

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

   4. Taylor expanded in z around inf 87.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{t - a}{x \cdot \left(b - y\right)} + \frac{y}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq -5 \cdot 10^{-276}\right) \land \left(t\_1 \leq 0 \lor \neg \left(t\_1 \leq 2 \cdot 10^{+244}\right)\right):\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))
   (if (or (<= t_1 (- INFINITY))
           (and (not (<= t_1 -5e-276))
                (or (<= t_1 0.0) (not (<= t_1 2e+244)))))
     (* x (+ (/ -1.0 (+ z -1.0)) (/ (- t a) (* x (- b y)))))
     t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || (!(t_1 <= -5e-276) && ((t_1 <= 0.0) || !(t_1 <= 2e+244)))) {
		tmp = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || (!(t_1 <= -5e-276) && ((t_1 <= 0.0) || !(t_1 <= 2e+244)))) {
		tmp = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	tmp = 0
	if (t_1 <= -math.inf) or (not (t_1 <= -5e-276) and ((t_1 <= 0.0) or not (t_1 <= 2e+244))):
		tmp = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || (!(t_1 <= -5e-276) && ((t_1 <= 0.0) || !(t_1 <= 2e+244))))
		tmp = Float64(x * Float64(Float64(-1.0 / Float64(z + -1.0)) + Float64(Float64(t - a) / Float64(x * Float64(b - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	tmp = 0.0;
	if ((t_1 <= -Inf) || (~((t_1 <= -5e-276)) && ((t_1 <= 0.0) || ~((t_1 <= 2e+244)))))
		tmp = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], And[N[Not[LessEqual[t$95$1, -5e-276]], $MachinePrecision], Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 2e+244]], $MachinePrecision]]]], N[(x * N[(N[(-1.0 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or -4.99999999999999967e-276 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 2.00000000000000015e244 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 21.0%

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

   3. Taylor expanded in x around inf 41.9%

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

   4. Taylor expanded in z around inf 73.9%

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

   5. Taylor expanded in y around inf 82.4%

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

      1. neg-mul-1 82.4%

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

      2. sub-neg 82.4%

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

   7. Simplified 82.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999967e-276 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000015e244

   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
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-276}\right) \land \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+244}\right)\right):\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (+ (/ -1.0 (+ z -1.0)) (/ (- t a) (* x (- b y)))))))
   (if (<= y -1.55e+31)
     t_1
     (if (<= y -5.5e-103)
       (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))
       (if (<= y 2.1e+30) (/ (- a t) (- y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	double tmp;
	if (y <= -1.55e+31) {
		tmp = t_1;
	} else if (y <= -5.5e-103) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 2.1e+30) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (((-1.0d0) / (z + (-1.0d0))) + ((t - a) / (x * (b - y))))
    if (y <= (-1.55d+31)) then
        tmp = t_1
    else if (y <= (-5.5d-103)) then
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    else if (y <= 2.1d+30) then
        tmp = (a - t) / (y - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	double tmp;
	if (y <= -1.55e+31) {
		tmp = t_1;
	} else if (y <= -5.5e-103) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (y <= 2.1e+30) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))))
	tmp = 0
	if y <= -1.55e+31:
		tmp = t_1
	elif y <= -5.5e-103:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	elif y <= 2.1e+30:
		tmp = (a - t) / (y - b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(-1.0 / Float64(z + -1.0)) + Float64(Float64(t - a) / Float64(x * Float64(b - y)))))
	tmp = 0.0
	if (y <= -1.55e+31)
		tmp = t_1;
	elseif (y <= -5.5e-103)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 2.1e+30)
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((-1.0 / (z + -1.0)) + ((t - a) / (x * (b - y))));
	tmp = 0.0;
	if (y <= -1.55e+31)
		tmp = t_1;
	elseif (y <= -5.5e-103)
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	elseif (y <= 2.1e+30)
		tmp = (a - t) / (y - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(-1.0 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(x * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+31], t$95$1, If[LessEqual[y, -5.5e-103], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+30], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5500000000000001e31 or 2.1e30 < y

   1. Initial program 48.4%

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

   3. Taylor expanded in x around inf 65.6%

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

   4. Taylor expanded in z around inf 68.2%

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

   5. Taylor expanded in y around inf 74.9%

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

      1. neg-mul-1 74.9%

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

      2. sub-neg 74.9%

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

   7. Simplified 74.9%

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

   if -1.5500000000000001e31 < y < -5.50000000000000032e-103

   1. Initial program 86.9%

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

   3. Taylor expanded in a around 0 78.1%

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

   if -5.50000000000000032e-103 < y < 2.1e30

   1. Initial program 79.4%

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

   3. Taylor expanded in z around inf 75.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{-1}{z + -1} + \frac{t - a}{x \cdot \left(b - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 32.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* x z))))
   (if (<= y -2.4e-43)
     t_1
     (if (<= y 8e-229)
       (/ t b)
       (if (<= y 1e+61) (/ a (- b)) (if (<= y 2.05e+222) t_1 (/ x (- z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (x * z);
	double tmp;
	if (y <= -2.4e-43) {
		tmp = t_1;
	} else if (y <= 8e-229) {
		tmp = t / b;
	} else if (y <= 1e+61) {
		tmp = a / -b;
	} else if (y <= 2.05e+222) {
		tmp = t_1;
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (x * z)
    if (y <= (-2.4d-43)) then
        tmp = t_1
    else if (y <= 8d-229) then
        tmp = t / b
    else if (y <= 1d+61) then
        tmp = a / -b
    else if (y <= 2.05d+222) then
        tmp = t_1
    else
        tmp = x / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (x * z);
	double tmp;
	if (y <= -2.4e-43) {
		tmp = t_1;
	} else if (y <= 8e-229) {
		tmp = t / b;
	} else if (y <= 1e+61) {
		tmp = a / -b;
	} else if (y <= 2.05e+222) {
		tmp = t_1;
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (x * z)
	tmp = 0
	if y <= -2.4e-43:
		tmp = t_1
	elif y <= 8e-229:
		tmp = t / b
	elif y <= 1e+61:
		tmp = a / -b
	elif y <= 2.05e+222:
		tmp = t_1
	else:
		tmp = x / -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (y <= -2.4e-43)
		tmp = t_1;
	elseif (y <= 8e-229)
		tmp = Float64(t / b);
	elseif (y <= 1e+61)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 2.05e+222)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (x * z);
	tmp = 0.0;
	if (y <= -2.4e-43)
		tmp = t_1;
	elseif (y <= 8e-229)
		tmp = t / b;
	elseif (y <= 1e+61)
		tmp = a / -b;
	elseif (y <= 2.05e+222)
		tmp = t_1;
	else
		tmp = x / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-43], t$95$1, If[LessEqual[y, 8e-229], N[(t / b), $MachinePrecision], If[LessEqual[y, 1e+61], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 2.05e+222], t$95$1, N[(x / (-z)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4000000000000002e-43 or 9.99999999999999949e60 < y < 2.04999999999999994e222

   1. Initial program 56.5%

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

   3. Taylor expanded in x around inf 34.5%

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

      1. associate-/l* 52.6%

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

      2. +-commutative 52.6%

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

      3. fma-undefine 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in y around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. unsub-neg 51.4%

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

   8. Simplified 51.4%

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

   9. Taylor expanded in z around 0 39.4%

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

       1. *-commutative 39.4%

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

   11. Simplified 39.4%

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

   if -2.4000000000000002e-43 < y < 8.00000000000000055e-229

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in y around 0 56.2%

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

   if 8.00000000000000055e-229 < y < 9.99999999999999949e60

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around inf 55.8%

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

   7. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in b around inf 38.4%

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

       1. associate-*r/ 38.4%

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

       2. mul-1-neg 38.4%

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

   12. Simplified 38.4%

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

   if 2.04999999999999994e222 < y

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 7.9%

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

      1. associate-/l* 34.0%

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

      2. +-commutative 34.0%

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

      3. fma-undefine 34.0%

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

   5. Simplified 34.0%

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

   6. Taylor expanded in y around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in z around inf 54.2%

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

       1. associate-*r/ 54.2%

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

       2. mul-1-neg 54.2%

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

   11. Simplified 54.2%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+222}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.1:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.6e+50)
     t_1
     (if (<= z -5.1)
       (/ x (- z))
       (if (<= z -4.5e-37) (/ a (- b)) (if (<= z 5.5e-55) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.6e+50) {
		tmp = t_1;
	} else if (z <= -5.1) {
		tmp = x / -z;
	} else if (z <= -4.5e-37) {
		tmp = a / -b;
	} else if (z <= 5.5e-55) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-1.6d+50)) then
        tmp = t_1
    else if (z <= (-5.1d0)) then
        tmp = x / -z
    else if (z <= (-4.5d-37)) then
        tmp = a / -b
    else if (z <= 5.5d-55) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.6e+50) {
		tmp = t_1;
	} else if (z <= -5.1) {
		tmp = x / -z;
	} else if (z <= -4.5e-37) {
		tmp = a / -b;
	} else if (z <= 5.5e-55) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1.6e+50:
		tmp = t_1
	elif z <= -5.1:
		tmp = x / -z
	elif z <= -4.5e-37:
		tmp = a / -b
	elif z <= 5.5e-55:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.6e+50)
		tmp = t_1;
	elseif (z <= -5.1)
		tmp = Float64(x / Float64(-z));
	elseif (z <= -4.5e-37)
		tmp = Float64(a / Float64(-b));
	elseif (z <= 5.5e-55)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.6e+50)
		tmp = t_1;
	elseif (z <= -5.1)
		tmp = x / -z;
	elseif (z <= -4.5e-37)
		tmp = a / -b;
	elseif (z <= 5.5e-55)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+50], t$95$1, If[LessEqual[z, -5.1], N[(x / (-z)), $MachinePrecision], If[LessEqual[z, -4.5e-37], N[(a / (-b)), $MachinePrecision], If[LessEqual[z, 5.5e-55], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.59999999999999991e50 or 5.4999999999999999e-55 < z

   1. Initial program 50.9%

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

   3. Taylor expanded in t around inf 31.2%

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

      1. *-commutative 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in z around inf 48.8%

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

   if -1.59999999999999991e50 < z < -5.0999999999999996

   1. Initial program 67.3%

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

   3. Taylor expanded in x around inf 24.5%

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

      1. associate-/l* 35.3%

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

      2. +-commutative 35.3%

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

      3. fma-undefine 35.3%

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

   5. Simplified 35.3%

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

   6. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in z around inf 54.8%

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

       1. associate-*r/ 54.8%

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

       2. mul-1-neg 54.8%

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

   11. Simplified 54.8%

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

   if -5.0999999999999996 < z < -4.5000000000000004e-37

   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 inf 72.2%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in z around inf 58.3%

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

   7. Taylor expanded in t around 0 46.4%

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

      1. mul-1-neg 46.4%

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

   9. Simplified 46.4%

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

   10. Taylor expanded in b around inf 44.9%

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

       1. associate-*r/ 44.9%

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

       2. mul-1-neg 44.9%

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

   12. Simplified 44.9%

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

   if -4.5000000000000004e-37 < z < 5.4999999999999999e-55

   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 53.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -5.1:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-34} \lor \neg \left(z \leq 3500\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e-34) (not (<= z 3500.0)))
   (/ (- a t) (- y b))
   (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e-34) || !(z <= 3500.0)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.6d-34)) .or. (.not. (z <= 3500.0d0))) then
        tmp = (a - t) / (y - b)
    else
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e-34) || !(z <= 3500.0)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.6e-34) or not (z <= 3500.0):
		tmp = (a - t) / (y - b)
	else:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e-34) || !(z <= 3500.0))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.6e-34) || ~((z <= 3500.0)))
		tmp = (a - t) / (y - b);
	else
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e-34], N[Not[LessEqual[z, 3500.0]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999999e-34 or 3500 < z

   1. Initial program 48.4%

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

   3. Taylor expanded in z around inf 77.6%

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

   if -2.5999999999999999e-34 < z < 3500

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 70.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-34} \lor \neg \left(z \leq 3500\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-228}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.9e-34)
   x
   (if (<= y 3.3e-228)
     (/ t b)
     (if (<= y 1.85e+61) (/ a (- b)) (if (<= y 1.66e+224) x (/ x (- z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.9e-34) {
		tmp = x;
	} else if (y <= 3.3e-228) {
		tmp = t / b;
	} else if (y <= 1.85e+61) {
		tmp = a / -b;
	} else if (y <= 1.66e+224) {
		tmp = x;
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.9d-34)) then
        tmp = x
    else if (y <= 3.3d-228) then
        tmp = t / b
    else if (y <= 1.85d+61) then
        tmp = a / -b
    else if (y <= 1.66d+224) then
        tmp = x
    else
        tmp = x / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.9e-34) {
		tmp = x;
	} else if (y <= 3.3e-228) {
		tmp = t / b;
	} else if (y <= 1.85e+61) {
		tmp = a / -b;
	} else if (y <= 1.66e+224) {
		tmp = x;
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.9e-34:
		tmp = x
	elif y <= 3.3e-228:
		tmp = t / b
	elif y <= 1.85e+61:
		tmp = a / -b
	elif y <= 1.66e+224:
		tmp = x
	else:
		tmp = x / -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.9e-34)
		tmp = x;
	elseif (y <= 3.3e-228)
		tmp = Float64(t / b);
	elseif (y <= 1.85e+61)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 1.66e+224)
		tmp = x;
	else
		tmp = Float64(x / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.9e-34)
		tmp = x;
	elseif (y <= 3.3e-228)
		tmp = t / b;
	elseif (y <= 1.85e+61)
		tmp = a / -b;
	elseif (y <= 1.66e+224)
		tmp = x;
	else
		tmp = x / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.9e-34], x, If[LessEqual[y, 3.3e-228], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.85e+61], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 1.66e+224], x, N[(x / (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.89999999999999962e-34 or 1.85000000000000001e61 < y < 1.65999999999999996e224

   1. Initial program 56.5%

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

   3. Taylor expanded in z around 0 39.2%

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

   if -4.89999999999999962e-34 < y < 3.30000000000000006e-228

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in y around 0 56.2%

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

   if 3.30000000000000006e-228 < y < 1.85000000000000001e61

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around inf 55.8%

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

   7. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in b around inf 38.4%

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

       1. associate-*r/ 38.4%

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

       2. mul-1-neg 38.4%

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

   12. Simplified 38.4%

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

   if 1.65999999999999996e224 < y

   1. Initial program 17.8%

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

   3. Taylor expanded in x around inf 7.9%

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

      1. associate-/l* 34.0%

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

      2. +-commutative 34.0%

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

      3. fma-undefine 34.0%

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

   5. Simplified 34.0%

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

   6. Taylor expanded in y around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   8. Simplified 79.4%

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

   9. Taylor expanded in z around inf 54.2%

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

       1. associate-*r/ 54.2%

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

       2. mul-1-neg 54.2%

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

   11. Simplified 54.2%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-228}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+61}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-50} \lor \neg \left(z \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e-50) (not (<= z 3.7e-56)))
   (/ (- a t) (- y b))
   (* x (/ y (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-50) || !(z <= 3.7e-56)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * (y / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.8d-50)) .or. (.not. (z <= 3.7d-56))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x * (y / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e-50) || !(z <= 3.7e-56)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * (y / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e-50) or not (z <= 3.7e-56):
		tmp = (a - t) / (y - b)
	else:
		tmp = x * (y / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e-50) || !(z <= 3.7e-56))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.8e-50) || ~((z <= 3.7e-56)))
		tmp = (a - t) / (y - b);
	else
		tmp = x * (y / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e-50], N[Not[LessEqual[z, 3.7e-56]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000029e-50 or 3.7000000000000002e-56 < z

   1. Initial program 54.9%

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

   3. Taylor expanded in z around inf 71.6%

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

   if -6.80000000000000029e-50 < z < 3.7000000000000002e-56

   1. Initial program 83.8%

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

   3. Taylor expanded in x around inf 54.1%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. fma-undefine 70.2%

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

   5. Simplified 70.2%

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

      1. fma-undefine 70.1%

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

   7. Applied egg-rr 70.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-50} \lor \neg \left(z \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -0.00055:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -0.00055)
     t_1
     (if (<= y 2.2e-228) (/ t (- b y)) (if (<= y 8.5e+60) (/ a (- b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -0.00055) {
		tmp = t_1;
	} else if (y <= 2.2e-228) {
		tmp = t / (b - y);
	} else if (y <= 8.5e+60) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-0.00055d0)) then
        tmp = t_1
    else if (y <= 2.2d-228) then
        tmp = t / (b - y)
    else if (y <= 8.5d+60) then
        tmp = a / -b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -0.00055) {
		tmp = t_1;
	} else if (y <= 2.2e-228) {
		tmp = t / (b - y);
	} else if (y <= 8.5e+60) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -0.00055:
		tmp = t_1
	elif y <= 2.2e-228:
		tmp = t / (b - y)
	elif y <= 8.5e+60:
		tmp = a / -b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -0.00055)
		tmp = t_1;
	elseif (y <= 2.2e-228)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 8.5e+60)
		tmp = Float64(a / Float64(-b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -0.00055)
		tmp = t_1;
	elseif (y <= 2.2e-228)
		tmp = t / (b - y);
	elseif (y <= 8.5e+60)
		tmp = a / -b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00055], t$95$1, If[LessEqual[y, 2.2e-228], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+60], N[(a / (-b)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000033e-4 or 8.50000000000000064e60 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in y around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   if -5.50000000000000033e-4 < y < 2.2e-228

   1. Initial program 85.8%

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

   3. Taylor expanded in t around inf 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in z around inf 59.8%

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

   if 2.2e-228 < y < 8.50000000000000064e60

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around inf 55.8%

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

   7. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in b around inf 38.4%

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

       1. associate-*r/ 38.4%

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

       2. mul-1-neg 38.4%

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

   12. Simplified 38.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00055:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.1e-26)
   x
   (if (<= y 2e-229) (/ t b) (if (<= y 1.2e+63) (/ a (- b)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.1e-26) {
		tmp = x;
	} else if (y <= 2e-229) {
		tmp = t / b;
	} else if (y <= 1.2e+63) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.1d-26)) then
        tmp = x
    else if (y <= 2d-229) then
        tmp = t / b
    else if (y <= 1.2d+63) then
        tmp = a / -b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.1e-26) {
		tmp = x;
	} else if (y <= 2e-229) {
		tmp = t / b;
	} else if (y <= 1.2e+63) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.1e-26:
		tmp = x
	elif y <= 2e-229:
		tmp = t / b
	elif y <= 1.2e+63:
		tmp = a / -b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.1e-26)
		tmp = x;
	elseif (y <= 2e-229)
		tmp = Float64(t / b);
	elseif (y <= 1.2e+63)
		tmp = Float64(a / Float64(-b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.1e-26)
		tmp = x;
	elseif (y <= 2e-229)
		tmp = t / b;
	elseif (y <= 1.2e+63)
		tmp = a / -b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.1e-26], x, If[LessEqual[y, 2e-229], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.2e+63], N[(a / (-b)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999995e-26 or 1.2e63 < y

   1. Initial program 50.5%

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

   3. Taylor expanded in z around 0 37.5%

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

   if -6.09999999999999995e-26 < y < 2.00000000000000014e-229

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in y around 0 56.2%

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

   if 2.00000000000000014e-229 < y < 1.2e63

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 59.4%

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

      1. associate-/l* 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around inf 55.8%

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

   7. Taylor expanded in t around 0 40.3%

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

      1. mul-1-neg 40.3%

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

   9. Simplified 40.3%

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

   10. Taylor expanded in b around inf 38.4%

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

       1. associate-*r/ 38.4%

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

       2. mul-1-neg 38.4%

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

   12. Simplified 38.4%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-50} \lor \neg \left(z \leq 1.56 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.8e-50) (not (<= z 1.56e-55))) (/ (- a t) (- y b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e-50) || !(z <= 1.56e-55)) {
		tmp = (a - t) / (y - 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 <= (-7.8d-50)) .or. (.not. (z <= 1.56d-55))) then
        tmp = (a - t) / (y - 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 <= -7.8e-50) || !(z <= 1.56e-55)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.8e-50) or not (z <= 1.56e-55):
		tmp = (a - t) / (y - b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.8e-50) || !(z <= 1.56e-55))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.8e-50) || ~((z <= 1.56e-55)))
		tmp = (a - t) / (y - b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.8e-50], N[Not[LessEqual[z, 1.56e-55]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000042e-50 or 1.56e-55 < z

   1. Initial program 54.9%

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

   3. Taylor expanded in z around inf 71.6%

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

   if -7.80000000000000042e-50 < z < 1.56e-55

   1. Initial program 83.8%

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

   3. Taylor expanded in z around 0 55.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-50} \lor \neg \left(z \leq 1.56 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-25} \lor \neg \left(y \leq 8.5 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e-25) (not (<= y 8.5e+60))) (/ 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 <= -2.9e-25) || !(y <= 8.5e+60)) {
		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 <= (-2.9d-25)) .or. (.not. (y <= 8.5d+60))) 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 <= -2.9e-25) || !(y <= 8.5e+60)) {
		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 <= -2.9e-25) or not (y <= 8.5e+60):
		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 <= -2.9e-25) || !(y <= 8.5e+60))
		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 <= -2.9e-25) || ~((y <= 8.5e+60)))
		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, -2.9e-25], N[Not[LessEqual[y, 8.5e+60]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000001e-25 or 8.50000000000000064e60 < y

   1. Initial program 50.5%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

   5. Simplified 55.8%

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

   if -2.9000000000000001e-25 < y < 8.50000000000000064e60

   1. Initial program 79.3%

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

   3. Taylor expanded in y around 0 65.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-25} \lor \neg \left(y \leq 8.5 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-37} \lor \neg \left(z \leq 1.1 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.6e-37) (not (<= z 1.1e+21))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.6e-37) || !(z <= 1.1e+21)) {
		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 <= (-4.6d-37)) .or. (.not. (z <= 1.1d+21))) 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 <= -4.6e-37) || !(z <= 1.1e+21)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.6e-37) or not (z <= 1.1e+21):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.6e-37) || !(z <= 1.1e+21))
		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 <= -4.6e-37) || ~((z <= 1.1e+21)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.6e-37], N[Not[LessEqual[z, 1.1e+21]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999999e-37 or 1.1e21 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in x around inf 36.3%

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

      1. associate-/l* 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in z around inf 61.0%

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

   7. Taylor expanded in t around 0 34.4%

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

      1. mul-1-neg 34.4%

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

   9. Simplified 34.4%

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

   10. Taylor expanded in b around 0 16.3%

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

   if -4.5999999999999999e-37 < z < 1.1e21

   1. Initial program 84.3%

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

   3. Taylor expanded in z around 0 45.5%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-37} \lor \neg \left(z \leq 1.1 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.3e-36) x (if (<= y 2.4e-61) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.3e-36) {
		tmp = x;
	} else if (y <= 2.4e-61) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.3d-36)) then
        tmp = x
    else if (y <= 2.4d-61) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.3e-36) {
		tmp = x;
	} else if (y <= 2.4e-61) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.3e-36:
		tmp = x
	elif y <= 2.4e-61:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.3e-36)
		tmp = x;
	elseif (y <= 2.4e-61)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.3e-36)
		tmp = x;
	elseif (y <= 2.4e-61)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.3e-36], x, If[LessEqual[y, 2.4e-61], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999991e-36 or 2.4000000000000001e-61 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in z around 0 34.0%

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

   if -3.29999999999999991e-36 < y < 2.4000000000000001e-61

   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 t around inf 43.7%

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

      1. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in y around 0 48.1%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.5%

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

3. Taylor expanded in z around 0 23.1%

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

4. Final simplification 23.1%

   \[\leadsto x \]
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 2024059 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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