Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 95.7%

Time: 18.0s

Alternatives: 15

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := z \cdot \frac{t - a}{t\_1} + x \cdot \frac{y}{t\_1}\\ t_4 := \frac{t - a}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - y \cdot t\_4}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{a}{y - b} - t\_4 \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (+ (* z (/ (- t a) t_1)) (* x (/ y t_1))))
        (t_4 (/ (- t a) (pow (- b y) 2.0))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -4e-246)
       t_2
       (if (<= t_2 0.0)
         (+ (/ (- (/ (* x y) (- b y)) (* y t_4)) z) (/ (- t a) (- b y)))
         (if (<= t_2 INFINITY)
           t_3
           (+
            (+ (/ t (- b y)) (* (/ x z) (/ y (- b y))))
            (- (/ a (- y b)) (* t_4 (/ y z))))))))))

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) + (z * (t - a))) / t_1;
	double t_3 = (z * ((t - a) / t_1)) + (x * (y / t_1));
	double t_4 = (t - a) / pow((b - y), 2.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -4e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y * t_4)) / z) + ((t - a) / (b - y));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((a / (y - b)) - (t_4 * (y / z)));
	}
	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) + (z * (t - a))) / t_1;
	double t_3 = (z * ((t - a) / t_1)) + (x * (y / t_1));
	double t_4 = (t - a) / Math.pow((b - y), 2.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -4e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y * t_4)) / z) + ((t - a) / (b - y));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((a / (y - b)) - (t_4 * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (z * ((t - a) / t_1)) + (x * (y / t_1))
	t_4 = (t - a) / math.pow((b - y), 2.0)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -4e-246:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((((x * y) / (b - y)) - (y * t_4)) / z) + ((t - a) / (b - y))
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((a / (y - b)) - (t_4 * (y / z)))
	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(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(z * Float64(Float64(t - a) / t_1)) + Float64(x * Float64(y / t_1)))
	t_4 = Float64(Float64(t - a) / (Float64(b - y) ^ 2.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -4e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(y * t_4)) / z) + Float64(Float64(t - a) / Float64(b - y)));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) + Float64(Float64(a / Float64(y - b)) - Float64(t_4 * Float64(y / z))));
	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) + (z * (t - a))) / t_1;
	t_3 = (z * ((t - a) / t_1)) + (x * (y / t_1));
	t_4 = (t - a) / ((b - y) ^ 2.0);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -4e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((((x * y) / (b - y)) - (y * t_4)) / z) + ((t - a) / (b - y));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + ((a / (y - b)) - (t_4 * (y / z)));
	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[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -4e-246], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$4), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(t$95$4 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 69.2%

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

      1. fma-define 69.2%

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

      2. +-commutative 69.2%

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

      3. fma-define 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in x around inf 79.1%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-/l* 78.9%

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

      3. associate-/l* 97.1%

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

   8. Simplified 97.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999982e-246

   1. Initial program 99.6%

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

   if -3.99999999999999982e-246 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 23.6%

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

      1. fma-define 23.6%

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

      2. +-commutative 23.6%

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

      3. fma-define 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in z around -inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. distribute-lft-out-- 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-/l* 84.2%

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

      6. div-sub 84.2%

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

   7. Simplified 84.2%

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

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

   1. Initial program 0.0%

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

      1. fma-define 0.0%

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

      2. +-commutative 0.0%

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

      3. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 18.2%

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

      1. times-frac 33.3%

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

      2. times-frac 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-246}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{a}{y - b} - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{t - a}{t\_1} + x \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= t_2 (- INFINITY))
     (+ (* z (/ (- t a) t_1)) (* x (/ y t_1)))
     (if (<= t_2 -4e-246)
       t_2
       (if (<= t_2 0.0)
         (+
          (/ (- (/ (* x y) (- b y)) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
          t_3)
         (if (<= t_2 5e+288)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (+ t_3 (/ x (- 1.0 z)))))))))

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) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z * ((t - a) / t_1)) + (x * (y / t_1));
	} else if (t_2 <= -4e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + t_3;
	} else if (t_2 <= 5e+288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_3 + (x / (1.0 - z));
	}
	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) + (z * (t - a))) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z * ((t - a) / t_1)) + (x * (y / t_1));
	} else if (t_2 <= -4e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((((x * y) / (b - y)) - (y * ((t - a) / Math.pow((b - y), 2.0)))) / z) + t_3;
	} else if (t_2 <= 5e+288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = t_3 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z * ((t - a) / t_1)) + (x * (y / t_1))
	elif t_2 <= -4e-246:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((((x * y) / (b - y)) - (y * ((t - a) / math.pow((b - y), 2.0)))) / z) + t_3
	elif t_2 <= 5e+288:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	else:
		tmp = t_3 + (x / (1.0 - z))
	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(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(Float64(t - a) / t_1)) + Float64(x * Float64(y / t_1)));
	elseif (t_2 <= -4e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z) + t_3);
	elseif (t_2 <= 5e+288)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	else
		tmp = Float64(t_3 + Float64(x / Float64(1.0 - z)));
	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) + (z * (t - a))) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z * ((t - a) / t_1)) + (x * (y / t_1));
	elseif (t_2 <= -4e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((((x * y) / (b - y)) - (y * ((t - a) / ((b - y) ^ 2.0)))) / z) + t_3;
	elseif (t_2 <= 5e+288)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	else
		tmp = t_3 + (x / (1.0 - z));
	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[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z * N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-246], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$2, 5e+288], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(t$95$3 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 30.4%

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

      1. fma-define 30.4%

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

      2. +-commutative 30.4%

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

      3. fma-define 30.4%

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

   3. Simplified 30.4%

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

   5. Taylor expanded in x around inf 66.5%

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

   6. Taylor expanded in x around 0 30.4%

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

      1. +-commutative 30.4%

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

      2. associate-/l* 63.1%

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

      3. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999982e-246

   1. Initial program 99.6%

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

   if -3.99999999999999982e-246 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 23.6%

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

      1. fma-define 23.6%

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

      2. +-commutative 23.6%

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

      3. fma-define 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in z around -inf 75.1%

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

      1. associate--l+ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. distribute-lft-out-- 75.1%

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

      4. *-commutative 75.1%

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

      5. associate-/l* 84.2%

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

      6. div-sub 84.2%

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

   7. Simplified 84.2%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000003e288

   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. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 5.0000000000000003e288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 10.3%

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

      1. fma-define 10.3%

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

      2. +-commutative 10.3%

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

      3. fma-define 10.3%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in x around inf 32.8%

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

   6. Taylor expanded in x around 0 10.3%

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

      1. +-commutative 10.3%

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

      2. associate-/l* 24.5%

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

      3. associate-/l* 49.1%

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

   8. Simplified 49.1%

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

   9. Taylor expanded in z around inf 80.0%

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

   10. Taylor expanded in y around inf 86.9%

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

       1. neg-mul-1 86.9%

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

       2. sub-neg 86.9%

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

   12. Simplified 86.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-246}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_4 := t\_2 + \frac{x}{1 - z}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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 (+ t_2 (/ x (- 1.0 z)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -2e-247)
       t_3
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 5e+288) (/ (+ (* x y) (- (* z t) (* z a))) t_1) 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 = t_2 + (x / (1.0 - z));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -2e-247) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 5e+288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} 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 = t_2 + (x / (1.0 - z));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -2e-247) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 5e+288) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} 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 = t_2 + (x / (1.0 - z))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -2e-247:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 5e+288:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	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(t_2 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -2e-247)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 5e+288)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	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 = t_2 + (x / (1.0 - z));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -2e-247)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 5e+288)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	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[(t$95$2 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -2e-247], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 5e+288], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 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 5.0000000000000003e288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.7%

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

      1. fma-define 15.7%

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

      2. +-commutative 15.7%

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

      3. fma-define 15.7%

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

   3. Simplified 15.7%

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

   5. Taylor expanded in x around inf 41.8%

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

   6. Taylor expanded in x around 0 15.7%

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

      1. +-commutative 15.7%

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

      2. associate-/l* 34.8%

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

      3. associate-/l* 62.7%

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

   8. Simplified 62.7%

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

   9. Taylor expanded in z around inf 82.9%

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

   10. Taylor expanded in y around inf 88.1%

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

       1. neg-mul-1 88.1%

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

       2. sub-neg 88.1%

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

   12. Simplified 88.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-247

   1. Initial program 99.6%

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

   if -2e-247 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 19.6%

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

      1. fma-define 19.6%

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

      2. +-commutative 19.6%

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

      3. fma-define 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000003e288

   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. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-247}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := t\_1 + \frac{x}{1 - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-247}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (+ t_1 (/ x (- 1.0 z)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-247)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 5e+288) 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 = t_1 + (x / (1.0 - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-247) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+288) {
		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 = t_1 + (x / (1.0 - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-247) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+288) {
		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 = t_1 + (x / (1.0 - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-247:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 5e+288:
		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(t_1 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-247)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+288)
		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 = t_1 + (x / (1.0 - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-247)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+288)
		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[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-247], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+288], 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 5.0000000000000003e288 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.7%

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

      1. fma-define 15.7%

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

      2. +-commutative 15.7%

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

      3. fma-define 15.7%

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

   3. Simplified 15.7%

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

   5. Taylor expanded in x around inf 41.8%

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

   6. Taylor expanded in x around 0 15.7%

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

      1. +-commutative 15.7%

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

      2. associate-/l* 34.8%

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

      3. associate-/l* 62.7%

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

   8. Simplified 62.7%

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

   9. Taylor expanded in z around inf 82.9%

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

   10. Taylor expanded in y around inf 88.1%

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

       1. neg-mul-1 88.1%

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

       2. sub-neg 88.1%

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

   12. Simplified 88.1%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-247 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.0000000000000003e288

   1. Initial program 99.6%

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

   if -2e-247 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 19.6%

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

      1. fma-define 19.6%

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

      2. +-commutative 19.6%

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

      3. fma-define 19.6%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in z around inf 69.0%

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

Alternative 5: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := x \cdot \frac{y}{t\_2}\\ \mathbf{if}\;z \leq -1220000000000:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{t - a}{t\_2} + t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (* x (/ y t_2))))
   (if (<= z -1220000000000.0)
     (+ t_3 t_1)
     (if (<= z 1.45e+58)
       (+ (* z (/ (- t a) t_2)) t_3)
       (+ t_1 (/ x (- 1.0 z)))))))

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 = y + (z * (b - y));
	double t_3 = x * (y / t_2);
	double tmp;
	if (z <= -1220000000000.0) {
		tmp = t_3 + t_1;
	} else if (z <= 1.45e+58) {
		tmp = (z * ((t - a) / t_2)) + t_3;
	} else {
		tmp = t_1 + (x / (1.0 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = y + (z * (b - y))
    t_3 = x * (y / t_2)
    if (z <= (-1220000000000.0d0)) then
        tmp = t_3 + t_1
    else if (z <= 1.45d+58) then
        tmp = (z * ((t - a) / t_2)) + t_3
    else
        tmp = t_1 + (x / (1.0d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = x * (y / t_2);
	double tmp;
	if (z <= -1220000000000.0) {
		tmp = t_3 + t_1;
	} else if (z <= 1.45e+58) {
		tmp = (z * ((t - a) / t_2)) + t_3;
	} else {
		tmp = t_1 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	t_3 = x * (y / t_2)
	tmp = 0
	if z <= -1220000000000.0:
		tmp = t_3 + t_1
	elif z <= 1.45e+58:
		tmp = (z * ((t - a) / t_2)) + t_3
	else:
		tmp = t_1 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(x * Float64(y / t_2))
	tmp = 0.0
	if (z <= -1220000000000.0)
		tmp = Float64(t_3 + t_1);
	elseif (z <= 1.45e+58)
		tmp = Float64(Float64(z * Float64(Float64(t - a) / t_2)) + t_3);
	else
		tmp = Float64(t_1 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	t_3 = x * (y / t_2);
	tmp = 0.0;
	if (z <= -1220000000000.0)
		tmp = t_3 + t_1;
	elseif (z <= 1.45e+58)
		tmp = (z * ((t - a) / t_2)) + t_3;
	else
		tmp = t_1 + (x / (1.0 - z));
	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[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1220000000000.0], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[z, 1.45e+58], N[(N[(z * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], N[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e12

   1. Initial program 43.8%

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

      1. fma-define 43.8%

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

      2. +-commutative 43.8%

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

      3. fma-define 43.8%

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

   3. Simplified 43.8%

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

   5. Taylor expanded in x around inf 41.1%

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

   6. Taylor expanded in x around 0 43.8%

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

      1. +-commutative 43.8%

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

      2. associate-/l* 53.5%

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

      3. associate-/l* 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in z around inf 88.2%

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

   if -1.22e12 < z < 1.45000000000000001e58

   1. Initial program 82.3%

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

      1. fma-define 82.3%

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

      2. +-commutative 82.3%

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

      3. fma-define 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in x around inf 85.9%

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

   6. Taylor expanded in x around 0 82.3%

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

      1. +-commutative 82.3%

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

      2. associate-/l* 79.4%

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

      3. associate-/l* 93.1%

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

   8. Simplified 93.1%

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

   if 1.45000000000000001e58 < z

   1. Initial program 42.0%

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

      1. fma-define 42.0%

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

      2. +-commutative 42.0%

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

      3. fma-define 42.0%

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

   3. Simplified 42.0%

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

   5. Taylor expanded in x around inf 37.7%

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

   6. Taylor expanded in x around 0 42.0%

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

      1. +-commutative 42.0%

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

      2. associate-/l* 55.3%

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

      3. associate-/l* 58.0%

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

   8. Simplified 58.0%

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

   9. Taylor expanded in z around inf 84.4%

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

   10. Taylor expanded in y around inf 90.4%

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

       1. neg-mul-1 90.4%

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

       2. sub-neg 90.4%

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

   12. Simplified 90.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1220000000000:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot \left(b - y\right)} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.05e-19)
     t_1
     (if (<= z 5.5e-8)
       (+ x (* z (/ (- t a) y)))
       (if (<= z 1.02e+85) (* (/ x z) (/ y (- b y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e-19) {
		tmp = t_1;
	} else if (z <= 5.5e-8) {
		tmp = x + (z * ((t - a) / y));
	} else if (z <= 1.02e+85) {
		tmp = (x / z) * (y / (b - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.05d-19)) then
        tmp = t_1
    else if (z <= 5.5d-8) then
        tmp = x + (z * ((t - a) / y))
    else if (z <= 1.02d+85) then
        tmp = (x / z) * (y / (b - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e-19) {
		tmp = t_1;
	} else if (z <= 5.5e-8) {
		tmp = x + (z * ((t - a) / y));
	} else if (z <= 1.02e+85) {
		tmp = (x / z) * (y / (b - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.05e-19:
		tmp = t_1
	elif z <= 5.5e-8:
		tmp = x + (z * ((t - a) / y))
	elif z <= 1.02e+85:
		tmp = (x / z) * (y / (b - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.05e-19)
		tmp = t_1;
	elseif (z <= 5.5e-8)
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	elseif (z <= 1.02e+85)
		tmp = Float64(Float64(x / z) * Float64(y / Float64(b - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.05e-19)
		tmp = t_1;
	elseif (z <= 5.5e-8)
		tmp = x + (z * ((t - a) / y));
	elseif (z <= 1.02e+85)
		tmp = (x / z) * (y / (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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-19], t$95$1, If[LessEqual[z, 5.5e-8], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+85], N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e-19 or 1.02e85 < z

   1. Initial program 48.3%

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

      1. fma-define 48.3%

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

      2. +-commutative 48.3%

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

      3. fma-define 48.3%

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

   3. Simplified 48.3%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -1.0499999999999999e-19 < z < 5.5000000000000003e-8

   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 63.1%

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

   4. Taylor expanded in x around 0 76.9%

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

      1. associate-/l* 74.6%

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

   6. Simplified 74.6%

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

   if 5.5000000000000003e-8 < z < 1.02e85

   1. Initial program 54.2%

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

      1. fma-define 54.2%

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

      2. +-commutative 54.2%

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

      3. fma-define 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in x around inf 60.4%

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

   6. Taylor expanded in x around inf 41.3%

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

      1. associate-/l* 48.1%

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

   8. Simplified 48.1%

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

   9. Taylor expanded in z around inf 41.3%

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

       1. times-frac 67.8%

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

   11. Simplified 67.8%

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

Alternative 7: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-24} \lor \neg \left(z \leq 2.55 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-24) (not (<= z 2.55e-45)))
   (+ (/ (- t a) (- b y)) (/ x (- 1.0 z)))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-24) || !(z <= 2.55e-45)) {
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.5d-24)) .or. (.not. (z <= 2.55d-45))) then
        tmp = ((t - a) / (b - y)) + (x / (1.0d0 - z))
    else
        tmp = x + (z * ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-24) || !(z <= 2.55e-45)) {
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e-24) or not (z <= 2.55e-45):
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z))
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e-24) || !(z <= 2.55e-45))
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(x / Float64(1.0 - z)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e-24) || ~((z <= 2.55e-45)))
		tmp = ((t - a) / (b - y)) + (x / (1.0 - z));
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e-24], N[Not[LessEqual[z, 2.55e-45]], $MachinePrecision]], N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999999e-24 or 2.5499999999999999e-45 < z

   1. Initial program 52.5%

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

      1. fma-define 52.5%

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

      2. +-commutative 52.5%

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

      3. fma-define 52.5%

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

   3. Simplified 52.5%

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

   5. Taylor expanded in x around inf 47.9%

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

   6. Taylor expanded in x around 0 52.5%

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

      1. +-commutative 52.5%

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

      2. associate-/l* 61.6%

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

      3. associate-/l* 66.5%

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

   8. Simplified 66.5%

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

   9. Taylor expanded in z around inf 85.4%

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

   10. Taylor expanded in y around inf 77.6%

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

       1. neg-mul-1 77.6%

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

       2. sub-neg 77.6%

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

   12. Simplified 77.6%

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

   if -5.4999999999999999e-24 < z < 2.5499999999999999e-45

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 65.1%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. associate-/l* 77.6%

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

   6. Simplified 77.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-24} \lor \neg \left(z \leq 2.55 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8200:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -8e-26)
     t_1
     (if (<= y -3.3e-251) (/ t b) (if (<= y 8200.0) (/ 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 <= -8e-26) {
		tmp = t_1;
	} else if (y <= -3.3e-251) {
		tmp = t / b;
	} else if (y <= 8200.0) {
		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 <= (-8d-26)) then
        tmp = t_1
    else if (y <= (-3.3d-251)) then
        tmp = t / b
    else if (y <= 8200.0d0) 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 <= -8e-26) {
		tmp = t_1;
	} else if (y <= -3.3e-251) {
		tmp = t / b;
	} else if (y <= 8200.0) {
		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 <= -8e-26:
		tmp = t_1
	elif y <= -3.3e-251:
		tmp = t / b
	elif y <= 8200.0:
		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 <= -8e-26)
		tmp = t_1;
	elseif (y <= -3.3e-251)
		tmp = Float64(t / b);
	elseif (y <= 8200.0)
		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 <= -8e-26)
		tmp = t_1;
	elseif (y <= -3.3e-251)
		tmp = t / b;
	elseif (y <= 8200.0)
		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, -8e-26], t$95$1, If[LessEqual[y, -3.3e-251], N[(t / b), $MachinePrecision], If[LessEqual[y, 8200.0], N[(a / (-b)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000003e-26 or 8200 < y

   1. Initial program 58.6%

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

      1. fma-define 58.6%

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

      2. +-commutative 58.6%

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

      3. fma-define 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   7. Simplified 54.6%

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

   if -8.0000000000000003e-26 < y < -3.3e-251

   1. Initial program 80.7%

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

      1. fma-define 80.7%

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

      2. +-commutative 80.7%

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

      3. fma-define 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in x around inf 67.7%

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

   6. Taylor expanded in b around inf 67.5%

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

      1. associate-/l* 63.9%

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

      2. associate--l+ 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in t around inf 45.7%

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

   if -3.3e-251 < y < 8200

   1. Initial program 74.1%

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

      1. fma-define 74.1%

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

      2. +-commutative 74.1%

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

      3. fma-define 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in x around inf 55.1%

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

   6. Taylor expanded in b around inf 47.0%

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

      1. associate-/l* 42.9%

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

      2. associate--l+ 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in a around inf 38.5%

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

       1. associate-*r/ 38.5%

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

       2. mul-1-neg 38.5%

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

   11. Simplified 38.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8200:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-24} \lor \neg \left(z \leq 8.5 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.26e-24) (not (<= z 8.5e-36)))
   (/ (- t a) (- b y))
   (* x (/ y (+ y (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.26e-24) || !(z <= 8.5e-36)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (y + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.26d-24)) .or. (.not. (z <= 8.5d-36))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * (y / (y + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.26e-24) || !(z <= 8.5e-36)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (y + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.26e-24) or not (z <= 8.5e-36):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * (y / (y + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.26e-24) || !(z <= 8.5e-36))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.26e-24) || ~((z <= 8.5e-36)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * (y / (y + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.26e-24], N[Not[LessEqual[z, 8.5e-36]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25999999999999992e-24 or 8.5000000000000007e-36 < z

   1. Initial program 51.5%

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

      1. fma-define 51.4%

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

      2. +-commutative 51.4%

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

      3. fma-define 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in z around inf 67.9%

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

   if -1.25999999999999992e-24 < z < 8.5000000000000007e-36

   1. Initial program 82.7%

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

      1. fma-define 82.7%

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

      2. +-commutative 82.7%

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

      3. fma-define 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around inf 88.8%

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

   6. Taylor expanded in x around inf 48.2%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in b around inf 62.8%

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

       1. *-commutative 62.8%

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

   11. Simplified 62.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-24} \lor \neg \left(z \leq 8.5 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4050:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+132}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -6.8e+19)
     t_1
     (if (<= z 4050.0) x (if (<= z 1.26e+132) (/ x (- z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -6.8e+19) {
		tmp = t_1;
	} else if (z <= 4050.0) {
		tmp = x;
	} else if (z <= 1.26e+132) {
		tmp = x / -z;
	} 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 = a / -b
    if (z <= (-6.8d+19)) then
        tmp = t_1
    else if (z <= 4050.0d0) then
        tmp = x
    else if (z <= 1.26d+132) then
        tmp = x / -z
    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 = a / -b;
	double tmp;
	if (z <= -6.8e+19) {
		tmp = t_1;
	} else if (z <= 4050.0) {
		tmp = x;
	} else if (z <= 1.26e+132) {
		tmp = x / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -6.8e+19:
		tmp = t_1
	elif z <= 4050.0:
		tmp = x
	elif z <= 1.26e+132:
		tmp = x / -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -6.8e+19)
		tmp = t_1;
	elseif (z <= 4050.0)
		tmp = x;
	elseif (z <= 1.26e+132)
		tmp = Float64(x / Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -6.8e+19)
		tmp = t_1;
	elseif (z <= 4050.0)
		tmp = x;
	elseif (z <= 1.26e+132)
		tmp = x / -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -6.8e+19], t$95$1, If[LessEqual[z, 4050.0], x, If[LessEqual[z, 1.26e+132], N[(x / (-z)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e19 or 1.25999999999999999e132 < z

   1. Initial program 41.3%

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

      1. fma-define 41.3%

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

      2. +-commutative 41.3%

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

      3. fma-define 41.3%

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

   3. Simplified 41.3%

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

   5. Taylor expanded in x around inf 38.3%

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

   6. Taylor expanded in b around inf 44.1%

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

      1. associate-/l* 40.9%

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

      2. associate--l+ 40.9%

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

   8. Simplified 40.9%

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

   9. Taylor expanded in a around inf 32.8%

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

       1. associate-*r/ 32.8%

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

       2. mul-1-neg 32.8%

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

   11. Simplified 32.8%

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

   if -6.8e19 < z < 4050

   1. Initial program 83.6%

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

      1. fma-define 83.6%

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

      2. +-commutative 83.6%

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

      3. fma-define 83.6%

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

   3. Simplified 83.6%

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

   5. Taylor expanded in z around 0 47.5%

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

   if 4050 < z < 1.25999999999999999e132

   1. Initial program 52.8%

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

      1. fma-define 52.7%

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

      2. +-commutative 52.7%

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

      3. fma-define 52.7%

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

   3. Simplified 52.7%

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

   5. Taylor expanded in y around inf 38.0%

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

      1. mul-1-neg 38.0%

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

      2. unsub-neg 38.0%

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

   7. Simplified 38.0%

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

   8. Taylor expanded in z around inf 37.9%

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

      1. associate-*r/ 37.9%

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

      2. mul-1-neg 37.9%

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

   10. Simplified 37.9%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq 4050:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+132}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-23} \lor \neg \left(z \leq 7.4 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e-23) (not (<= z 7.4e-60))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e-23) || !(z <= 7.4e-60)) {
		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 <= (-1.3d-23)) .or. (.not. (z <= 7.4d-60))) 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 <= -1.3e-23) || !(z <= 7.4e-60)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e-23) or not (z <= 7.4e-60):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e-23) || !(z <= 7.4e-60))
		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 <= -1.3e-23) || ~((z <= 7.4e-60)))
		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, -1.3e-23], N[Not[LessEqual[z, 7.4e-60]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-23 or 7.4000000000000005e-60 < z

   1. Initial program 53.7%

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

      1. fma-define 53.7%

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

      2. +-commutative 53.7%

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

      3. fma-define 53.7%

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

   3. Simplified 53.7%

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

   5. Taylor expanded in z around inf 66.3%

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

   if -1.3e-23 < z < 7.4000000000000005e-60

   1. Initial program 81.6%

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

      1. fma-define 81.6%

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

      2. +-commutative 81.6%

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

      3. fma-define 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around 0 57.0%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-23} \lor \neg \left(z \leq 7.4 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-25} \lor \neg \left(y \leq 12000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.95e-25) (not (<= y 12000.0))) (/ 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 <= -1.95e-25) || !(y <= 12000.0)) {
		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 <= (-1.95d-25)) .or. (.not. (y <= 12000.0d0))) 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 <= -1.95e-25) || !(y <= 12000.0)) {
		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 <= -1.95e-25) or not (y <= 12000.0):
		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 <= -1.95e-25) || !(y <= 12000.0))
		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 <= -1.95e-25) || ~((y <= 12000.0)))
		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, -1.95e-25], N[Not[LessEqual[y, 12000.0]], $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 < -1.95e-25 or 12000 < y

   1. Initial program 58.6%

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

      1. fma-define 58.6%

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

      2. +-commutative 58.6%

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

      3. fma-define 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   7. Simplified 54.6%

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

   if -1.95e-25 < y < 12000

   1. Initial program 76.1%

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

      1. fma-define 76.1%

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

      2. +-commutative 76.1%

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

      3. fma-define 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in y around 0 56.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-25} \lor \neg \left(y \leq 12000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+18} \lor \neg \left(z \leq 3.05 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.2e+18) (not (<= z 3.05e-56))) (/ a (- b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.2e+18) || !(z <= 3.05e-56)) {
		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 ((z <= (-7.2d+18)) .or. (.not. (z <= 3.05d-56))) 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 ((z <= -7.2e+18) || !(z <= 3.05e-56)) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.2e+18) or not (z <= 3.05e-56):
		tmp = a / -b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.2e+18) || !(z <= 3.05e-56))
		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 ((z <= -7.2e+18) || ~((z <= 3.05e-56)))
		tmp = a / -b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.2e+18], N[Not[LessEqual[z, 3.05e-56]], $MachinePrecision]], N[(a / (-b)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e18 or 3.0499999999999999e-56 < z

   1. Initial program 49.6%

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

      1. fma-define 49.6%

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

      2. +-commutative 49.6%

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

      3. fma-define 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in x around inf 45.3%

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

   6. Taylor expanded in b around inf 44.4%

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

      1. associate-/l* 41.4%

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

      2. associate--l+ 41.4%

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

   8. Simplified 41.4%

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

   9. Taylor expanded in a around inf 28.2%

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

       1. associate-*r/ 28.2%

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

       2. mul-1-neg 28.2%

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

   11. Simplified 28.2%

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

   if -7.2e18 < z < 3.0499999999999999e-56

   1. Initial program 81.9%

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

      1. fma-define 81.9%

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

      2. +-commutative 81.9%

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

      3. fma-define 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 51.0%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+18} \lor \neg \left(z \leq 3.05 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-19} \lor \neg \left(z \leq 1.05 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-19) (not (<= z 1.05e-35))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-19) || !(z <= 1.05e-35)) {
		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 <= (-1.05d-19)) .or. (.not. (z <= 1.05d-35))) 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 <= -1.05e-19) || !(z <= 1.05e-35)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-19) or not (z <= 1.05e-35):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-19) || !(z <= 1.05e-35))
		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 <= -1.05e-19) || ~((z <= 1.05e-35)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-19], N[Not[LessEqual[z, 1.05e-35]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e-19 or 1.05e-35 < z

   1. Initial program 50.8%

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

      1. fma-define 50.7%

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

      2. +-commutative 50.7%

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

      3. fma-define 50.8%

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

   3. Simplified 50.8%

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

   5. Taylor expanded in x around inf 46.7%

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

   6. Taylor expanded in b around inf 40.9%

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

      1. associate-/l* 38.0%

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

      2. associate--l+ 38.0%

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

   8. Simplified 38.0%

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

   9. Taylor expanded in t around inf 22.1%

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

   if -1.0499999999999999e-19 < z < 1.05e-35

   1. Initial program 83.0%

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

      1. fma-define 83.0%

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

      2. +-commutative 83.0%

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

      3. fma-define 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around 0 55.3%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-19} \lor \neg \left(z \leq 1.05 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.5%

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

   1. fma-define 65.5%

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

   2. +-commutative 65.5%

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

   3. fma-define 65.5%

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

3. Simplified 65.5%

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

5. Taylor expanded in z around 0 27.4%

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

Developer Target 1: 73.8% 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 2024163 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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