Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 91.1%

Time: 24.4s

Alternatives: 19

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.2% 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: 91.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(y, \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}, \frac{a}{b - y}\right)\\ t_2 := \mathsf{fma}\left(z, b - y, y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{y + z \cdot \left(b - y\right)}\\ t_5 := t\_4 \leq \infty\\ t_6 := x \cdot \left(\frac{y}{t\_2} + \frac{z}{x} \cdot \frac{t - a}{t\_2}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_2}\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_5:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_5:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (-
          (fma (/ x z) (/ y (- b y)) (/ t (- b y)))
          (fma y (/ (- t a) (* z (pow (- b y) 2.0))) (/ a (- b y)))))
        (t_2 (fma z (- b y) y))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) (+ y (* z (- b y)))))
        (t_5 (<= t_4 INFINITY))
        (t_6 (* x (+ (/ y t_2) (* (/ z x) (/ (- t a) t_2))))))
   (if (<= t_4 (- INFINITY))
     t_6
     (if (<= t_4 -2e-301)
       (/ (fma x y t_3) t_2)
       (if (<= t_4 0.0) t_1 (if t_5 t_4 (if t_5 t_6 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((x / z), (y / (b - y)), (t / (b - y))) - fma(y, ((t - a) / (z * pow((b - y), 2.0))), (a / (b - y)));
	double t_2 = fma(z, (b - y), y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / (y + (z * (b - y)));
	int t_5 = t_4 <= ((double) INFINITY);
	double t_6 = x * ((y / t_2) + ((z / x) * ((t - a) / t_2)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_4 <= -2e-301) {
		tmp = fma(x, y, t_3) / t_2;
	} else if (t_4 <= 0.0) {
		tmp = t_1;
	} else if (t_5) {
		tmp = t_4;
	} else if (t_5) {
		tmp = t_6;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(x / z), Float64(y / Float64(b - y)), Float64(t / Float64(b - y))) - fma(y, Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0))), Float64(a / Float64(b - y))))
	t_2 = fma(z, Float64(b - y), y)
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / Float64(y + Float64(z * Float64(b - y))))
	t_5 = t_4 <= Inf
	t_6 = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(z / x) * Float64(Float64(t - a) / t_2))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_4 <= -2e-301)
		tmp = Float64(fma(x, y, t_3) / t_2);
	elseif (t_4 <= 0.0)
		tmp = t_1;
	elseif (t_5)
		tmp = t_4;
	elseif (t_5)
		tmp = t_6;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = LessEqual[t$95$4, Infinity]}, Block[{t$95$6 = N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$6, If[LessEqual[t$95$4, -2e-301], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$1, If[t$95$5, t$95$4, If[t$95$5, t$95$6, t$95$1]]]]]]]]]]]

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

   1. Initial program 28.0%

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

   3. Taylor expanded in x around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. fma-define 44.9%

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

      3. times-frac 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-define 90.8%

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

   5. Simplified 90.8%

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

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

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

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

   1. Initial program 13.3%

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

   3. Taylor expanded in z around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. times-frac 60.7%

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

      3. fma-define 60.7%

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

      4. +-commutative 60.7%

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

      5. associate-/l* 99.9%

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

      6. fma-define 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 76.9%

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

4. Final simplification 89.8%

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

Alternative 2: 87.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, b - y, y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{y + z \cdot \left(b - y\right)}\\ t_4 := t\_3 \leq \infty\\ t_5 := x \cdot \left(\frac{y}{t\_1} + \frac{z}{x} \cdot \frac{t - a}{t\_1}\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_2\right)}{t\_1}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{\frac{x \cdot y}{b - y} - \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\right) + \frac{a}{y - b}\\ \mathbf{elif}\;t\_4:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- b y) y))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) (+ y (* z (- b y)))))
        (t_4 (<= t_3 INFINITY))
        (t_5 (* x (+ (/ y t_1) (* (/ z x) (/ (- t a) t_1))))))
   (if (<= t_3 (- INFINITY))
     t_5
     (if (<= t_3 -2e-301)
       (/ (fma x y t_2) t_1)
       (if (<= t_3 0.0)
         (+
          (+
           (/ t (- b y))
           (/ (- (/ (* x y) (- b y)) (/ (* y (- t a)) (pow (- b y) 2.0))) z))
          (/ a (- y b)))
         (if t_4 t_3 (if t_4 t_5 (/ (- t a) (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (b - y), y);
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / (y + (z * (b - y)));
	int t_4 = t_3 <= ((double) INFINITY);
	double t_5 = x * ((y / t_1) + ((z / x) * ((t - a) / t_1)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_3 <= -2e-301) {
		tmp = fma(x, y, t_2) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = ((t / (b - y)) + ((((x * y) / (b - y)) - ((y * (t - a)) / pow((b - y), 2.0))) / z)) + (a / (y - b));
	} else if (t_4) {
		tmp = t_3;
	} else if (t_4) {
		tmp = t_5;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(b - y), y)
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * Float64(b - y))))
	t_4 = t_3 <= Inf
	t_5 = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z / x) * Float64(Float64(t - a) / t_1))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_3 <= -2e-301)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(Float64(y * Float64(t - a)) / (Float64(b - y) ^ 2.0))) / z)) + Float64(a / Float64(y - b)));
	elseif (t_4)
		tmp = t_3;
	elseif (t_4)
		tmp = t_5;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = LessEqual[t$95$3, Infinity]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z / x), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$5, If[LessEqual[t$95$3, -2e-301], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[t$95$4, t$95$3, If[t$95$4, t$95$5, N[(N[(t - a), $MachinePrecision] / N[(b - y), $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 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   3. Taylor expanded in x around inf 44.9%

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

      1. +-commutative 44.9%

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

      2. fma-define 44.9%

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

      3. times-frac 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-define 90.8%

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

   5. Simplified 90.8%

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

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

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

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

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

   1. Initial program 29.5%

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

   3. Taylor expanded in z around -inf 86.9%

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

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

   1. Initial program 76.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 70.3%

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

4. Final simplification 85.4%

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

Alternative 3: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{t\_1}{t\_2}\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{x \cdot y - z \cdot a}{y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-251}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-288}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y}{t\_2}\\ \mathbf{elif}\;z \leq 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{t\_1}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 9.3 \cdot 10^{-60}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{1 - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ t_1 t_2))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ (- (* x y) (* z a)) y)))
   (if (<= z -6e+16)
     t_4
     (if (<= z -1.18e-91)
       t_3
       (if (<= z -1.62e-251)
         t_5
         (if (<= z -2.1e-288)
           t_3
           (if (<= z 4e-262)
             (/ (* x y) t_2)
             (if (<= z 1e-197)
               (/ (* x (+ y (/ t_1 x))) y)
               (if (<= z 9.3e-60)
                 t_3
                 (if (<= z 7.2e-50)
                   t_5
                   (if (<= z 2.1e-20)
                     t_3
                     (if (<= z 1.78e+53)
                       (/ 1.0 (/ (- 1.0 z) x))
                       t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = ((x * y) - (z * a)) / y;
	double tmp;
	if (z <= -6e+16) {
		tmp = t_4;
	} else if (z <= -1.18e-91) {
		tmp = t_3;
	} else if (z <= -1.62e-251) {
		tmp = t_5;
	} else if (z <= -2.1e-288) {
		tmp = t_3;
	} else if (z <= 4e-262) {
		tmp = (x * y) / t_2;
	} else if (z <= 1e-197) {
		tmp = (x * (y + (t_1 / x))) / y;
	} else if (z <= 9.3e-60) {
		tmp = t_3;
	} else if (z <= 7.2e-50) {
		tmp = t_5;
	} else if (z <= 2.1e-20) {
		tmp = t_3;
	} else if (z <= 1.78e+53) {
		tmp = 1.0 / ((1.0 - z) / x);
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = t_1 / t_2
    t_4 = (t - a) / (b - y)
    t_5 = ((x * y) - (z * a)) / y
    if (z <= (-6d+16)) then
        tmp = t_4
    else if (z <= (-1.18d-91)) then
        tmp = t_3
    else if (z <= (-1.62d-251)) then
        tmp = t_5
    else if (z <= (-2.1d-288)) then
        tmp = t_3
    else if (z <= 4d-262) then
        tmp = (x * y) / t_2
    else if (z <= 1d-197) then
        tmp = (x * (y + (t_1 / x))) / y
    else if (z <= 9.3d-60) then
        tmp = t_3
    else if (z <= 7.2d-50) then
        tmp = t_5
    else if (z <= 2.1d-20) then
        tmp = t_3
    else if (z <= 1.78d+53) then
        tmp = 1.0d0 / ((1.0d0 - z) / x)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = ((x * y) - (z * a)) / y;
	double tmp;
	if (z <= -6e+16) {
		tmp = t_4;
	} else if (z <= -1.18e-91) {
		tmp = t_3;
	} else if (z <= -1.62e-251) {
		tmp = t_5;
	} else if (z <= -2.1e-288) {
		tmp = t_3;
	} else if (z <= 4e-262) {
		tmp = (x * y) / t_2;
	} else if (z <= 1e-197) {
		tmp = (x * (y + (t_1 / x))) / y;
	} else if (z <= 9.3e-60) {
		tmp = t_3;
	} else if (z <= 7.2e-50) {
		tmp = t_5;
	} else if (z <= 2.1e-20) {
		tmp = t_3;
	} else if (z <= 1.78e+53) {
		tmp = 1.0 / ((1.0 - z) / x);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = t_1 / t_2
	t_4 = (t - a) / (b - y)
	t_5 = ((x * y) - (z * a)) / y
	tmp = 0
	if z <= -6e+16:
		tmp = t_4
	elif z <= -1.18e-91:
		tmp = t_3
	elif z <= -1.62e-251:
		tmp = t_5
	elif z <= -2.1e-288:
		tmp = t_3
	elif z <= 4e-262:
		tmp = (x * y) / t_2
	elif z <= 1e-197:
		tmp = (x * (y + (t_1 / x))) / y
	elif z <= 9.3e-60:
		tmp = t_3
	elif z <= 7.2e-50:
		tmp = t_5
	elif z <= 2.1e-20:
		tmp = t_3
	elif z <= 1.78e+53:
		tmp = 1.0 / ((1.0 - z) / x)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(t_1 / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(Float64(Float64(x * y) - Float64(z * a)) / y)
	tmp = 0.0
	if (z <= -6e+16)
		tmp = t_4;
	elseif (z <= -1.18e-91)
		tmp = t_3;
	elseif (z <= -1.62e-251)
		tmp = t_5;
	elseif (z <= -2.1e-288)
		tmp = t_3;
	elseif (z <= 4e-262)
		tmp = Float64(Float64(x * y) / t_2);
	elseif (z <= 1e-197)
		tmp = Float64(Float64(x * Float64(y + Float64(t_1 / x))) / y);
	elseif (z <= 9.3e-60)
		tmp = t_3;
	elseif (z <= 7.2e-50)
		tmp = t_5;
	elseif (z <= 2.1e-20)
		tmp = t_3;
	elseif (z <= 1.78e+53)
		tmp = Float64(1.0 / Float64(Float64(1.0 - z) / x));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = t_1 / t_2;
	t_4 = (t - a) / (b - y);
	t_5 = ((x * y) - (z * a)) / y;
	tmp = 0.0;
	if (z <= -6e+16)
		tmp = t_4;
	elseif (z <= -1.18e-91)
		tmp = t_3;
	elseif (z <= -1.62e-251)
		tmp = t_5;
	elseif (z <= -2.1e-288)
		tmp = t_3;
	elseif (z <= 4e-262)
		tmp = (x * y) / t_2;
	elseif (z <= 1e-197)
		tmp = (x * (y + (t_1 / x))) / y;
	elseif (z <= 9.3e-60)
		tmp = t_3;
	elseif (z <= 7.2e-50)
		tmp = t_5;
	elseif (z <= 2.1e-20)
		tmp = t_3;
	elseif (z <= 1.78e+53)
		tmp = 1.0 / ((1.0 - z) / x);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -6e+16], t$95$4, If[LessEqual[z, -1.18e-91], t$95$3, If[LessEqual[z, -1.62e-251], t$95$5, If[LessEqual[z, -2.1e-288], t$95$3, If[LessEqual[z, 4e-262], N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[z, 1e-197], N[(N[(x * N[(y + N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 9.3e-60], t$95$3, If[LessEqual[z, 7.2e-50], t$95$5, If[LessEqual[z, 2.1e-20], t$95$3, If[LessEqual[z, 1.78e+53], N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -6e16 or 1.77999999999999999e53 < z

   1. Initial program 37.9%

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

   3. Taylor expanded in z around inf 83.4%

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

   if -6e16 < z < -1.18e-91 or -1.62e-251 < z < -2.09999999999999996e-288 or 9.9999999999999999e-198 < z < 9.30000000000000019e-60 or 7.19999999999999958e-50 < z < 2.0999999999999999e-20

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 68.3%

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

   if -1.18e-91 < z < -1.62e-251 or 9.30000000000000019e-60 < z < 7.19999999999999958e-50

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. mul-1-neg 85.1%

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

      3. unsub-neg 85.1%

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

      4. *-commutative 85.1%

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

      5. *-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in z around 0 66.1%

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

   if -2.09999999999999996e-288 < z < 4.00000000000000005e-262

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   if 4.00000000000000005e-262 < z < 9.9999999999999999e-198

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf 90.3%

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

   4. Taylor expanded in z around 0 76.4%

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

   if 2.0999999999999999e-20 < z < 1.77999999999999999e53

   1. Initial program 64.1%

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

      1. fma-define 64.1%

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

      2. clear-num 64.1%

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

      3. inv-pow 64.1%

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

      4. +-commutative 64.1%

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

      5. fma-undefine 64.1%

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

      6. fma-define 64.1%

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

      7. +-commutative 64.1%

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

      8. fma-define 64.1%

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

   4. Applied egg-rr 64.1%

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

      1. unpow-1 64.1%

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

      2. *-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in y around inf 65.4%

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

      1. neg-mul-1 65.4%

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

   9. Simplified 65.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{1 + \left(-z\right)}{x}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -1.62 \cdot 10^{-251}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-288}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 9.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-20}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{\frac{1 - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+56} \lor \neg \left(z \leq 2.45 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -2e+56) (not (<= z 2.45e+53)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2e+56) || !(z <= 2.45e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-2d+56)) .or. (.not. (z <= 2.45d+53))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -2e+56) || !(z <= 2.45e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -2e+56) or not (z <= 2.45e+53):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -2e+56) || !(z <= 2.45e+53))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -2e+56) || ~((z <= 2.45e+53)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2e+56], N[Not[LessEqual[z, 2.45e+53]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000018e56 or 2.45000000000000009e53 < z

   1. Initial program 36.6%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -2.00000000000000018e56 < z < 2.45000000000000009e53

   1. Initial program 86.5%

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

   3. Taylor expanded in x around inf 87.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+56} \lor \neg \left(z \leq 2.45 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-31} \lor \neg \left(y \leq 6.6 \cdot 10^{+37}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.8e+197)
     t_2
     (if (<= y -2.4e+142)
       t_1
       (if (<= y -3.4e+59)
         t_2
         (if (<= y -6.5e+25)
           t_1
           (if (or (<= y -1.85e-31) (not (<= y 6.6e+37)))
             t_2
             (/ (- t a) b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e+197) {
		tmp = t_2;
	} else if (y <= -2.4e+142) {
		tmp = t_1;
	} else if (y <= -3.4e+59) {
		tmp = t_2;
	} else if (y <= -6.5e+25) {
		tmp = t_1;
	} else if ((y <= -1.85e-31) || !(y <= 6.6e+37)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / y
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.8d+197)) then
        tmp = t_2
    else if (y <= (-2.4d+142)) then
        tmp = t_1
    else if (y <= (-3.4d+59)) then
        tmp = t_2
    else if (y <= (-6.5d+25)) then
        tmp = t_1
    else if ((y <= (-1.85d-31)) .or. (.not. (y <= 6.6d+37))) then
        tmp = t_2
    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 t_1 = (a - t) / y;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e+197) {
		tmp = t_2;
	} else if (y <= -2.4e+142) {
		tmp = t_1;
	} else if (y <= -3.4e+59) {
		tmp = t_2;
	} else if (y <= -6.5e+25) {
		tmp = t_1;
	} else if ((y <= -1.85e-31) || !(y <= 6.6e+37)) {
		tmp = t_2;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.8e+197:
		tmp = t_2
	elif y <= -2.4e+142:
		tmp = t_1
	elif y <= -3.4e+59:
		tmp = t_2
	elif y <= -6.5e+25:
		tmp = t_1
	elif (y <= -1.85e-31) or not (y <= 6.6e+37):
		tmp = t_2
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.8e+197)
		tmp = t_2;
	elseif (y <= -2.4e+142)
		tmp = t_1;
	elseif (y <= -3.4e+59)
		tmp = t_2;
	elseif (y <= -6.5e+25)
		tmp = t_1;
	elseif ((y <= -1.85e-31) || !(y <= 6.6e+37))
		tmp = t_2;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.8e+197)
		tmp = t_2;
	elseif (y <= -2.4e+142)
		tmp = t_1;
	elseif (y <= -3.4e+59)
		tmp = t_2;
	elseif (y <= -6.5e+25)
		tmp = t_1;
	elseif ((y <= -1.85e-31) || ~((y <= 6.6e+37)))
		tmp = t_2;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+197], t$95$2, If[LessEqual[y, -2.4e+142], t$95$1, If[LessEqual[y, -3.4e+59], t$95$2, If[LessEqual[y, -6.5e+25], t$95$1, If[Or[LessEqual[y, -1.85e-31], N[Not[LessEqual[y, 6.6e+37]], $MachinePrecision]], t$95$2, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999999e197 or -2.3999999999999999e142 < y < -3.40000000000000006e59 or -6.50000000000000005e25 < y < -1.8499999999999999e-31 or 6.6000000000000002e37 < y

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. unsub-neg 62.0%

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

   5. Simplified 62.0%

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

   if -2.7999999999999999e197 < y < -2.3999999999999999e142 or -3.40000000000000006e59 < y < -6.50000000000000005e25

   1. Initial program 57.0%

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

   3. Taylor expanded in z around inf 66.5%

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

   4. Taylor expanded in b around 0 55.5%

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

      1. mul-1-neg 55.5%

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

   6. Simplified 55.5%

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

   if -1.8499999999999999e-31 < y < 6.6000000000000002e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-31} \lor \neg \left(y \leq 6.6 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{t\_1}\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -6e+16)
     t_2
     (if (<= z -1.05e-91)
       (/ (* z (- t a)) t_1)
       (if (<= z -2.95e-220)
         (/ (- (* x y) (* z a)) (+ y (* z b)))
         (if (<= z 1.78e+53) (/ (+ (* x y) (* z t)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_2;
	} else if (z <= -1.05e-91) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -2.95e-220) {
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	} else if (z <= 1.78e+53) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-6d+16)) then
        tmp = t_2
    else if (z <= (-1.05d-91)) then
        tmp = (z * (t - a)) / t_1
    else if (z <= (-2.95d-220)) then
        tmp = ((x * y) - (z * a)) / (y + (z * b))
    else if (z <= 1.78d+53) then
        tmp = ((x * y) + (z * t)) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_2;
	} else if (z <= -1.05e-91) {
		tmp = (z * (t - a)) / t_1;
	} else if (z <= -2.95e-220) {
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	} else if (z <= 1.78e+53) {
		tmp = ((x * y) + (z * t)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -6e+16:
		tmp = t_2
	elif z <= -1.05e-91:
		tmp = (z * (t - a)) / t_1
	elif z <= -2.95e-220:
		tmp = ((x * y) - (z * a)) / (y + (z * b))
	elif z <= 1.78e+53:
		tmp = ((x * y) + (z * t)) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6e+16)
		tmp = t_2;
	elseif (z <= -1.05e-91)
		tmp = Float64(Float64(z * Float64(t - a)) / t_1);
	elseif (z <= -2.95e-220)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * b)));
	elseif (z <= 1.78e+53)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6e+16)
		tmp = t_2;
	elseif (z <= -1.05e-91)
		tmp = (z * (t - a)) / t_1;
	elseif (z <= -2.95e-220)
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	elseif (z <= 1.78e+53)
		tmp = ((x * y) + (z * t)) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+16], t$95$2, If[LessEqual[z, -1.05e-91], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, -2.95e-220], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.78e+53], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e16 or 1.77999999999999999e53 < z

   1. Initial program 37.9%

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

   3. Taylor expanded in z around inf 83.4%

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

   if -6e16 < z < -1.05e-91

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 76.4%

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

   if -1.05e-91 < z < -2.9499999999999998e-220

   1. Initial program 93.4%

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

   3. Taylor expanded in t around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

      4. *-commutative 80.5%

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

      5. *-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in b around inf 80.5%

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

      1. *-commutative 80.5%

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

   8. Simplified 80.5%

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

   if -2.9499999999999998e-220 < z < 1.77999999999999999e53

   1. Initial program 88.7%

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

   3. Taylor expanded in a around 0 71.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-220}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (+ y (/ (* z (- t a)) x))) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5.5e-46)
     t_2
     (if (<= z -1e-288)
       t_1
       (if (<= z 2.6e-262)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z 3.1e-6) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (y + ((z * (t - a)) / x))) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.5e-46) {
		tmp = t_2;
	} else if (z <= -1e-288) {
		tmp = t_1;
	} else if (z <= 2.6e-262) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 3.1e-6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (y + ((z * (t - a)) / x))) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-5.5d-46)) then
        tmp = t_2
    else if (z <= (-1d-288)) then
        tmp = t_1
    else if (z <= 2.6d-262) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= 3.1d-6) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (y + ((z * (t - a)) / x))) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.5e-46) {
		tmp = t_2;
	} else if (z <= -1e-288) {
		tmp = t_1;
	} else if (z <= 2.6e-262) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 3.1e-6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (y + ((z * (t - a)) / x))) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.5e-46:
		tmp = t_2
	elif z <= -1e-288:
		tmp = t_1
	elif z <= 2.6e-262:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= 3.1e-6:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64(y + Float64(Float64(z * Float64(t - a)) / x))) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.5e-46)
		tmp = t_2;
	elseif (z <= -1e-288)
		tmp = t_1;
	elseif (z <= 2.6e-262)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 3.1e-6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (y + ((z * (t - a)) / x))) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.5e-46)
		tmp = t_2;
	elseif (z <= -1e-288)
		tmp = t_1;
	elseif (z <= 2.6e-262)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= 3.1e-6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(y + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e-46], t$95$2, If[LessEqual[z, -1e-288], t$95$1, If[LessEqual[z, 2.6e-262], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-6], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999983e-46 or 3.1e-6 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -5.49999999999999983e-46 < z < -1.00000000000000006e-288 or 2.5999999999999999e-262 < z < 3.1e-6

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf 85.5%

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

   4. Taylor expanded in z around 0 60.2%

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

   if -1.00000000000000006e-288 < z < 2.5999999999999999e-262

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \left(y + \frac{z \cdot \left(t - a\right)}{x}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z a)) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -8e-40)
     t_2
     (if (<= z -5.2e-288)
       t_1
       (if (<= z 1.16e-231)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= z 4.8e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) - (z * a)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8e-40) {
		tmp = t_2;
	} else if (z <= -5.2e-288) {
		tmp = t_1;
	} else if (z <= 1.16e-231) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 4.8e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) - (z * a)) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-8d-40)) then
        tmp = t_2
    else if (z <= (-5.2d-288)) then
        tmp = t_1
    else if (z <= 1.16d-231) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= 4.8d-14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) - (z * a)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8e-40) {
		tmp = t_2;
	} else if (z <= -5.2e-288) {
		tmp = t_1;
	} else if (z <= 1.16e-231) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= 4.8e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) - (z * a)) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -8e-40:
		tmp = t_2
	elif z <= -5.2e-288:
		tmp = t_1
	elif z <= 1.16e-231:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= 4.8e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * a)) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -8e-40)
		tmp = t_2;
	elseif (z <= -5.2e-288)
		tmp = t_1;
	elseif (z <= 1.16e-231)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 4.8e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) - (z * a)) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -8e-40)
		tmp = t_2;
	elseif (z <= -5.2e-288)
		tmp = t_1;
	elseif (z <= 1.16e-231)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= 4.8e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-40], t$95$2, If[LessEqual[z, -5.2e-288], t$95$1, If[LessEqual[z, 1.16e-231], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999994e-40 or 4.8e-14 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -7.9999999999999994e-40 < z < -5.19999999999999979e-288 or 1.16e-231 < z < 4.8e-14

   1. Initial program 90.6%

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

   3. Taylor expanded in t around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

      5. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in z around 0 50.9%

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

   if -5.19999999999999979e-288 < z < 1.16e-231

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.00047:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -6e+16)
     t_1
     (if (<= z -1.2e-91)
       (/ (* z (- t a)) (+ y (* z (- b y))))
       (if (<= z 0.00047) (/ (- (* x y) (* z a)) (+ y (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_1;
	} else if (z <= -1.2e-91) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 0.00047) {
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-6d+16)) then
        tmp = t_1
    else if (z <= (-1.2d-91)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= 0.00047d0) then
        tmp = ((x * y) - (z * a)) / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e+16) {
		tmp = t_1;
	} else if (z <= -1.2e-91) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 0.00047) {
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -6e+16:
		tmp = t_1
	elif z <= -1.2e-91:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= 0.00047:
		tmp = ((x * y) - (z * a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6e+16)
		tmp = t_1;
	elseif (z <= -1.2e-91)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 0.00047)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6e+16)
		tmp = t_1;
	elseif (z <= -1.2e-91)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= 0.00047)
		tmp = ((x * y) - (z * a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+16], t$95$1, If[LessEqual[z, -1.2e-91], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00047], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e16 or 4.69999999999999986e-4 < z

   1. Initial program 39.5%

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

   3. Taylor expanded in z around inf 81.1%

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

   if -6e16 < z < -1.20000000000000005e-91

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 76.4%

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

   if -1.20000000000000005e-91 < z < 4.69999999999999986e-4

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0 69.5%

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

      1. +-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. *-commutative 69.5%

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

      5. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in b around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.00047:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+49} \lor \neg \left(z \leq 3.25 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.2e+49) (not (<= z 3.25e+53)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.2e+49) || !(z <= 3.25e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.2d+49)) .or. (.not. (z <= 3.25d+53))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.2e+49) || !(z <= 3.25e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.2e+49) or not (z <= 3.25e+53):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.2e+49) || !(z <= 3.25e+53))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.2e+49) || ~((z <= 3.25e+53)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.2e+49], N[Not[LessEqual[z, 3.25e+53]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e49 or 3.25000000000000008e53 < z

   1. Initial program 36.6%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -8.2e49 < z < 3.25000000000000008e53

   1. Initial program 86.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+49} \lor \neg \left(z \leq 3.25 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-31} \lor \neg \left(y \leq 2.95 \cdot 10^{+37}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e+58)
     t_1
     (if (<= y -1.35e+26)
       (/ a (- y b))
       (if (or (<= y -2.8e-31) (not (<= y 2.95e+37))) t_1 (/ (- t a) b))))))

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 <= -7.8e+58) {
		tmp = t_1;
	} else if (y <= -1.35e+26) {
		tmp = a / (y - b);
	} else if ((y <= -2.8e-31) || !(y <= 2.95e+37)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.8d+58)) then
        tmp = t_1
    else if (y <= (-1.35d+26)) then
        tmp = a / (y - b)
    else if ((y <= (-2.8d-31)) .or. (.not. (y <= 2.95d+37))) then
        tmp = t_1
    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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e+58) {
		tmp = t_1;
	} else if (y <= -1.35e+26) {
		tmp = a / (y - b);
	} else if ((y <= -2.8e-31) || !(y <= 2.95e+37)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7.8e+58:
		tmp = t_1
	elif y <= -1.35e+26:
		tmp = a / (y - b)
	elif (y <= -2.8e-31) or not (y <= 2.95e+37):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.8e+58)
		tmp = t_1;
	elseif (y <= -1.35e+26)
		tmp = Float64(a / Float64(y - b));
	elseif ((y <= -2.8e-31) || !(y <= 2.95e+37))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	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 <= -7.8e+58)
		tmp = t_1;
	elseif (y <= -1.35e+26)
		tmp = a / (y - b);
	elseif ((y <= -2.8e-31) || ~((y <= 2.95e+37)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	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, -7.8e+58], t$95$1, If[LessEqual[y, -1.35e+26], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.8e-31], N[Not[LessEqual[y, 2.95e+37]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000002e58 or -1.35e26 < y < -2.7999999999999999e-31 or 2.95e37 < y

   1. Initial program 57.2%

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

   3. Taylor expanded in y around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   if -7.8000000000000002e58 < y < -1.35e26

   1. Initial program 51.3%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. distribute-lft-neg-out 31.9%

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

      3. *-commutative 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in z around inf 49.5%

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

      1. mul-1-neg 49.5%

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

   8. Simplified 49.5%

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

   if -2.7999999999999999e-31 < y < 2.95e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-31} \lor \neg \left(y \leq 2.95 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-50} \lor \neg \left(z \leq 2.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-50) (not (<= z 2.2e-14)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* z a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-50) || !(z <= 2.2e-14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * 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-50)) .or. (.not. (z <= 2.2d-14))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (z * 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-50) || !(z <= 2.2e-14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e-50) or not (z <= 2.2e-14):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e-50) || !(z <= 2.2e-14))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e-50) || ~((z <= 2.2e-14)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e-50], N[Not[LessEqual[z, 2.2e-14]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999975e-50 or 2.2000000000000001e-14 < z

   1. Initial program 43.0%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -5.49999999999999975e-50 < z < 2.2000000000000001e-14

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in z around 0 52.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-50} \lor \neg \left(z \leq 2.2 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+235}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-91} \lor \neg \left(z \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.8e+235)
   (/ (- a) b)
   (if (or (<= z -1.9e-91) (not (<= z 2.7e-6))) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.8e+235) {
		tmp = -a / b;
	} else if ((z <= -1.9e-91) || !(z <= 2.7e-6)) {
		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 <= (-7.8d+235)) then
        tmp = -a / b
    else if ((z <= (-1.9d-91)) .or. (.not. (z <= 2.7d-6))) 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 <= -7.8e+235) {
		tmp = -a / b;
	} else if ((z <= -1.9e-91) || !(z <= 2.7e-6)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.8e+235:
		tmp = -a / b
	elif (z <= -1.9e-91) or not (z <= 2.7e-6):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.8e+235)
		tmp = Float64(Float64(-a) / b);
	elseif ((z <= -1.9e-91) || !(z <= 2.7e-6))
		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 <= -7.8e+235)
		tmp = -a / b;
	elseif ((z <= -1.9e-91) || ~((z <= 2.7e-6)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.8e+235], N[((-a) / b), $MachinePrecision], If[Or[LessEqual[z, -1.9e-91], N[Not[LessEqual[z, 2.7e-6]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000005e235

   1. Initial program 11.0%

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

   3. Taylor expanded in a around inf 10.9%

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

      1. mul-1-neg 10.9%

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

      2. distribute-lft-neg-out 10.9%

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

      3. *-commutative 10.9%

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

   5. Simplified 10.9%

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

   6. Taylor expanded in y around 0 46.6%

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

      1. mul-1-neg 46.6%

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

   8. Simplified 46.6%

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

   if -7.8000000000000005e235 < z < -1.89999999999999989e-91 or 2.69999999999999998e-6 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in t around inf 29.0%

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

      1. associate-/l* 40.1%

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

      2. +-commutative 40.1%

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

      3. fma-define 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in b around inf 31.3%

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

   if -1.89999999999999989e-91 < z < 2.69999999999999998e-6

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 48.8%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+235}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-91} \lor \neg \left(z \leq 2.7 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-91} \lor \neg \left(z \leq 1.78 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e-91) (not (<= z 1.78e+53)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-91) || !(z <= 1.78e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.7d-91)) .or. (.not. (z <= 1.78d+53))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-91) || !(z <= 1.78e+53)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.7e-91) or not (z <= 1.78e+53):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e-91) || !(z <= 1.78e+53))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.7e-91) || ~((z <= 1.78e+53)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e-91], N[Not[LessEqual[z, 1.78e+53]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000013e-91 or 1.77999999999999999e53 < z

   1. Initial program 44.0%

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

   3. Taylor expanded in z around inf 77.8%

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

   if -1.70000000000000013e-91 < z < 1.77999999999999999e53

   1. Initial program 89.7%

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

   3. Taylor expanded in y around inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. unsub-neg 49.1%

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

   5. Simplified 49.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-91} \lor \neg \left(z \leq 1.78 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-91} \lor \neg \left(z \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e-91) (not (<= z 3.8e-13))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-91) || !(z <= 3.8e-13)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.8d-91)) .or. (.not. (z <= 3.8d-13))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-91) || !(z <= 3.8e-13)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e-91) or not (z <= 3.8e-13):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e-91) || !(z <= 3.8e-13))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.8e-91) || ~((z <= 3.8e-13)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e-91], N[Not[LessEqual[z, 3.8e-13]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-91 or 3.8e-13 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 26.8%

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

      1. associate-/l* 37.8%

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

      2. +-commutative 37.8%

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

      3. fma-define 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in z around inf 45.9%

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

   if -1.8e-91 < z < 3.8e-13

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 48.8%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-91} \lor \neg \left(z \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-48} \lor \neg \left(y \leq 3.85 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e-48) (not (<= y 3.85e-25))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-48) || !(y <= 3.85e-25)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.4d-48)) .or. (.not. (y <= 3.85d-25))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-48) || !(y <= 3.85e-25)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e-48) or not (y <= 3.85e-25):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e-48) || !(y <= 3.85e-25))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.4e-48) || ~((y <= 3.85e-25)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e-48], N[Not[LessEqual[y, 3.85e-25]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e-48 or 3.8500000000000001e-25 < y

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if -2.4e-48 < y < 3.8500000000000001e-25

   1. Initial program 80.4%

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

   3. Taylor expanded in t around inf 37.8%

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

      1. associate-/l* 45.6%

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

      2. +-commutative 45.6%

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

      3. fma-define 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in z around inf 45.9%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-48} \lor \neg \left(y \leq 3.85 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31} \lor \neg \left(y \leq 2.7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.8e-31) (not (<= y 2.7e+37))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e-31) || !(y <= 2.7e+37)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.8d-31)) .or. (.not. (y <= 2.7d+37))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.8e-31) || !(y <= 2.7e+37)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.8e-31) or not (y <= 2.7e+37):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.8e-31) || !(y <= 2.7e+37))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.8e-31) || ~((y <= 2.7e+37)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.8e-31], N[Not[LessEqual[y, 2.7e+37]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e-31 or 2.69999999999999986e37 < y

   1. Initial program 56.7%

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

   3. Taylor expanded in y around inf 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

   5. Simplified 53.6%

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

   if -2.7999999999999999e-31 < y < 2.69999999999999986e37

   1. Initial program 78.8%

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

   3. Taylor expanded in y around 0 53.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31} \lor \neg \left(y \leq 2.7 \cdot 10^{+37}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-91} \lor \neg \left(z \leq 6.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e-91) (not (<= z 6.2e-7))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e-91) || !(z <= 6.2e-7)) {
		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 <= (-1.9d-91)) .or. (.not. (z <= 6.2d-7))) 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 <= -1.9e-91) || !(z <= 6.2e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e-91) or not (z <= 6.2e-7):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e-91) || !(z <= 6.2e-7))
		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 <= -1.9e-91) || ~((z <= 6.2e-7)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e-91], N[Not[LessEqual[z, 6.2e-7]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999989e-91 or 6.1999999999999999e-7 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in t around inf 26.8%

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

      1. associate-/l* 37.8%

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

      2. +-commutative 37.8%

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

      3. fma-define 37.8%

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

   5. Simplified 37.8%

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

   6. Taylor expanded in b around inf 28.9%

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

   if -1.89999999999999989e-91 < z < 6.1999999999999999e-7

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 48.8%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-91} \lor \neg \left(z \leq 6.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.4%

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

3. Taylor expanded in z around 0 25.7%

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

4. Final simplification 25.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.0% 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 2024055 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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