Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.3% → 95.1%

Time: 18.7s

Alternatives: 18

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := x \cdot \left(\frac{y}{t\_1} + \frac{\frac{t - a}{x}}{b - y}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z \cdot \left(\frac{t}{b - y} - \frac{a}{b - y}\right) + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot \frac{y}{z}}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (* x (+ (/ y t_1) (/ (/ (- t a) x) (- b y))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-301)
       t_2
       (if (<= t_2 0.0)
         (/ (+ (* z (- (/ t (- b y)) (/ a (- b y)))) (/ (* x y) (- b y))) z)
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY)
             t_3
             (+
              (+ (/ (* x (/ y z)) (- b y)) (/ (- t a) (- b y)))
              (* y (/ (- a t) (* z (pow (- b y) 2.0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-301:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(Float64(t - a) / x) / Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(z * Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)))) + Float64(Float64(x * y) / Float64(b - y))) / z);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / z)) / Float64(b - y)) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (((x * (y / z)) / (b - y)) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-301], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(z * N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 26.1%

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

   3. Taylor expanded in x around inf 66.4%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r* 86.6%

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

   6. Simplified 86.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000013e-301 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.5%

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

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

   1. Initial program 26.5%

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

   3. Taylor expanded in x around inf 26.5%

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

   4. Taylor expanded in z around inf 73.6%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. fma-define 73.6%

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

      2. div-sub 73.6%

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

      3. times-frac 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in z around 0 100.0%

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

   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 32.4%

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

      1. associate--r+ 32.4%

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

      2. +-commutative 32.4%

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

      3. associate--l+ 32.4%

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

      4. associate-/r* 32.8%

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

      5. associate-/l* 41.3%

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

      6. div-sub 41.3%

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

      7. associate-/l* 88.6%

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

   5. Simplified 88.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{\frac{t - a}{x}}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{z \cdot \left(\frac{t}{b - y} - \frac{a}{b - y}\right) + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{\frac{t - a}{x}}{b - y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot \frac{y}{z}}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := x \cdot \left(\frac{y}{t\_1} + \frac{\frac{t - a}{x}}{b - y}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{z \cdot \left(\frac{t}{b - y} - \frac{a}{b - y}\right) + \frac{x \cdot y}{b - y}}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (* x (+ (/ y t_1) (/ (/ (- t a) x) (- b y))))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-301)
       t_2
       (if (<= t_2 0.0)
         (/ (+ (* z (- (/ t (- b y)) (/ a (- b y)))) (/ (* x y) (- b y))) z)
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) t_3 (/ (- t a) (- b y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-301) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-301:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(Float64(t - a) / x) / Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(z * Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)))) + Float64(Float64(x * y) / Float64(b - y))) / z);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	t_3 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-301)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = ((z * ((t / (b - y)) - (a / (b - y)))) + ((x * y) / (b - y))) / z;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-301], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(N[(z * N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 26.1%

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

   3. Taylor expanded in x around inf 66.4%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r* 86.6%

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

   6. Simplified 86.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000013e-301 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.5%

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

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

   1. Initial program 26.5%

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

   3. Taylor expanded in x around inf 26.5%

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

   4. Taylor expanded in z around inf 73.6%

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

      1. associate-/r* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in z around inf 73.6%

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

      1. fma-define 73.6%

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

      2. div-sub 73.6%

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

      3. times-frac 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in z around 0 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 77.4%

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

Alternative 3: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_4 := x \cdot \left(\frac{y}{t\_1} + \frac{\frac{t - a}{x}}{b - y}\right)\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-238}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (* x (+ (/ y t_1) (/ (/ (- t a) x) (- b y))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -2e-238)
       t_3
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 2e+306) t_3 (if (<= t_3 INFINITY) t_4 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 t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -2e-238) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+306) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -2e-238) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+306) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} 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)
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = x * ((y / t_1) + (((t - a) / x) / (b - y)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -2e-238:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 2e+306:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_4
	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))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(Float64(t - a) / x) / Float64(b - y))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -2e-238)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+306)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	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);
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = x * ((y / t_1) + (((t - a) / x) / (b - y)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -2e-238)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+306)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	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]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -2e-238], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 2e+306], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$4, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 26.1%

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

   3. Taylor expanded in x around inf 66.4%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r* 86.6%

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

   6. Simplified 86.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-238 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.5%

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

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

   1. Initial program 10.9%

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

   3. Taylor expanded in z around inf 78.4%

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

Alternative 4: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-215}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x \cdot y + t\_1}{y - y \cdot z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{t\_1}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -6e-64)
     t_2
     (if (<= z -1.6e-215)
       (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))
       (if (<= z 3.4e-168)
         (/ (+ (* x y) t_1) (- y (* y z)))
         (if (<= z 1.0) (/ t_1 (+ y (* z b))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e-64) {
		tmp = t_2;
	} else if (z <= -1.6e-215) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (z <= 3.4e-168) {
		tmp = ((x * y) + t_1) / (y - (y * z));
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-6d-64)) then
        tmp = t_2
    else if (z <= (-1.6d-215)) then
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    else if (z <= 3.4d-168) then
        tmp = ((x * y) + t_1) / (y - (y * z))
    else if (z <= 1.0d0) then
        tmp = t_1 / (y + (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -6e-64) {
		tmp = t_2;
	} else if (z <= -1.6e-215) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (z <= 3.4e-168) {
		tmp = ((x * y) + t_1) / (y - (y * z));
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -6e-64:
		tmp = t_2
	elif z <= -1.6e-215:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	elif z <= 3.4e-168:
		tmp = ((x * y) + t_1) / (y - (y * z))
	elif z <= 1.0:
		tmp = t_1 / (y + (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6e-64)
		tmp = t_2;
	elseif (z <= -1.6e-215)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 3.4e-168)
		tmp = Float64(Float64(Float64(x * y) + t_1) / Float64(y - Float64(y * z)));
	elseif (z <= 1.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6e-64)
		tmp = t_2;
	elseif (z <= -1.6e-215)
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	elseif (z <= 3.4e-168)
		tmp = ((x * y) + t_1) / (y - (y * z));
	elseif (z <= 1.0)
		tmp = t_1 / (y + (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-64], t$95$2, If[LessEqual[z, -1.6e-215], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-168], N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e-64 or 1 < z

   1. Initial program 45.1%

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

   3. Taylor expanded in z around inf 77.5%

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

   if -6.0000000000000001e-64 < z < -1.6000000000000001e-215

   1. Initial program 87.1%

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

   3. Taylor expanded in t around inf 70.9%

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

      1. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -1.6000000000000001e-215 < z < 3.40000000000000022e-168

   1. Initial program 83.6%

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

   3. Taylor expanded in b around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if 3.40000000000000022e-168 < z < 1

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in b around inf 66.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-215}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - y \cdot z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-199}:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot a - x \cdot y}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{t\_1}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.7e+27)
     t_2
     (if (<= z -8e-199)
       (/ t_1 (+ y (* z (- b y))))
       (if (<= z 4.2e-169)
         (/ (- (* z a) (* x y)) (* y (+ z -1.0)))
         (if (<= z 1.0) (/ t_1 (+ y (* z b))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_2;
	} else if (z <= -8e-199) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 4.2e-169) {
		tmp = ((z * a) - (x * y)) / (y * (z + -1.0));
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-1.7d+27)) then
        tmp = t_2
    else if (z <= (-8d-199)) then
        tmp = t_1 / (y + (z * (b - y)))
    else if (z <= 4.2d-169) then
        tmp = ((z * a) - (x * y)) / (y * (z + (-1.0d0)))
    else if (z <= 1.0d0) then
        tmp = t_1 / (y + (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_2;
	} else if (z <= -8e-199) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 4.2e-169) {
		tmp = ((z * a) - (x * y)) / (y * (z + -1.0));
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.7e+27:
		tmp = t_2
	elif z <= -8e-199:
		tmp = t_1 / (y + (z * (b - y)))
	elif z <= 4.2e-169:
		tmp = ((z * a) - (x * y)) / (y * (z + -1.0))
	elif z <= 1.0:
		tmp = t_1 / (y + (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.7e+27)
		tmp = t_2;
	elseif (z <= -8e-199)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 4.2e-169)
		tmp = Float64(Float64(Float64(z * a) - Float64(x * y)) / Float64(y * Float64(z + -1.0)));
	elseif (z <= 1.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.7e+27)
		tmp = t_2;
	elseif (z <= -8e-199)
		tmp = t_1 / (y + (z * (b - y)));
	elseif (z <= 4.2e-169)
		tmp = ((z * a) - (x * y)) / (y * (z + -1.0));
	elseif (z <= 1.0)
		tmp = t_1 / (y + (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+27], t$95$2, If[LessEqual[z, -8e-199], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-169], N[(N[(N[(z * a), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7e27 or 1 < z

   1. Initial program 40.0%

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

   3. Taylor expanded in z around inf 79.8%

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

   if -1.7e27 < z < -7.99999999999999986e-199

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 54.9%

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

   if -7.99999999999999986e-199 < z < 4.2000000000000001e-169

   1. Initial program 85.0%

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

   3. Taylor expanded in b around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

      5. cancel-sign-sub-inv 65.8%

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

      6. *-lft-identity 65.8%

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

      7. distribute-rgt-in 65.8%

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

      8. sub-neg 65.8%

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

   8. Simplified 65.8%

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

   if 4.2000000000000001e-169 < z < 1

   1. Initial program 90.4%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in b around inf 66.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot a - x \cdot y}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -52000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{t\_1}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -52000000.0)
     t_2
     (if (<= z -2.2e-174)
       (/ t_1 (+ y (* z (- b y))))
       (if (<= z 5.5e-142)
         (/ x (- 1.0 z))
         (if (<= z 1.0) (/ t_1 (+ y (* z b))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -52000000.0) {
		tmp = t_2;
	} else if (z <= -2.2e-174) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 5.5e-142) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-52000000.0d0)) then
        tmp = t_2
    else if (z <= (-2.2d-174)) then
        tmp = t_1 / (y + (z * (b - y)))
    else if (z <= 5.5d-142) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.0d0) then
        tmp = t_1 / (y + (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -52000000.0) {
		tmp = t_2;
	} else if (z <= -2.2e-174) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 5.5e-142) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.0) {
		tmp = t_1 / (y + (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -52000000.0:
		tmp = t_2
	elif z <= -2.2e-174:
		tmp = t_1 / (y + (z * (b - y)))
	elif z <= 5.5e-142:
		tmp = x / (1.0 - z)
	elif z <= 1.0:
		tmp = t_1 / (y + (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -52000000.0)
		tmp = t_2;
	elseif (z <= -2.2e-174)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 5.5e-142)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.0)
		tmp = Float64(t_1 / Float64(y + Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -52000000.0)
		tmp = t_2;
	elseif (z <= -2.2e-174)
		tmp = t_1 / (y + (z * (b - y)));
	elseif (z <= 5.5e-142)
		tmp = x / (1.0 - z);
	elseif (z <= 1.0)
		tmp = t_1 / (y + (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -52000000.0], t$95$2, If[LessEqual[z, -2.2e-174], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-142], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(t$95$1 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e7 or 1 < z

   1. Initial program 40.8%

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

   3. Taylor expanded in z around inf 78.6%

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

   if -5.2e7 < z < -2.20000000000000022e-174

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 60.8%

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

   if -2.20000000000000022e-174 < z < 5.50000000000000023e-142

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

   5. Simplified 59.3%

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

   if 5.50000000000000023e-142 < z < 1

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 68.8%

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

   4. Taylor expanded in b around inf 68.8%

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

Alternative 7: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.7e+27)
     t_2
     (if (<= z -4e-166)
       t_1
       (if (<= z 1.2e-139) (/ x (- 1.0 z)) (if (<= z 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_2;
	} else if (z <= -4e-166) {
		tmp = t_1;
	} else if (z <= 1.2e-139) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (t - a)) / (y + (z * b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.7d+27)) then
        tmp = t_2
    else if (z <= (-4d-166)) then
        tmp = t_1
    else if (z <= 1.2d-139) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_2;
	} else if (z <= -4e-166) {
		tmp = t_1;
	} else if (z <= 1.2e-139) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.7e+27:
		tmp = t_2
	elif z <= -4e-166:
		tmp = t_1
	elif z <= 1.2e-139:
		tmp = x / (1.0 - z)
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.7e+27)
		tmp = t_2;
	elseif (z <= -4e-166)
		tmp = t_1;
	elseif (z <= 1.2e-139)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) / (y + (z * b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.7e+27)
		tmp = t_2;
	elseif (z <= -4e-166)
		tmp = t_1;
	elseif (z <= 1.2e-139)
		tmp = x / (1.0 - z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+27], t$95$2, If[LessEqual[z, -4e-166], t$95$1, If[LessEqual[z, 1.2e-139], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e27 or 1 < z

   1. Initial program 40.0%

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

   3. Taylor expanded in z around inf 79.8%

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

   if -1.7e27 < z < -4.00000000000000016e-166 or 1.20000000000000007e-139 < z < 1

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 63.6%

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

   4. Taylor expanded in b around inf 62.8%

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

   if -4.00000000000000016e-166 < z < 1.20000000000000007e-139

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

   5. Simplified 59.3%

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

Alternative 8: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+42} \lor \neg \left(z \leq 6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+42) (not (<= z 6e+63)))
   (/ (- 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 <= -3.8e+42) || !(z <= 6e+63)) {
		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 <= (-3.8d+42)) .or. (.not. (z <= 6d+63))) 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 <= -3.8e+42) || !(z <= 6e+63)) {
		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 <= -3.8e+42) or not (z <= 6e+63):
		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 <= -3.8e+42) || !(z <= 6e+63))
		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 <= -3.8e+42) || ~((z <= 6e+63)))
		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, -3.8e+42], N[Not[LessEqual[z, 6e+63]], $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 < -3.7999999999999998e42 or 5.99999999999999998e63 < z

   1. Initial program 32.1%

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

   3. Taylor expanded in z around inf 80.8%

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

   if -3.7999999999999998e42 < z < 5.99999999999999998e63

   1. Initial program 86.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+42} \lor \neg \left(z \leq 6 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-64) (not (<= z 1.6e-6)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-64) || !(z <= 1.6e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6d-64)) .or. (.not. (z <= 1.6d-6))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-64) || !(z <= 1.6e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-64) or not (z <= 1.6e-6):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-64) || !(z <= 1.6e-6))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-64) || ~((z <= 1.6e-6)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-64], N[Not[LessEqual[z, 1.6e-6]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000001e-64 or 1.5999999999999999e-6 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in z around inf 77.1%

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

   if -6.0000000000000001e-64 < z < 1.5999999999999999e-6

   1. Initial program 86.5%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-64} \lor \neg \left(z \leq 1.6 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 0.00035:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.8e+35)
     t_1
     (if (<= y -2.15e-32)
       (/ (- a t) y)
       (if (<= y 0.00035) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e+35) {
		tmp = t_1;
	} else if (y <= -2.15e-32) {
		tmp = (a - t) / y;
	} else if (y <= 0.00035) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.8d+35)) then
        tmp = t_1
    else if (y <= (-2.15d-32)) then
        tmp = (a - t) / y
    else if (y <= 0.00035d0) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e+35) {
		tmp = t_1;
	} else if (y <= -2.15e-32) {
		tmp = (a - t) / y;
	} else if (y <= 0.00035) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.8e+35:
		tmp = t_1
	elif y <= -2.15e-32:
		tmp = (a - t) / y
	elif y <= 0.00035:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.8e+35)
		tmp = t_1;
	elseif (y <= -2.15e-32)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 0.00035)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.8e+35)
		tmp = t_1;
	elseif (y <= -2.15e-32)
		tmp = (a - t) / y;
	elseif (y <= 0.00035)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+35], t$95$1, If[LessEqual[y, -2.15e-32], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 0.00035], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e35 or 3.49999999999999996e-4 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

   5. Simplified 53.8%

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

   if -3.8e35 < y < -2.14999999999999995e-32

   1. Initial program 58.8%

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

   3. Taylor expanded in z around inf 69.4%

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

   4. Taylor expanded in b around 0 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-neg-frac2 59.0%

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

   6. Simplified 59.0%

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

   if -2.14999999999999995e-32 < y < 3.49999999999999996e-4

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 59.1%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 0.00035:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-64} \lor \neg \left(z \leq 1.32 \cdot 10^{-135}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e-64) (not (<= z 1.32e-135)))
   (/ (- t a) (- b y))
   (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-64) || !(z <= 1.32e-135)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.2d-64)) .or. (.not. (z <= 1.32d-135))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-64) || !(z <= 1.32e-135)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e-64) or not (z <= 1.32e-135):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e-64) || !(z <= 1.32e-135))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e-64) || ~((z <= 1.32e-135)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e-64], N[Not[LessEqual[z, 1.32e-135]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999975e-64 or 1.32000000000000007e-135 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 69.0%

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

   if -3.19999999999999975e-64 < z < 1.32000000000000007e-135

   1. Initial program 84.7%

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

   3. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in z around 0 51.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-64} \lor \neg \left(z \leq 1.32 \cdot 10^{-135}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-32} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e-32) (not (<= y 6.5e-6))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e-32) || !(y <= 6.5e-6)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2d-32)) .or. (.not. (y <= 6.5d-6))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e-32) || !(y <= 6.5e-6)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2e-32) or not (y <= 6.5e-6):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2e-32) || !(y <= 6.5e-6))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2e-32) || ~((y <= 6.5e-6)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2e-32], N[Not[LessEqual[y, 6.5e-6]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000011e-32 or 6.4999999999999996e-6 < y

   1. Initial program 53.4%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

   if -2.00000000000000011e-32 < y < 6.4999999999999996e-6

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 59.1%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-32} \lor \neg \left(y \leq 6.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46} \lor \neg \left(y \leq 17000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.8e+46) (not (<= y 17000.0))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.8e+46) || !(y <= 17000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.8d+46)) .or. (.not. (y <= 17000.0d0))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.8e+46) || !(y <= 17000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.8e+46) or not (y <= 17000.0):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.8e+46) || !(y <= 17000.0))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.8e+46) || ~((y <= 17000.0)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.8e+46], N[Not[LessEqual[y, 17000.0]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e46 or 17000 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

   5. Simplified 54.7%

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

   if -1.7999999999999999e46 < y < 17000

   1. Initial program 77.7%

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

   3. Taylor expanded in z around inf 67.4%

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

   4. Taylor expanded in t around inf 39.5%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46} \lor \neg \left(y \leq 17000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-64) (not (<= z 8.6e-48))) (/ t (- b y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-64) || !(z <= 8.6e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.8d-64)) .or. (.not. (z <= 8.6d-48))) then
        tmp = t / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-64) || !(z <= 8.6e-48)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-64) or not (z <= 8.6e-48):
		tmp = t / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-64) || !(z <= 8.6e-48))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.8e-64) || ~((z <= 8.6e-48)))
		tmp = t / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-64], N[Not[LessEqual[z, 8.6e-48]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999997e-64 or 8.6e-48 < z

   1. Initial program 48.8%

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

   3. Taylor expanded in z around inf 75.5%

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

   4. Taylor expanded in t around inf 42.8%

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

   if -4.79999999999999997e-64 < z < 8.6e-48

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in z around 0 46.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-64} \lor \neg \left(z \leq 8.6 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 32.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -16000000000:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -16000000000.0)
   (/ x (- z))
   (if (<= z 1.45e-43) (+ x (* x z)) (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -16000000000.0) {
		tmp = x / -z;
	} else if (z <= 1.45e-43) {
		tmp = x + (x * z);
	} else {
		tmp = 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 <= (-16000000000.0d0)) then
        tmp = x / -z
    else if (z <= 1.45d-43) then
        tmp = x + (x * z)
    else
        tmp = 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 <= -16000000000.0) {
		tmp = x / -z;
	} else if (z <= 1.45e-43) {
		tmp = x + (x * z);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -16000000000.0:
		tmp = x / -z
	elif z <= 1.45e-43:
		tmp = x + (x * z)
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -16000000000.0)
		tmp = Float64(x / Float64(-z));
	elseif (z <= 1.45e-43)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -16000000000.0)
		tmp = x / -z;
	elseif (z <= 1.45e-43)
		tmp = x + (x * z);
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -16000000000.0], N[(x / (-z)), $MachinePrecision], If[LessEqual[z, 1.45e-43], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e10

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf 21.9%

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

      1. mul-1-neg 21.9%

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

      2. unsub-neg 21.9%

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

   5. Simplified 21.9%

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

   6. Taylor expanded in z around inf 21.9%

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

      1. associate-*r/ 21.9%

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

      2. mul-1-neg 21.9%

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

   8. Simplified 21.9%

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

   if -1.6e10 < z < 1.4500000000000001e-43

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. unsub-neg 42.7%

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

   5. Simplified 42.7%

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

   6. Taylor expanded in z around 0 42.8%

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

   if 1.4500000000000001e-43 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in b around 0 26.7%

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

      1. mul-1-neg 26.7%

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

      2. *-commutative 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in t around 0 16.4%

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

      1. +-commutative 16.4%

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

      2. mul-1-neg 16.4%

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

      3. unsub-neg 16.4%

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

      4. *-commutative 16.4%

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

      5. cancel-sign-sub-inv 16.4%

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

      6. *-lft-identity 16.4%

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

      7. distribute-rgt-in 16.4%

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

      8. sub-neg 16.4%

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

   8. Simplified 16.4%

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

   9. Taylor expanded in z around inf 23.1%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -16000000000:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0001 \lor \neg \left(z \leq 1.45 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.0001) (not (<= z 1.45e-43))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.0001) || !(z <= 1.45e-43)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.0001d0)) .or. (.not. (z <= 1.45d-43))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.0001) || !(z <= 1.45e-43)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.0001) or not (z <= 1.45e-43):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.0001) || !(z <= 1.45e-43))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.0001) || ~((z <= 1.45e-43)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.0001], N[Not[LessEqual[z, 1.45e-43]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000005e-4 or 1.4500000000000001e-43 < z

   1. Initial program 45.5%

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

   3. Taylor expanded in b around 0 25.2%

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

      1. mul-1-neg 25.2%

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

      2. *-commutative 25.2%

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

   5. Simplified 25.2%

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

   6. Taylor expanded in t around 0 15.0%

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

      1. +-commutative 15.0%

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

      2. mul-1-neg 15.0%

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

      3. unsub-neg 15.0%

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

      4. *-commutative 15.0%

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

      5. cancel-sign-sub-inv 15.0%

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

      6. *-lft-identity 15.0%

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

      7. distribute-rgt-in 15.0%

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

      8. sub-neg 15.0%

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

   8. Simplified 15.0%

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

   9. Taylor expanded in z around inf 20.3%

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

   if -1.00000000000000005e-4 < z < 1.4500000000000001e-43

   1. Initial program 86.1%

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

   3. Taylor expanded in z around 0 43.6%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0001 \lor \neg \left(z \leq 1.45 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0001:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.0001) (/ x (- z)) (if (<= z 1.45e-43) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.0001) {
		tmp = x / -z;
	} else if (z <= 1.45e-43) {
		tmp = x;
	} else {
		tmp = 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 <= (-0.0001d0)) then
        tmp = x / -z
    else if (z <= 1.45d-43) then
        tmp = x
    else
        tmp = 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 <= -0.0001) {
		tmp = x / -z;
	} else if (z <= 1.45e-43) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.0001:
		tmp = x / -z
	elif z <= 1.45e-43:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.0001)
		tmp = Float64(x / Float64(-z));
	elseif (z <= 1.45e-43)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.0001)
		tmp = x / -z;
	elseif (z <= 1.45e-43)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.0001], N[(x / (-z)), $MachinePrecision], If[LessEqual[z, 1.45e-43], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000005e-4

   1. Initial program 40.6%

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

   3. Taylor expanded in y around inf 20.7%

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

      1. mul-1-neg 20.7%

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

      2. unsub-neg 20.7%

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

   5. Simplified 20.7%

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

   6. Taylor expanded in z around inf 20.7%

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

      1. associate-*r/ 20.7%

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

      2. mul-1-neg 20.7%

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

   8. Simplified 20.7%

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

   if -1.00000000000000005e-4 < z < 1.4500000000000001e-43

   1. Initial program 86.1%

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

   3. Taylor expanded in z around 0 43.6%

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

   if 1.4500000000000001e-43 < z

   1. Initial program 48.6%

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

   3. Taylor expanded in b around 0 26.7%

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

      1. mul-1-neg 26.7%

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

      2. *-commutative 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in t around 0 16.4%

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

      1. +-commutative 16.4%

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

      2. mul-1-neg 16.4%

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

      3. unsub-neg 16.4%

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

      4. *-commutative 16.4%

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

      5. cancel-sign-sub-inv 16.4%

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

      6. *-lft-identity 16.4%

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

      7. distribute-rgt-in 16.4%

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

      8. sub-neg 16.4%

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

   8. Simplified 16.4%

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

   9. Taylor expanded in z around inf 23.1%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0001:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.3%

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

3. Taylor expanded in z around 0 23.9%

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

Developer Target 1: 74.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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