Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.9% → 94.6%

Time: 18.2s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := x \cdot y + t\_2\\ t_4 := \frac{t\_3}{t\_1}\\ t_5 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + t\_5\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{t\_3}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t\_4 \leq 10^{-198}:\\ \;\;\;\;\left(t\_5 + \frac{y}{z} \cdot \frac{x}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_5 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ (* x y) t_2))
        (t_4 (/ t_3 t_1))
        (t_5 (/ (- a t) (- y b))))
   (if (<= t_4 (- INFINITY))
     (+ (* x (/ y (- y (* y z)))) t_5)
     (if (<= t_4 -2e-292)
       (/ t_3 (+ y (- (* z b) (* y z))))
       (if (<= t_4 1e-198)
         (+
          (+ t_5 (* (/ y z) (/ x (- b y))))
          (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
         (if (<= t_4 5e+257)
           (+ (/ (* x y) t_1) (/ t_2 t_1))
           (+ t_5 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (x * y) + t_2;
	double t_4 = t_3 / t_1;
	double t_5 = (a - t) / (y - b);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (x * (y / (y - (y * z)))) + t_5;
	} else if (t_4 <= -2e-292) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= 1e-198) {
		tmp = (t_5 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else if (t_4 <= 5e+257) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_5 + (x / (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (x * y) + t_2;
	double t_4 = t_3 / t_1;
	double t_5 = (a - t) / (y - b);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / (y - (y * z)))) + t_5;
	} else if (t_4 <= -2e-292) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= 1e-198) {
		tmp = (t_5 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else if (t_4 <= 5e+257) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_5 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (x * y) + t_2
	t_4 = t_3 / t_1
	t_5 = (a - t) / (y - b)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (x * (y / (y - (y * z)))) + t_5
	elif t_4 <= -2e-292:
		tmp = t_3 / (y + ((z * b) - (y * z)))
	elif t_4 <= 1e-198:
		tmp = (t_5 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	elif t_4 <= 5e+257:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	else:
		tmp = t_5 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(x * y) + t_2)
	t_4 = Float64(t_3 / t_1)
	t_5 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / Float64(y - Float64(y * z)))) + t_5);
	elseif (t_4 <= -2e-292)
		tmp = Float64(t_3 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_4 <= 1e-198)
		tmp = Float64(Float64(t_5 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	elseif (t_4 <= 5e+257)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(t_5 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (x * y) + t_2;
	t_4 = t_3 / t_1;
	t_5 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (x * (y / (y - (y * z)))) + t_5;
	elseif (t_4 <= -2e-292)
		tmp = t_3 / (y + ((z * b) - (y * z)));
	elseif (t_4 <= 1e-198)
		tmp = (t_5 + ((y / z) * (x / (b - y)))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	elseif (t_4 <= 5e+257)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	else
		tmp = t_5 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(x * N[(y / N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision], If[LessEqual[t$95$4, -2e-292], N[(t$95$3 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e-198], N[(N[(t$95$5 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $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], If[LessEqual[t$95$4, 5e+257], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$5 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 24.7%

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

   3. Taylor expanded in x around 0 24.7%

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

   4. Taylor expanded in z around inf 43.1%

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

   5. Taylor expanded in b around 0 43.1%

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

      1. associate-/l* 96.0%

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

      2. associate-*r* 96.0%

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

      3. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-292

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 9.9999999999999991e-199

   1. Initial program 42.7%

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

   3. Taylor expanded in z around inf 73.1%

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

      1. associate--r+ 73.1%

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

      2. +-commutative 73.1%

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

      3. associate--l+ 73.1%

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

      4. *-commutative 73.1%

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

      5. times-frac 96.0%

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

      6. div-sub 96.0%

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

      7. associate-/l* 96.4%

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

   5. Simplified 96.4%

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

   if 9.9999999999999991e-199 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.6%

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

   if 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.3%

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

   3. Taylor expanded in x around 0 17.3%

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

   4. Taylor expanded in z around inf 69.7%

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

   5. Taylor expanded in y around -inf 95.3%

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

      1. associate-*r/ 95.3%

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

      2. mul-1-neg 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-198}:\\ \;\;\;\;\left(\frac{a - t}{y - b} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := x \cdot y + t\_2\\ t_4 := \frac{t\_3}{t\_1}\\ t_5 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + t\_5\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{t\_3}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t\_4 \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_5 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ (* x y) t_2))
        (t_4 (/ t_3 t_1))
        (t_5 (/ (- a t) (- y b))))
   (if (<= t_4 (- INFINITY))
     (+ (* x (/ y (- y (* y z)))) t_5)
     (if (<= t_4 -2e-292)
       (/ t_3 (+ y (- (* z b) (* y z))))
       (if (<= t_4 1e-224)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_4 5e+257)
           (+ (/ (* x y) t_1) (/ t_2 t_1))
           (+ t_5 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (x * y) + t_2;
	double t_4 = t_3 / t_1;
	double t_5 = (a - t) / (y - b);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = (x * (y / (y - (y * z)))) + t_5;
	} else if (t_4 <= -2e-292) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_4 <= 5e+257) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_5 + (x / (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (x * y) + t_2;
	double t_4 = t_3 / t_1;
	double t_5 = (a - t) / (y - b);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / (y - (y * z)))) + t_5;
	} else if (t_4 <= -2e-292) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_4 <= 5e+257) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_5 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (x * y) + t_2
	t_4 = t_3 / t_1
	t_5 = (a - t) / (y - b)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = (x * (y / (y - (y * z)))) + t_5
	elif t_4 <= -2e-292:
		tmp = t_3 / (y + ((z * b) - (y * z)))
	elif t_4 <= 1e-224:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_4 <= 5e+257:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	else:
		tmp = t_5 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(x * y) + t_2)
	t_4 = Float64(t_3 / t_1)
	t_5 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / Float64(y - Float64(y * z)))) + t_5);
	elseif (t_4 <= -2e-292)
		tmp = Float64(t_3 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_4 <= 1e-224)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_4 <= 5e+257)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	else
		tmp = Float64(t_5 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (x * y) + t_2;
	t_4 = t_3 / t_1;
	t_5 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = (x * (y / (y - (y * z)))) + t_5;
	elseif (t_4 <= -2e-292)
		tmp = t_3 / (y + ((z * b) - (y * z)));
	elseif (t_4 <= 1e-224)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_4 <= 5e+257)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	else
		tmp = t_5 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(x * N[(y / N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision], If[LessEqual[t$95$4, -2e-292], N[(t$95$3 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e-224], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$4, 5e+257], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], N[(t$95$5 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 24.7%

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

   3. Taylor expanded in x around 0 24.7%

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

   4. Taylor expanded in z around inf 43.1%

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

   5. Taylor expanded in b around 0 43.1%

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

      1. associate-/l* 96.0%

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

      2. associate-*r* 96.0%

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

      3. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-292

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e-224

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.3%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in b around inf 83.9%

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

   if 1e-224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 99.6%

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

   if 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.3%

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

   3. Taylor expanded in x around 0 17.3%

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

   4. Taylor expanded in z around inf 69.7%

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

   5. Taylor expanded in y around -inf 95.3%

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

      1. associate-*r/ 95.3%

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

      2. mul-1-neg 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t\_1}{y + \left(z \cdot b - y \cdot z\right)}\\ t_3 := \frac{t\_1}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + t\_4\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ t_1 (+ y (- (* z b) (* y z)))))
        (t_3 (/ t_1 (+ y (* z (- b y)))))
        (t_4 (/ (- a t) (- y b))))
   (if (<= t_3 (- INFINITY))
     (+ (* x (/ y (- y (* y z)))) t_4)
     (if (<= t_3 -2e-292)
       t_2
       (if (<= t_3 1e-224)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_3 5e+257) t_2 (+ t_4 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + ((z * b) - (y * z)));
	double t_3 = t_1 / (y + (z * (b - y)));
	double t_4 = (a - t) / (y - b);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (x * (y / (y - (y * z)))) + t_4;
	} else if (t_3 <= -2e-292) {
		tmp = t_2;
	} else if (t_3 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_3 <= 5e+257) {
		tmp = t_2;
	} else {
		tmp = t_4 + (x / (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + ((z * b) - (y * z)));
	double t_3 = t_1 / (y + (z * (b - y)));
	double t_4 = (a - t) / (y - b);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / (y - (y * z)))) + t_4;
	} else if (t_3 <= -2e-292) {
		tmp = t_2;
	} else if (t_3 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_3 <= 5e+257) {
		tmp = t_2;
	} else {
		tmp = t_4 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = t_1 / (y + ((z * b) - (y * z)))
	t_3 = t_1 / (y + (z * (b - y)))
	t_4 = (a - t) / (y - b)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (x * (y / (y - (y * z)))) + t_4
	elif t_3 <= -2e-292:
		tmp = t_2
	elif t_3 <= 1e-224:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_3 <= 5e+257:
		tmp = t_2
	else:
		tmp = t_4 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(Float64(z * b) - Float64(y * z))))
	t_3 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_4 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / Float64(y - Float64(y * z)))) + t_4);
	elseif (t_3 <= -2e-292)
		tmp = t_2;
	elseif (t_3 <= 1e-224)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_3 <= 5e+257)
		tmp = t_2;
	else
		tmp = Float64(t_4 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = t_1 / (y + ((z * b) - (y * z)));
	t_3 = t_1 / (y + (z * (b - y)));
	t_4 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (x * (y / (y - (y * z)))) + t_4;
	elseif (t_3 <= -2e-292)
		tmp = t_2;
	elseif (t_3 <= 1e-224)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_3 <= 5e+257)
		tmp = t_2;
	else
		tmp = t_4 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(x * N[(y / N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[t$95$3, -2e-292], t$95$2, If[LessEqual[t$95$3, 1e-224], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$3, 5e+257], t$95$2, N[(t$95$4 + N[(x / N[(1.0 - z), $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

   1. Initial program 24.7%

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

   3. Taylor expanded in x around 0 24.7%

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

   4. Taylor expanded in z around inf 43.1%

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

   5. Taylor expanded in b around 0 43.1%

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

      1. associate-/l* 96.0%

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

      2. associate-*r* 96.0%

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

      3. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-292 or 1e-224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e-224

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.3%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in b around inf 83.9%

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

   if 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.3%

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

   3. Taylor expanded in x around 0 17.3%

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

   4. Taylor expanded in z around inf 69.7%

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

   5. Taylor expanded in y around -inf 95.3%

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

      1. associate-*r/ 95.3%

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

      2. mul-1-neg 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (/ (- a t) (- y b))))
   (if (<= t_1 (- INFINITY))
     (+ (* x (/ y (- y (* y z)))) t_2)
     (if (<= t_1 -2e-292)
       t_1
       (if (<= t_1 1e-224)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_1 5e+257) t_1 (+ t_2 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (y / (y - (y * z)))) + t_2;
	} else if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 5e+257) {
		tmp = t_1;
	} else {
		tmp = t_2 + (x / (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / (y - (y * z)))) + t_2;
	} else if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 5e+257) {
		tmp = t_1;
	} else {
		tmp = t_2 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = (a - t) / (y - b)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x * (y / (y - (y * z)))) + t_2
	elif t_1 <= -2e-292:
		tmp = t_1
	elif t_1 <= 1e-224:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_1 <= 5e+257:
		tmp = t_1
	else:
		tmp = t_2 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / Float64(y - Float64(y * z)))) + t_2);
	elseif (t_1 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-224)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_1 <= 5e+257)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * (y / (y - (y * z)))) + t_2;
	elseif (t_1 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-224)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_1 <= 5e+257)
		tmp = t_1;
	else
		tmp = t_2 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y / N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$1, -2e-292], t$95$1, If[LessEqual[t$95$1, 1e-224], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+257], t$95$1, N[(t$95$2 + N[(x / N[(1.0 - z), $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

   1. Initial program 24.7%

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

   3. Taylor expanded in x around 0 24.7%

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

   4. Taylor expanded in z around inf 43.1%

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

   5. Taylor expanded in b around 0 43.1%

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

      1. associate-/l* 96.0%

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

      2. associate-*r* 96.0%

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

      3. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-292 or 1e-224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.6%

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

   if -2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e-224

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.3%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in b around inf 83.9%

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

   if 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.3%

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

   3. Taylor expanded in x around 0 17.3%

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

   4. Taylor expanded in z around inf 69.7%

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

   5. Taylor expanded in y around -inf 95.3%

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

      1. associate-*r/ 95.3%

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

      2. mul-1-neg 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{y - y \cdot z} + \frac{a - t}{y - b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (+ (/ (- a t) (- y b)) (/ x (- 1.0 z)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e-292)
       t_1
       (if (<= t_1 1e-224)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_1 5e+257) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 5e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -2e-292) {
		tmp = t_1;
	} else if (t_1 <= 1e-224) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 5e+257) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((a - t) / (y - b)) + (x / (1.0 - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -2e-292:
		tmp = t_1
	elif t_1 <= 1e-224:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_1 <= 5e+257:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / Float64(y - b)) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-224)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_1 <= 5e+257)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((a - t) / (y - b)) + (x / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -2e-292)
		tmp = t_1;
	elseif (t_1 <= 1e-224)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_1 <= 5e+257)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e-292], t$95$1, If[LessEqual[t$95$1, 1e-224], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+257], t$95$1, 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 5.00000000000000028e257 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.1%

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

   3. Taylor expanded in x around 0 19.1%

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

   4. Taylor expanded in z around inf 63.2%

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

   5. Taylor expanded in y around -inf 95.4%

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

      1. associate-*r/ 95.4%

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

      2. mul-1-neg 95.4%

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

      3. sub-neg 95.4%

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

      4. metadata-eval 95.4%

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

   7. Simplified 95.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-292 or 1e-224 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000028e257

   1. Initial program 99.6%

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

   if -2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e-224

   1. Initial program 40.3%

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

   3. Taylor expanded in x around 0 40.3%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in b around inf 83.9%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-292}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{-224}:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t}{b - y}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-72}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -1.3e+51)
     t_1
     (if (<= z -9e+15)
       (+ (/ x (- 1.0 z)) (/ t (- b y)))
       (if (<= z -6.1e-72)
         (/ (* z (- t a)) (+ y (* z (- b y))))
         (if (<= z 7.2e-106) (+ x (/ (* z (- t (+ a (* x b)))) y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.3e+51) {
		tmp = t_1;
	} else if (z <= -9e+15) {
		tmp = (x / (1.0 - z)) + (t / (b - y));
	} else if (z <= -6.1e-72) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 7.2e-106) {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-1.3d+51)) then
        tmp = t_1
    else if (z <= (-9d+15)) then
        tmp = (x / (1.0d0 - z)) + (t / (b - y))
    else if (z <= (-6.1d-72)) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else if (z <= 7.2d-106) then
        tmp = x + ((z * (t - (a + (x * b)))) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.3e+51) {
		tmp = t_1;
	} else if (z <= -9e+15) {
		tmp = (x / (1.0 - z)) + (t / (b - y));
	} else if (z <= -6.1e-72) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else if (z <= 7.2e-106) {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -1.3e+51:
		tmp = t_1
	elif z <= -9e+15:
		tmp = (x / (1.0 - z)) + (t / (b - y))
	elif z <= -6.1e-72:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	elif z <= 7.2e-106:
		tmp = x + ((z * (t - (a + (x * b)))) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -1.3e+51)
		tmp = t_1;
	elseif (z <= -9e+15)
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(t / Float64(b - y)));
	elseif (z <= -6.1e-72)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 7.2e-106)
		tmp = Float64(x + Float64(Float64(z * Float64(t - Float64(a + Float64(x * b)))) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -1.3e+51)
		tmp = t_1;
	elseif (z <= -9e+15)
		tmp = (x / (1.0 - z)) + (t / (b - y));
	elseif (z <= -6.1e-72)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	elseif (z <= 7.2e-106)
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+51], t$95$1, If[LessEqual[z, -9e+15], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.1e-72], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-106], N[(x + N[(N[(z * N[(t - N[(a + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3000000000000001e51 or 7.20000000000000025e-106 < 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 77.8%

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

   if -1.3000000000000001e51 < z < -9e15

   1. Initial program 35.8%

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

   3. Taylor expanded in x around 0 36.0%

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

   4. Taylor expanded in z around inf 57.0%

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

   5. Taylor expanded in y around -inf 88.8%

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

      1. associate-*r/ 88.8%

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

      2. mul-1-neg 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in a around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

      5. unsub-neg 88.8%

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

      6. +-commutative 88.8%

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

   10. Simplified 88.8%

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

   if -9e15 < z < -6.09999999999999997e-72

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0 76.8%

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

   if -6.09999999999999997e-72 < z < 7.20000000000000025e-106

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in y around 0 73.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t}{b - y}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-72}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := t\_1 + \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-27}:\\ \;\;\;\;t\_1 + x \cdot \frac{y}{z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (+ t_1 (/ x (- 1.0 z)))))
   (if (<= y -5e-42)
     t_2
     (if (<= y -8.7e-131)
       (/ (- (* x y) (* z a)) (+ y (* z (- b y))))
       (if (<= y 2.65e-27) (+ t_1 (* x (/ y (* z b)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = t_1 + (x / (1.0 - z));
	double tmp;
	if (y <= -5e-42) {
		tmp = t_2;
	} else if (y <= -8.7e-131) {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	} else if (y <= 2.65e-27) {
		tmp = t_1 + (x * (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 = (a - t) / (y - b)
    t_2 = t_1 + (x / (1.0d0 - z))
    if (y <= (-5d-42)) then
        tmp = t_2
    else if (y <= (-8.7d-131)) then
        tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
    else if (y <= 2.65d-27) then
        tmp = t_1 + (x * (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 = (a - t) / (y - b);
	double t_2 = t_1 + (x / (1.0 - z));
	double tmp;
	if (y <= -5e-42) {
		tmp = t_2;
	} else if (y <= -8.7e-131) {
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	} else if (y <= 2.65e-27) {
		tmp = t_1 + (x * (y / (z * b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = t_1 + (x / (1.0 - z))
	tmp = 0
	if y <= -5e-42:
		tmp = t_2
	elif y <= -8.7e-131:
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)))
	elif y <= 2.65e-27:
		tmp = t_1 + (x * (y / (z * b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(t_1 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (y <= -5e-42)
		tmp = t_2;
	elseif (y <= -8.7e-131)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 2.65e-27)
		tmp = Float64(t_1 + Float64(x * 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 = (a - t) / (y - b);
	t_2 = t_1 + (x / (1.0 - z));
	tmp = 0.0;
	if (y <= -5e-42)
		tmp = t_2;
	elseif (y <= -8.7e-131)
		tmp = ((x * y) - (z * a)) / (y + (z * (b - y)));
	elseif (y <= 2.65e-27)
		tmp = t_1 + (x * (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[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-42], t$95$2, If[LessEqual[y, -8.7e-131], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-27], N[(t$95$1 + N[(x * N[(y / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000003e-42 or 2.65000000000000003e-27 < y

   1. Initial program 42.2%

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

   3. Taylor expanded in x around 0 42.2%

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

   4. Taylor expanded in z around inf 57.7%

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

   5. Taylor expanded in y around -inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

   7. Simplified 85.6%

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

   if -5.00000000000000003e-42 < y < -8.6999999999999996e-131

   1. Initial program 88.0%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. mul-1-neg 81.4%

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

      3. unsub-neg 81.4%

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

      4. *-commutative 81.4%

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

      5. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -8.6999999999999996e-131 < y < 2.65000000000000003e-27

   1. Initial program 81.8%

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

   3. Taylor expanded in x around 0 81.9%

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

   4. Taylor expanded in z around inf 88.2%

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

   5. Taylor expanded in y around 0 80.4%

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

      1. associate-/l* 80.5%

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

      2. *-commutative 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-42}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -8.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-27}:\\ \;\;\;\;\frac{a - t}{y - b} + x \cdot \frac{y}{z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (- a t) (- y b)) (/ x (- 1.0 z)))))
   (if (<= z -2.25e-39)
     t_1
     (if (<= z 2.9e-106)
       (+ x (/ (* z (- t (+ a (* x b)))) y))
       (if (<= z 1.8e-6) (/ (* z (- t a)) (+ y (* z (- b y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -2.25e-39) {
		tmp = t_1;
	} else if (z <= 2.9e-106) {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	} else if (z <= 1.8e-6) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) + (x / (1.0d0 - z))
    if (z <= (-2.25d-39)) then
        tmp = t_1
    else if (z <= 2.9d-106) then
        tmp = x + ((z * (t - (a + (x * b)))) / y)
    else if (z <= 1.8d-6) then
        tmp = (z * (t - a)) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -2.25e-39) {
		tmp = t_1;
	} else if (z <= 2.9e-106) {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	} else if (z <= 1.8e-6) {
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z))
	tmp = 0
	if z <= -2.25e-39:
		tmp = t_1
	elif z <= 2.9e-106:
		tmp = x + ((z * (t - (a + (x * b)))) / y)
	elif z <= 1.8e-6:
		tmp = (z * (t - a)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -2.25e-39)
		tmp = t_1;
	elseif (z <= 2.9e-106)
		tmp = Float64(x + Float64(Float64(z * Float64(t - Float64(a + Float64(x * b)))) / y));
	elseif (z <= 1.8e-6)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	tmp = 0.0;
	if (z <= -2.25e-39)
		tmp = t_1;
	elseif (z <= 2.9e-106)
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	elseif (z <= 1.8e-6)
		tmp = (z * (t - a)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-39], t$95$1, If[LessEqual[z, 2.9e-106], N[(x + N[(N[(z * N[(t - N[(a + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-6], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e-39 or 1.79999999999999992e-6 < z

   1. Initial program 42.2%

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

   3. Taylor expanded in x around 0 42.2%

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

   4. Taylor expanded in z around inf 80.6%

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

   5. Taylor expanded in y around -inf 85.2%

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

      1. associate-*r/ 85.2%

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

      2. mul-1-neg 85.2%

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

      3. sub-neg 85.2%

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

      4. metadata-eval 85.2%

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

   7. Simplified 85.2%

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

   if -2.25e-39 < z < 2.9e-106

   1. Initial program 82.6%

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

   3. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 72.8%

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

   if 2.9e-106 < z < 1.79999999999999992e-6

   1. Initial program 94.8%

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

   3. Taylor expanded in x around 0 75.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-44} \lor \neg \left(y \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;t\_1 + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \frac{y}{z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (or (<= y -4.5e-44) (not (<= y 7.5e-28)))
     (+ t_1 (/ x (- 1.0 z)))
     (+ t_1 (* x (/ y (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if ((y <= -4.5e-44) || !(y <= 7.5e-28)) {
		tmp = t_1 + (x / (1.0 - z));
	} else {
		tmp = t_1 + (x * (y / (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if ((y <= (-4.5d-44)) .or. (.not. (y <= 7.5d-28))) then
        tmp = t_1 + (x / (1.0d0 - z))
    else
        tmp = t_1 + (x * (y / (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if ((y <= -4.5e-44) || !(y <= 7.5e-28)) {
		tmp = t_1 + (x / (1.0 - z));
	} else {
		tmp = t_1 + (x * (y / (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if (y <= -4.5e-44) or not (y <= 7.5e-28):
		tmp = t_1 + (x / (1.0 - z))
	else:
		tmp = t_1 + (x * (y / (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if ((y <= -4.5e-44) || !(y <= 7.5e-28))
		tmp = Float64(t_1 + Float64(x / Float64(1.0 - z)));
	else
		tmp = Float64(t_1 + Float64(x * Float64(y / Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if ((y <= -4.5e-44) || ~((y <= 7.5e-28)))
		tmp = t_1 + (x / (1.0 - z));
	else
		tmp = t_1 + (x * (y / (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -4.5e-44], N[Not[LessEqual[y, 7.5e-28]], $MachinePrecision]], N[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x * N[(y / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-44 or 7.5000000000000003e-28 < y

   1. Initial program 42.2%

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

   3. Taylor expanded in x around 0 42.2%

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

   4. Taylor expanded in z around inf 57.7%

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

   5. Taylor expanded in y around -inf 85.6%

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

      1. associate-*r/ 85.6%

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

      2. mul-1-neg 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

   7. Simplified 85.6%

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

   if -4.4999999999999999e-44 < y < 7.5000000000000003e-28

   1. Initial program 82.6%

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

   3. Taylor expanded in x around 0 82.7%

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

   4. Taylor expanded in z around inf 85.5%

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

   5. Taylor expanded in y around 0 76.8%

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

      1. associate-/l* 76.9%

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

      2. *-commutative 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-44} \lor \neg \left(y \leq 7.5 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + x \cdot \frac{y}{z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-40} \lor \neg \left(z \leq 7.5 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-40) (not (<= z 7.5e-106)))
   (/ (- a t) (- y b))
   (+ x (/ (* z (- t (+ a (* x b)))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-40) || !(z <= 7.5e-106)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.3d-40)) .or. (.not. (z <= 7.5d-106))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x + ((z * (t - (a + (x * b)))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-40) || !(z <= 7.5e-106)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e-40) or not (z <= 7.5e-106):
		tmp = (a - t) / (y - b)
	else:
		tmp = x + ((z * (t - (a + (x * b)))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-40) || !(z <= 7.5e-106))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - Float64(a + Float64(x * b)))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e-40) || ~((z <= 7.5e-106)))
		tmp = (a - t) / (y - b);
	else
		tmp = x + ((z * (t - (a + (x * b)))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-40], N[Not[LessEqual[z, 7.5e-106]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - N[(a + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e-40 or 7.5000000000000002e-106 < z

   1. Initial program 48.9%

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

   3. Taylor expanded in z around inf 73.9%

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

   if -2.3e-40 < z < 7.5000000000000002e-106

   1. Initial program 82.6%

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

   3. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around 0 72.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-40} \lor \neg \left(z \leq 7.5 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - \left(a + x \cdot b\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.55e+61)
     t_1
     (if (<= y 8.2e-127)
       (/ (- t a) b)
       (if (<= y 1.2e+50) (/ a (- y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.55e+61) {
		tmp = t_1;
	} else if (y <= 8.2e-127) {
		tmp = (t - a) / b;
	} else if (y <= 1.2e+50) {
		tmp = a / (y - b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.55d+61)) then
        tmp = t_1
    else if (y <= 8.2d-127) then
        tmp = (t - a) / b
    else if (y <= 1.2d+50) then
        tmp = a / (y - b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.55e+61) {
		tmp = t_1;
	} else if (y <= 8.2e-127) {
		tmp = (t - a) / b;
	} else if (y <= 1.2e+50) {
		tmp = a / (y - 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 <= -2.55e+61:
		tmp = t_1
	elif y <= 8.2e-127:
		tmp = (t - a) / b
	elif y <= 1.2e+50:
		tmp = a / (y - 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 <= -2.55e+61)
		tmp = t_1;
	elseif (y <= 8.2e-127)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 1.2e+50)
		tmp = Float64(a / Float64(y - b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.55e+61)
		tmp = t_1;
	elseif (y <= 8.2e-127)
		tmp = (t - a) / b;
	elseif (y <= 1.2e+50)
		tmp = a / (y - b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+61], t$95$1, If[LessEqual[y, 8.2e-127], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.2e+50], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55000000000000005e61 or 1.2000000000000001e50 < y

   1. Initial program 38.9%

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

   3. Taylor expanded in y around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   if -2.55000000000000005e61 < y < 8.199999999999999e-127

   1. Initial program 80.2%

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

   3. Taylor expanded in y around 0 61.4%

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

   if 8.199999999999999e-127 < y < 1.2000000000000001e50

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 65.3%

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

   4. Taylor expanded in t around 0 47.5%

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

      1. associate-*r/ 47.5%

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

      2. neg-mul-1 47.5%

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

   6. Simplified 47.5%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-127}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.26 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-66}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.26e-85)
     t_1
     (if (<= y 1.35e-66) (/ (- a) b) (if (<= y 2.6e+49) (/ a y) 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 <= -1.26e-85) {
		tmp = t_1;
	} else if (y <= 1.35e-66) {
		tmp = -a / b;
	} else if (y <= 2.6e+49) {
		tmp = a / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.26d-85)) then
        tmp = t_1
    else if (y <= 1.35d-66) then
        tmp = -a / b
    else if (y <= 2.6d+49) then
        tmp = a / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.26e-85) {
		tmp = t_1;
	} else if (y <= 1.35e-66) {
		tmp = -a / b;
	} else if (y <= 2.6e+49) {
		tmp = a / y;
	} 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 <= -1.26e-85:
		tmp = t_1
	elif y <= 1.35e-66:
		tmp = -a / b
	elif y <= 2.6e+49:
		tmp = a / y
	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 <= -1.26e-85)
		tmp = t_1;
	elseif (y <= 1.35e-66)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 2.6e+49)
		tmp = Float64(a / y);
	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 <= -1.26e-85)
		tmp = t_1;
	elseif (y <= 1.35e-66)
		tmp = -a / b;
	elseif (y <= 2.6e+49)
		tmp = a / y;
	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, -1.26e-85], t$95$1, If[LessEqual[y, 1.35e-66], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 2.6e+49], N[(a / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.26e-85 or 2.59999999999999989e49 < y

   1. Initial program 42.0%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   if -1.26e-85 < y < 1.34999999999999998e-66

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf 34.8%

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

      1. mul-1-neg 34.8%

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

      2. distribute-lft-neg-out 34.8%

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

      3. *-commutative 34.8%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in y around 0 36.6%

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

      1. associate-*r/ 36.6%

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

      2. neg-mul-1 36.6%

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

   8. Simplified 36.6%

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

   if 1.34999999999999998e-66 < y < 2.59999999999999989e49

   1. Initial program 65.0%

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

   3. Taylor expanded in z around inf 69.6%

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

   4. Taylor expanded in t around 0 44.0%

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

      1. associate-*r/ 44.0%

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

      2. neg-mul-1 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in b around 0 39.0%

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

Alternative 13: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-62} \lor \neg \left(z \leq 6.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e-62) (not (<= z 6.8e-106)))
   (/ (- a t) (- y b))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-62) || !(z <= 6.8e-106)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * t) / 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 <= (-1.5d-62)) .or. (.not. (z <= 6.8d-106))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x + ((z * t) / 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 <= -1.5e-62) || !(z <= 6.8e-106)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e-62) or not (z <= 6.8e-106):
		tmp = (a - t) / (y - b)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e-62) || !(z <= 6.8e-106))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e-62) || ~((z <= 6.8e-106)))
		tmp = (a - t) / (y - b);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e-62], N[Not[LessEqual[z, 6.8e-106]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5000000000000001e-62 or 6.79999999999999965e-106 < z

   1. Initial program 50.2%

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

   3. Taylor expanded in z around inf 73.3%

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

   if -1.5000000000000001e-62 < z < 6.79999999999999965e-106

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 47.5%

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

      1. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in x around 0 69.9%

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

      1. div-sub 69.9%

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

   8. Simplified 69.9%

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

   9. Taylor expanded in t around inf 72.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-62} \lor \neg \left(z \leq 6.8 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.45e+61) (not (<= y 1.9e+45))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.45e+61) || !(y <= 1.9e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.45d+61)) .or. (.not. (y <= 1.9d+45))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.45e+61) || !(y <= 1.9e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.45e+61) or not (y <= 1.9e+45):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.45e+61) || !(y <= 1.9e+45))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.45e+61) || ~((y <= 1.9e+45)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.45e+61], N[Not[LessEqual[y, 1.9e+45]], $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 < -2.45000000000000013e61 or 1.9000000000000001e45 < y

   1. Initial program 38.6%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. mul-1-neg 63.7%

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

      2. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   if -2.45000000000000013e61 < y < 1.9000000000000001e45

   1. Initial program 79.3%

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

   3. Taylor expanded in y around 0 54.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+61} \lor \neg \left(y \leq 1.9 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-63} \lor \neg \left(z \leq 3.8 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e-63) (not (<= z 3.8e-97))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e-63) || !(z <= 3.8e-97)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.1d-63)) .or. (.not. (z <= 3.8d-97))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e-63) || !(z <= 3.8e-97)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.1e-63) or not (z <= 3.8e-97):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e-63) || !(z <= 3.8e-97))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.1e-63) || ~((z <= 3.8e-97)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e-63], N[Not[LessEqual[z, 3.8e-97]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e-63 or 3.8000000000000001e-97 < z

   1. Initial program 49.9%

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

   3. Taylor expanded in t around inf 21.8%

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

      1. *-commutative 21.8%

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

   5. Simplified 21.8%

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

   6. Taylor expanded in z around inf 35.3%

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

   if -1.1e-63 < z < 3.8000000000000001e-97

   1. Initial program 82.1%

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

   3. Taylor expanded in z around 0 62.1%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-63} \lor \neg \left(z \leq 3.8 \cdot 10^{-97}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-67} \lor \neg \left(z \leq 6.3 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-67) (not (<= z 6.3e-90))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-67) || !(z <= 6.3e-90)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6d-67)) .or. (.not. (z <= 6.3d-90))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-67) || !(z <= 6.3e-90)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-67) or not (z <= 6.3e-90):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-67) || !(z <= 6.3e-90))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-67) || ~((z <= 6.3e-90)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-67], N[Not[LessEqual[z, 6.3e-90]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000065e-67 or 6.29999999999999977e-90 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in a around inf 27.8%

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

      1. mul-1-neg 27.8%

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

      2. distribute-lft-neg-out 27.8%

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

      3. *-commutative 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in y around 0 29.9%

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

      1. associate-*r/ 29.9%

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

      2. neg-mul-1 29.9%

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

   8. Simplified 29.9%

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

   if -6.00000000000000065e-67 < z < 6.29999999999999977e-90

   1. Initial program 81.7%

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

   3. Taylor expanded in z around 0 61.3%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-67} \lor \neg \left(z \leq 6.3 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \lor \neg \left(z \leq 1.02\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.85) (not (<= z 1.02))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.85) || !(z <= 1.02)) {
		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 <= (-1.85d0)) .or. (.not. (z <= 1.02d0))) 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 <= -1.85) || !(z <= 1.02)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85) or not (z <= 1.02):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.85) || !(z <= 1.02))
		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 <= -1.85) || ~((z <= 1.02)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.85], N[Not[LessEqual[z, 1.02]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001 or 1.02 < z

   1. Initial program 39.7%

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

   3. Taylor expanded in z around inf 78.8%

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

   4. Taylor expanded in t around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. neg-mul-1 49.6%

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

   6. Simplified 49.6%

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

   7. Taylor expanded in b around 0 23.4%

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

   if -1.8500000000000001 < z < 1.02

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 49.3%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \lor \neg \left(z \leq 1.02\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -52.0) (/ a y) (if (<= z 3.8e-97) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -52.0) {
		tmp = a / y;
	} else if (z <= 3.8e-97) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-52.0d0)) then
        tmp = a / y
    else if (z <= 3.8d-97) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -52.0) {
		tmp = a / y;
	} else if (z <= 3.8e-97) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -52.0:
		tmp = a / y
	elif z <= 3.8e-97:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -52.0)
		tmp = Float64(a / y);
	elseif (z <= 3.8e-97)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -52.0)
		tmp = a / y;
	elseif (z <= 3.8e-97)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -52.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 3.8e-97], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -52

   1. Initial program 42.8%

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

   3. Taylor expanded in z around inf 80.1%

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

   4. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   6. Simplified 51.6%

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

   7. Taylor expanded in b around 0 28.0%

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

   if -52 < z < 3.8000000000000001e-97

   1. Initial program 83.3%

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

   3. Taylor expanded in z around 0 56.1%

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

   if 3.8000000000000001e-97 < z

   1. Initial program 49.4%

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

   3. Taylor expanded in t around inf 21.0%

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

      1. *-commutative 21.0%

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

   5. Simplified 21.0%

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

   6. Taylor expanded in y around 0 24.7%

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

Alternative 19: 25.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= z -6.2e+27) (/ a b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+27) {
		tmp = a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.2d+27)) then
        tmp = a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+27) {
		tmp = a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.2e+27:
		tmp = a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.2e+27)
		tmp = Float64(a / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.2e+27)
		tmp = a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.2e+27], N[(a / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999992e27

   1. Initial program 41.1%

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

   3. Taylor expanded in a around inf 26.2%

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

      1. mul-1-neg 26.2%

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

      2. distribute-lft-neg-out 26.2%

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

      3. *-commutative 26.2%

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

   5. Simplified 26.2%

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

   6. Taylor expanded in y around 0 28.4%

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

      1. associate-*r/ 28.4%

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

      2. neg-mul-1 28.4%

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

   8. Simplified 28.4%

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

      1. div-inv 28.3%

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

      2. add-sqr-sqrt 16.7%

         \[\leadsto \color{blue}{\left(\sqrt{-a} \cdot \sqrt{-a}\right)} \cdot \frac{1}{b} \]

      3. sqrt-unprod 18.2%

         \[\leadsto \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \cdot \frac{1}{b} \]

      4. sqr-neg 18.2%

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

      5. sqrt-unprod 4.6%

         \[\leadsto \color{blue}{\left(\sqrt{a} \cdot \sqrt{a}\right)} \cdot \frac{1}{b} \]

      6. add-sqr-sqrt 10.9%

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

   10. Applied egg-rr 10.9%

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

       1. associate-*r/ 10.9%

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

       2. *-rgt-identity 10.9%

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

   12. Simplified 10.9%

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

   if -6.19999999999999992e27 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0 34.4%

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

Alternative 20: 24.8% 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 62.0%

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

3. Taylor expanded in z around 0 26.5%

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

Developer Target 1: 74.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024116 
(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)))))