Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 90.5%

Time: 13.4s

Alternatives: 18

Speedup: 1.5×

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: 66.8% 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: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ t_4 := {\left(b - y\right)}^{2}\\ t_5 := \frac{y}{\frac{b - y}{x}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{z}{z + -1} \cdot \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2 + \frac{\frac{y}{\frac{t_4}{a - t}} + t_5}{z}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+245}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_5 + \frac{a - t}{\frac{t_4}{y}}}{z} + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_4 (pow (- b y) 2.0))
        (t_5 (/ y (/ (- b y) x))))
   (if (<= t_3 (- INFINITY))
     (- (* (/ z (+ z -1.0)) (/ (- a t) y)) (/ x (+ z -1.0)))
     (if (<= t_3 -5e-262)
       t_3
       (if (<= t_3 0.0)
         (+ t_2 (/ (+ (/ y (/ t_4 (- a t))) t_5) z))
         (if (<= t_3 2e+245)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (+ (/ (+ t_5 (/ (- a t) (/ t_4 y))) z) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = pow((b - y), 2.0);
	double t_5 = y / ((b - y) / x);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	} else if (t_3 <= -5e-262) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2 + (((y / (t_4 / (a - t))) + t_5) / z);
	} else if (t_3 <= 2e+245) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = ((t_5 + ((a - t) / (t_4 / y))) / z) + t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((x * y) + (z * (t - a))) / t_1;
	double t_4 = Math.pow((b - y), 2.0);
	double t_5 = y / ((b - y) / x);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	} else if (t_3 <= -5e-262) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2 + (((y / (t_4 / (a - t))) + t_5) / z);
	} else if (t_3 <= 2e+245) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else {
		tmp = ((t_5 + ((a - t) / (t_4 / y))) / z) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = ((x * y) + (z * (t - a))) / t_1
	t_4 = math.pow((b - y), 2.0)
	t_5 = y / ((b - y) / x)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0))
	elif t_3 <= -5e-262:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2 + (((y / (t_4 / (a - t))) + t_5) / z)
	elif t_3 <= 2e+245:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	else:
		tmp = ((t_5 + ((a - t) / (t_4 / y))) / z) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_4 = Float64(b - y) ^ 2.0
	t_5 = Float64(y / Float64(Float64(b - y) / x))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(Float64(a - t) / y)) - Float64(x / Float64(z + -1.0)));
	elseif (t_3 <= -5e-262)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(Float64(y / Float64(t_4 / Float64(a - t))) + t_5) / z));
	elseif (t_3 <= 2e+245)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	else
		tmp = Float64(Float64(Float64(t_5 + Float64(Float64(a - t) / Float64(t_4 / y))) / z) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = ((x * y) + (z * (t - a))) / t_1;
	t_4 = (b - y) ^ 2.0;
	t_5 = y / ((b - y) / x);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	elseif (t_3 <= -5e-262)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2 + (((y / (t_4 / (a - t))) + t_5) / z);
	elseif (t_3 <= 2e+245)
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	else
		tmp = ((t_5 + ((a - t) / (t_4 / y))) / z) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$5 = N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-262], t$95$3, If[LessEqual[t$95$3, 0.0], N[(t$95$2 + N[(N[(N[(y / N[(t$95$4 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+245], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(N[(t$95$5 + N[(N[(a - t), $MachinePrecision] / N[(t$95$4 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$2), $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 41.0%

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

   2. Taylor expanded in y around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

      3. mul-1-neg 57.2%

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

      4. distribute-neg-frac 57.2%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in b around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. times-frac 75.6%

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

      3. sub-neg 75.6%

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

      4. metadata-eval 75.6%

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

   7. Simplified 75.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999992e-262

   1. Initial program 99.7%

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

   if -4.99999999999999992e-262 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 10.6%

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

      1. sub-neg 10.6%

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

      2. distribute-lft-in 10.6%

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

   3. Applied egg-rr 10.6%

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

   4. Taylor expanded in z around -inf 82.0%

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

      1. +-commutative 82.0%

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

      2. mul-1-neg 82.0%

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

      3. unsub-neg 82.0%

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

      4. associate-*r/ 82.0%

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

      5. mul-1-neg 82.0%

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

      6. +-commutative 82.0%

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

      7. mul-1-neg 82.0%

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

      8. unsub-neg 82.0%

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

   6. Simplified 82.5%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000009e245

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

   if 2.00000000000000009e245 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.2%

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

   2. Taylor expanded in z around -inf 36.0%

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

      1. +-commutative 36.0%

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

      2. associate--l+ 36.0%

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

   4. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{z + -1} \cdot \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{{\left(b - y\right)}^{2}}{a - t}} + \frac{y}{\frac{b - y}{x}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+245}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 90.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{z}{z + -1} \cdot \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0 \lor \neg \left(t_2 \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (+ (* x y) (* z (- t a))) t_1)))
   (if (<= t_2 (- INFINITY))
     (- (* (/ z (+ z -1.0)) (/ (- a t) y)) (/ x (+ z -1.0)))
     (if (<= t_2 -5e-262)
       t_2
       (if (or (<= t_2 0.0) (not (<= t_2 2e+245)))
         (+
          (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
          (/ (- t a) (- b y)))
         (/ (+ (* x y) (- (* z t) (* z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	} else if (t_2 <= -5e-262) {
		tmp = t_2;
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+245)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	} else if (t_2 <= -5e-262) {
		tmp = t_2;
	} else if ((t_2 <= 0.0) || !(t_2 <= 2e+245)) {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((x * y) + (z * (t - a))) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0))
	elif t_2 <= -5e-262:
		tmp = t_2
	elif (t_2 <= 0.0) or not (t_2 <= 2e+245):
		tmp = (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y))
	else:
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z / Float64(z + -1.0)) * Float64(Float64(a - t) / y)) - Float64(x / Float64(z + -1.0)));
	elseif (t_2 <= -5e-262)
		tmp = t_2;
	elseif ((t_2 <= 0.0) || !(t_2 <= 2e+245))
		tmp = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((x * y) + (z * (t - a))) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = ((z / (z + -1.0)) * ((a - t) / y)) - (x / (z + -1.0));
	elseif (t_2 <= -5e-262)
		tmp = t_2;
	elseif ((t_2 <= 0.0) || ~((t_2 <= 2e+245)))
		tmp = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z) + ((t - a) / (b - y));
	else
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e-262], t$95$2, If[Or[LessEqual[t$95$2, 0.0], N[Not[LessEqual[t$95$2, 2e+245]], $MachinePrecision]], N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $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 41.0%

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

   2. Taylor expanded in y around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

      3. mul-1-neg 57.2%

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

      4. distribute-neg-frac 57.2%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in b around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. times-frac 75.6%

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

      3. sub-neg 75.6%

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

      4. metadata-eval 75.6%

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

   7. Simplified 75.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999992e-262

   1. Initial program 99.7%

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

   if -4.99999999999999992e-262 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 2.00000000000000009e245 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.5%

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

   2. Taylor expanded in z around -inf 47.2%

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

      1. +-commutative 47.2%

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

      2. associate--l+ 47.2%

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

   4. Simplified 82.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000009e245

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   3. Applied egg-rr 99.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{z}{z + -1} \cdot \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-262}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0 \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-13}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.45e+80)
     t_1
     (if (<= z -8e-13)
       (- (/ (- a t) y) (/ x (+ z -1.0)))
       (if (<= z 6.2e-206)
         (+ x (* (* z (- t a)) (/ 1.0 y)))
         (if (<= z 6e-160)
           (/ (+ (* x y) (* z t)) (+ y (* z (- b y))))
           (if (<= z 7.8e-28) (+ x (/ (- t a) (/ y z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.45e+80) {
		tmp = t_1;
	} else if (z <= -8e-13) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (z <= 6.2e-206) {
		tmp = x + ((z * (t - a)) * (1.0 / y));
	} else if (z <= 6e-160) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (z <= 7.8e-28) {
		tmp = x + ((t - a) / (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.45d+80)) then
        tmp = t_1
    else if (z <= (-8d-13)) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    else if (z <= 6.2d-206) then
        tmp = x + ((z * (t - a)) * (1.0d0 / y))
    else if (z <= 6d-160) then
        tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
    else if (z <= 7.8d-28) then
        tmp = x + ((t - a) / (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.45e+80) {
		tmp = t_1;
	} else if (z <= -8e-13) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (z <= 6.2e-206) {
		tmp = x + ((z * (t - a)) * (1.0 / y));
	} else if (z <= 6e-160) {
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	} else if (z <= 7.8e-28) {
		tmp = x + ((t - a) / (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.45e+80:
		tmp = t_1
	elif z <= -8e-13:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif z <= 6.2e-206:
		tmp = x + ((z * (t - a)) * (1.0 / y))
	elif z <= 6e-160:
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)))
	elif z <= 7.8e-28:
		tmp = x + ((t - a) / (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.45e+80)
		tmp = t_1;
	elseif (z <= -8e-13)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 6.2e-206)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) * Float64(1.0 / y)));
	elseif (z <= 6e-160)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 7.8e-28)
		tmp = Float64(x + Float64(Float64(t - a) / Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.45e+80)
		tmp = t_1;
	elseif (z <= -8e-13)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (z <= 6.2e-206)
		tmp = x + ((z * (t - a)) * (1.0 / y));
	elseif (z <= 6e-160)
		tmp = ((x * y) + (z * t)) / (y + (z * (b - y)));
	elseif (z <= 7.8e-28)
		tmp = x + ((t - a) / (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+80], t$95$1, If[LessEqual[z, -8e-13], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-206], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-160], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-28], N[(x + N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.44999999999999993e80 or 7.79999999999999998e-28 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -1.44999999999999993e80 < z < -8.0000000000000002e-13

   1. Initial program 72.8%

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

   2. Taylor expanded in y around -inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. mul-1-neg 53.7%

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

      4. distribute-neg-frac 53.7%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around inf 69.3%

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

   if -8.0000000000000002e-13 < z < 6.2000000000000005e-206

   1. Initial program 84.5%

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

      1. add-cube-cbrt 84.4%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 84.4%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 84.4%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 83.5%

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

      1. div-inv 83.5%

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

      2. *-commutative 83.5%

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

   6. Applied egg-rr 83.5%

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

   if 6.2000000000000005e-206 < z < 5.99999999999999993e-160

   1. Initial program 99.6%

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

   2. Taylor expanded in a around 0 99.6%

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

   if 5.99999999999999993e-160 < z < 7.79999999999999998e-28

   1. Initial program 77.1%

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

      1. add-cube-cbrt 76.8%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 76.8%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 76.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 77.8%

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

   6. Simplified 77.8%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-13}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-206}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-160}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+60} \lor \neg \left(z \leq 8.5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+60) (not (<= z 8.5e+59)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (- (* z t) (* z a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+60) || !(z <= 8.5e+59)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9d+60)) .or. (.not. (z <= 8.5d+59))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+60) || !(z <= 8.5e+59)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e+60) or not (z <= 8.5e+59):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e+60) || !(z <= 8.5e+59))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9e+60) || ~((z <= 8.5e+59)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+60], N[Not[LessEqual[z, 8.5e+59]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000026e60 or 8.4999999999999999e59 < z

   1. Initial program 34.0%

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

   2. Taylor expanded in z around inf 83.2%

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

   if -9.00000000000000026e60 < z < 8.4999999999999999e59

   1. Initial program 82.3%

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

      1. sub-neg 82.3%

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

      2. distribute-lft-in 82.3%

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

   3. Applied egg-rr 82.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+60} \lor \neg \left(z \leq 8.5 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+64} \lor \neg \left(z \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e+64) (not (<= z 3.8e+63)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e+64) || !(z <= 3.8e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d+64)) .or. (.not. (z <= 3.8d+63))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e+64) || !(z <= 3.8e+63)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e+64) or not (z <= 3.8e+63):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e+64) || !(z <= 3.8e+63))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e+64) || ~((z <= 3.8e+63)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e+64], N[Not[LessEqual[z, 3.8e+63]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000028e64 or 3.8000000000000001e63 < z

   1. Initial program 34.0%

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

   2. Taylor expanded in z around inf 83.2%

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

   if -9.50000000000000028e64 < z < 3.8000000000000001e63

   1. Initial program 82.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+64} \lor \neg \left(z \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 6: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-27}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.7e+80)
     t_1
     (if (<= z -1.05e-12)
       (- (/ (- a t) y) (/ x (+ z -1.0)))
       (if (<= z 4.9e-27) (+ x (* (* z (- t a)) (/ 1.0 y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+80) {
		tmp = t_1;
	} else if (z <= -1.05e-12) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (z <= 4.9e-27) {
		tmp = x + ((z * (t - a)) * (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.7d+80)) then
        tmp = t_1
    else if (z <= (-1.05d-12)) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    else if (z <= 4.9d-27) then
        tmp = x + ((z * (t - a)) * (1.0d0 / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.7e+80) {
		tmp = t_1;
	} else if (z <= -1.05e-12) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (z <= 4.9e-27) {
		tmp = x + ((z * (t - a)) * (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.7e+80:
		tmp = t_1
	elif z <= -1.05e-12:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif z <= 4.9e-27:
		tmp = x + ((z * (t - a)) * (1.0 / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.7e+80)
		tmp = t_1;
	elseif (z <= -1.05e-12)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 4.9e-27)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) * Float64(1.0 / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.7e+80)
		tmp = t_1;
	elseif (z <= -1.05e-12)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif (z <= 4.9e-27)
		tmp = x + ((z * (t - a)) * (1.0 / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+80], t$95$1, If[LessEqual[z, -1.05e-12], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e-27], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999996e80 or 4.89999999999999976e-27 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -1.69999999999999996e80 < z < -1.04999999999999997e-12

   1. Initial program 72.8%

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

   2. Taylor expanded in y around -inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. mul-1-neg 53.7%

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

      4. distribute-neg-frac 53.7%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around inf 69.3%

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

   if -1.04999999999999997e-12 < z < 4.89999999999999976e-27

   1. Initial program 83.4%

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

      1. add-cube-cbrt 83.2%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.3%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.3%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 78.7%

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

      1. div-inv 78.8%

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

      2. *-commutative 78.8%

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

   6. Applied egg-rr 78.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-27}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 75.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -195.0) (not (<= z 4.9e-27)))
   (/ (- t a) (- b y))
   (+ x (* (* z (- t a)) (/ 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 4.9e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) * (1.0 / 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 <= (-195.0d0)) .or. (.not. (z <= 4.9d-27))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) * (1.0d0 / 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 <= -195.0) || !(z <= 4.9e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) * (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -195.0) or not (z <= 4.9e-27):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) * (1.0 / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -195.0) || !(z <= 4.9e-27))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) * Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -195.0) || ~((z <= 4.9e-27)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) * (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -195.0], N[Not[LessEqual[z, 4.9e-27]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 4.89999999999999976e-27 < z

   1. Initial program 41.2%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -195 < z < 4.89999999999999976e-27

   1. Initial program 83.7%

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

      1. add-cube-cbrt 83.5%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.6%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 78.2%

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

      1. div-inv 78.2%

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

      2. *-commutative 78.2%

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

   6. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(t - a\right)\right) \cdot \frac{1}{y}\\ \end{array} \]

Alternative 8: 53.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+22} \lor \neg \left(y \leq 15000000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5.2e+241)
     t_1
     (if (<= y -1.6e+204)
       (/ (- a t) y)
       (if (or (<= y -9e+22) (not (<= y 15000000000.0))) t_1 (/ (- t a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e+241) {
		tmp = t_1;
	} else if (y <= -1.6e+204) {
		tmp = (a - t) / y;
	} else if ((y <= -9e+22) || !(y <= 15000000000.0)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-5.2d+241)) then
        tmp = t_1
    else if (y <= (-1.6d+204)) then
        tmp = (a - t) / y
    else if ((y <= (-9d+22)) .or. (.not. (y <= 15000000000.0d0))) then
        tmp = t_1
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e+241) {
		tmp = t_1;
	} else if (y <= -1.6e+204) {
		tmp = (a - t) / y;
	} else if ((y <= -9e+22) || !(y <= 15000000000.0)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -5.2e+241:
		tmp = t_1
	elif y <= -1.6e+204:
		tmp = (a - t) / y
	elif (y <= -9e+22) or not (y <= 15000000000.0):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.2e+241)
		tmp = t_1;
	elseif (y <= -1.6e+204)
		tmp = Float64(Float64(a - t) / y);
	elseif ((y <= -9e+22) || !(y <= 15000000000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.2e+241)
		tmp = t_1;
	elseif (y <= -1.6e+204)
		tmp = (a - t) / y;
	elseif ((y <= -9e+22) || ~((y <= 15000000000.0)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+241], t$95$1, If[LessEqual[y, -1.6e+204], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[y, -9e+22], N[Not[LessEqual[y, 15000000000.0]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000015e241 or -1.6e204 < y < -8.9999999999999996e22 or 1.5e10 < y

   1. Initial program 48.8%

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

   2. Taylor expanded in y around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

   4. Simplified 54.9%

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

   if -5.20000000000000015e241 < y < -1.6e204

   1. Initial program 15.7%

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

   2. Taylor expanded in z around inf 79.0%

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

   3. Taylor expanded in b around 0 79.0%

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

      1. associate-*r/ 79.0%

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

      2. mul-1-neg 79.0%

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

   5. Simplified 79.0%

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

   if -8.9999999999999996e22 < y < 1.5e10

   1. Initial program 75.9%

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

   2. Taylor expanded in y around 0 57.7%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+204}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+22} \lor \neg \left(y \leq 15000000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 9: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 1.3 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -195.0) (not (<= z 1.3e-28)))
   (/ (- t a) (- b y))
   (+ x (/ (- t a) (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 1.3e-28)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-195.0d0)) .or. (.not. (z <= 1.3d-28))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((t - a) / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 1.3e-28)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t - a) / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -195.0) or not (z <= 1.3e-28):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((t - a) / (y / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -195.0) || !(z <= 1.3e-28))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(t - a) / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -195.0) || ~((z <= 1.3e-28)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((t - a) / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -195.0], N[Not[LessEqual[z, 1.3e-28]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - a), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 1.3e-28 < z

   1. Initial program 41.2%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -195 < z < 1.3e-28

   1. Initial program 83.7%

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

      1. add-cube-cbrt 83.5%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.6%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 78.2%

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

      1. +-commutative 78.2%

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

      2. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 1.3 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - a}{\frac{y}{z}}\\ \end{array} \]

Alternative 10: 75.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -195.0) (not (<= z 4.9e-27)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 4.9e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-195.0d0)) .or. (.not. (z <= 4.9d-27))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 4.9e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -195.0) or not (z <= 4.9e-27):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -195.0) || !(z <= 4.9e-27))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -195.0) || ~((z <= 4.9e-27)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -195.0], N[Not[LessEqual[z, 4.9e-27]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 4.89999999999999976e-27 < z

   1. Initial program 41.2%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -195 < z < 4.89999999999999976e-27

   1. Initial program 83.7%

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

      1. add-cube-cbrt 83.5%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.6%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 78.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 11: 50.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -105000000.0) (not (<= z 4.9e-27)))
   (/ t (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -105000000.0) || !(z <= 4.9e-27)) {
		tmp = t / (b - y);
	} 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 <= (-105000000.0d0)) .or. (.not. (z <= 4.9d-27))) then
        tmp = t / (b - y)
    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 <= -105000000.0) || !(z <= 4.9e-27)) {
		tmp = t / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -105000000.0) or not (z <= 4.9e-27):
		tmp = t / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -105000000.0) || !(z <= 4.9e-27))
		tmp = Float64(t / Float64(b - y));
	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 <= -105000000.0) || ~((z <= 4.9e-27)))
		tmp = t / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -105000000.0], N[Not[LessEqual[z, 4.9e-27]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 4.89999999999999976e-27 < z

   1. Initial program 40.4%

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

   2. Taylor expanded in a around 0 29.9%

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

   3. Taylor expanded in z around inf 50.1%

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

   if -1.05e8 < z < 4.89999999999999976e-27

   1. Initial program 84.0%

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

      1. add-cube-cbrt 83.8%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.8%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.8%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 77.1%

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

   5. Taylor expanded in t around inf 69.0%

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

      1. *-commutative 69.0%

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

   7. Simplified 69.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000000 \lor \neg \left(z \leq 4.9 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 12: 69.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -195.0) (not (<= z 4.6e-27)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 4.6e-27)) {
		tmp = (t - a) / (b - y);
	} 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 <= (-195.0d0)) .or. (.not. (z <= 4.6d-27))) then
        tmp = (t - a) / (b - y)
    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 <= -195.0) || !(z <= 4.6e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -195.0) or not (z <= 4.6e-27):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -195.0) || !(z <= 4.6e-27))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	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 <= -195.0) || ~((z <= 4.6e-27)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -195.0], N[Not[LessEqual[z, 4.6e-27]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 4.5999999999999999e-27 < z

   1. Initial program 41.2%

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

   2. Taylor expanded in z around inf 76.7%

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

   if -195 < z < 4.5999999999999999e-27

   1. Initial program 83.7%

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

      1. add-cube-cbrt 83.5%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{\left(\sqrt[3]{z \cdot \left(b - y\right)} \cdot \sqrt[3]{z \cdot \left(b - y\right)}\right) \cdot \sqrt[3]{z \cdot \left(b - y\right)}}} \]

      2. pow3 83.6%

         \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   3. Applied egg-rr 83.6%

      \[\leadsto \frac{x \cdot y + z \cdot \left(t - a\right)}{y + \color{blue}{{\left(\sqrt[3]{z \cdot \left(b - y\right)}\right)}^{3}}} \]

   4. Taylor expanded in y around inf 78.2%

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

   5. Taylor expanded in t around inf 70.1%

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

      1. *-commutative 70.1%

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

   7. Simplified 70.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 4.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 13: 37.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 2.7 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -195.0) (not (<= z 2.7e-28))) (/ t b) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 2.7e-28)) {
		tmp = t / b;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-195.0d0)) .or. (.not. (z <= 2.7d-28))) then
        tmp = t / b
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -195.0) || !(z <= 2.7e-28)) {
		tmp = t / b;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -195.0) or not (z <= 2.7e-28):
		tmp = t / b
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -195.0) || !(z <= 2.7e-28))
		tmp = Float64(t / b);
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -195.0) || ~((z <= 2.7e-28)))
		tmp = t / b;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -195.0], N[Not[LessEqual[z, 2.7e-28]], $MachinePrecision]], N[(t / b), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 2.6999999999999999e-28 < z

   1. Initial program 41.2%

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

   2. Taylor expanded in a around 0 30.2%

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

   3. Taylor expanded in y around 0 28.1%

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

   if -195 < z < 2.6999999999999999e-28

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in z around 0 53.7%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195 \lor \neg \left(z \leq 2.7 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 14: 45.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-5} \lor \neg \left(z \leq 2.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.2e-5) (not (<= z 2.6e-27))) (/ t (- b y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.2e-5) || !(z <= 2.6e-27)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.2d-5)) .or. (.not. (z <= 2.6d-27))) then
        tmp = t / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.2e-5) || !(z <= 2.6e-27)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.2e-5) or not (z <= 2.6e-27):
		tmp = t / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.2e-5) || !(z <= 2.6e-27))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.2e-5) || ~((z <= 2.6e-27)))
		tmp = t / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.2e-5], N[Not[LessEqual[z, 2.6e-27]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-5 or 2.60000000000000017e-27 < z

   1. Initial program 41.6%

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

   2. Taylor expanded in a around 0 30.7%

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

   3. Taylor expanded in z around inf 49.2%

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

   if -2.1999999999999999e-5 < z < 2.60000000000000017e-27

   1. Initial program 83.6%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around 0 54.2%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-5} \lor \neg \left(z \leq 2.6 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 15: 44.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+80} \lor \neg \left(z \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e+80) (not (<= z 6.5e+33))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+80) || !(z <= 6.5e+33)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4d+80)) .or. (.not. (z <= 6.5d+33))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+80) || !(z <= 6.5e+33)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e+80) or not (z <= 6.5e+33):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e+80) || !(z <= 6.5e+33))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4e+80) || ~((z <= 6.5e+33)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e+80], N[Not[LessEqual[z, 6.5e+33]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e80 or 6.49999999999999993e33 < z

   1. Initial program 36.0%

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

   2. Taylor expanded in a around 0 27.8%

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

   3. Taylor expanded in z around inf 54.7%

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

   if -4e80 < z < 6.49999999999999993e33

   1. Initial program 81.3%

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

   2. Taylor expanded in y around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

   4. Simplified 51.4%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+80} \lor \neg \left(z \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 16: 54.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+24} \lor \neg \left(y \leq 160000000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.7e+24) (not (<= y 160000000000.0)))
   (/ x (- 1.0 z))
   (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+24) || !(y <= 160000000000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.7d+24)) .or. (.not. (y <= 160000000000.0d0))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.7e+24) || !(y <= 160000000000.0)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.7e+24) or not (y <= 160000000000.0):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.7e+24) || !(y <= 160000000000.0))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.7e+24) || ~((y <= 160000000000.0)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.7e+24], N[Not[LessEqual[y, 160000000000.0]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e24 or 1.6e11 < y

   1. Initial program 47.1%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   4. Simplified 53.0%

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

   if -1.7e24 < y < 1.6e11

   1. Initial program 75.9%

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

   2. Taylor expanded in y around 0 57.7%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+24} \lor \neg \left(y \leq 160000000000\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 17: 37.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -105000000.0) (/ t b) (if (<= z 2.25e-29) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = t / b;
	} else if (z <= 2.25e-29) {
		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 <= (-105000000.0d0)) then
        tmp = t / b
    else if (z <= 2.25d-29) 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 <= -105000000.0) {
		tmp = t / b;
	} else if (z <= 2.25e-29) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -105000000.0:
		tmp = t / b
	elif z <= 2.25e-29:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -105000000.0)
		tmp = Float64(t / b);
	elseif (z <= 2.25e-29)
		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 <= -105000000.0)
		tmp = t / b;
	elseif (z <= 2.25e-29)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -105000000.0], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.25e-29], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 2.2499999999999999e-29 < z

   1. Initial program 40.4%

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

   2. Taylor expanded in a around 0 29.9%

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

   3. Taylor expanded in y around 0 28.5%

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

   if -1.05e8 < z < 2.2499999999999999e-29

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 52.9%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 18: 25.8% 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 60.6%

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

2. Taylor expanded in z around 0 26.4%

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

3. Final simplification 26.4%

   \[\leadsto x \]

Developer target: 73.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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