Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.8% → 96.0%

Time: 16.8s

Alternatives: 20

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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y}{t_1}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := \frac{x}{1 - z} + t_4\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{z \cdot t}{t_1} + t_2\right) - \frac{z \cdot a}{t_1}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;\left(t_4 + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_2 + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (* x y) t_1))
        (t_3 (* z (- t a)))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ (+ t_3 (* x y)) t_1))
        (t_6 (+ (/ x (- 1.0 z)) t_4)))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -2e-263)
       (- (+ (/ (* z t) t_1) t_2) (/ (* z a) t_1))
       (if (<= t_5 0.0)
         (-
          (+ t_4 (* (/ y z) (/ x (- b y))))
          (/ y (/ (pow (- b y) 2.0) (/ (- t a) z))))
         (if (<= t_5 2e+298) (+ t_2 (/ t_3 t_1)) t_6))))))

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) / t_1;
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	} else if (t_5 <= 0.0) {
		tmp = (t_4 + ((y / z) * (x / (b - y)))) - (y / (pow((b - y), 2.0) / ((t - a) / z)));
	} else if (t_5 <= 2e+298) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_6;
	}
	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) / t_1;
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	} else if (t_5 <= 0.0) {
		tmp = (t_4 + ((y / z) * (x / (b - y)))) - (y / (Math.pow((b - y), 2.0) / ((t - a) / z)));
	} else if (t_5 <= 2e+298) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (x * y) / t_1
	t_3 = z * (t - a)
	t_4 = (t - a) / (b - y)
	t_5 = (t_3 + (x * y)) / t_1
	t_6 = (x / (1.0 - z)) + t_4
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6
	elif t_5 <= -2e-263:
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1)
	elif t_5 <= 0.0:
		tmp = (t_4 + ((y / z) * (x / (b - y)))) - (y / (math.pow((b - y), 2.0) / ((t - a) / z)))
	elif t_5 <= 2e+298:
		tmp = t_2 + (t_3 / t_1)
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(x * y) / t_1)
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_6 = Float64(Float64(x / Float64(1.0 - z)) + t_4)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + t_2) - Float64(Float64(z * a) / t_1));
	elseif (t_5 <= 0.0)
		tmp = Float64(Float64(t_4 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(Float64(t - a) / z))));
	elseif (t_5 <= 2e+298)
		tmp = Float64(t_2 + Float64(t_3 / t_1));
	else
		tmp = t_6;
	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) / t_1;
	t_3 = z * (t - a);
	t_4 = (t - a) / (b - y);
	t_5 = (t_3 + (x * y)) / t_1;
	t_6 = (x / (1.0 - z)) + t_4;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	elseif (t_5 <= 0.0)
		tmp = (t_4 + ((y / z) * (x / (b - y)))) - (y / (((b - y) ^ 2.0) / ((t - a) / z)));
	elseif (t_5 <= 2e+298)
		tmp = t_2 + (t_3 / t_1);
	else
		tmp = t_6;
	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[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -2e-263], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], N[(N[(t$95$4 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+298], N[(t$95$2 + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.9999999999999999e298 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   2. Taylor expanded in x around 0 17.8%

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

   3. Taylor expanded in z around inf 61.9%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. sub-neg 92.4%

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

   6. Simplified 92.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-263

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   if -2e-263 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 14.8%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. associate--r+ 74.2%

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

      2. +-commutative 74.2%

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

      3. associate--l+ 74.2%

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

      4. *-commutative 74.2%

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

      5. times-frac 84.0%

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

      6. div-sub 84.1%

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

      7. associate-/l* 89.7%

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

      8. *-commutative 89.7%

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

      9. associate-/l* 89.7%

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

   4. Simplified 89.7%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e298

   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 x around 0 99.7%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\right) - \frac{z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y}{t_1} + \frac{t_2}{t_1}\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{t_2 + x \cdot y}{t_1}\\ t_6 := \frac{x}{1 - z} + t_4\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ (/ (* x y) t_1) (/ t_2 t_1)))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ (+ t_2 (* x y)) t_1))
        (t_6 (+ (/ x (- 1.0 z)) t_4)))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -2e-263)
       t_3
       (if (<= t_5 0.0) t_4 (if (<= t_5 2e+298) t_3 t_6))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) / t_1) + (t_2 / t_1);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_2 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = t_3;
	} else if (t_5 <= 0.0) {
		tmp = t_4;
	} else if (t_5 <= 2e+298) {
		tmp = t_3;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) / t_1) + (t_2 / t_1);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_2 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = t_3;
	} else if (t_5 <= 0.0) {
		tmp = t_4;
	} else if (t_5 <= 2e+298) {
		tmp = t_3;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) / t_1) + (t_2 / t_1)
	t_4 = (t - a) / (b - y)
	t_5 = (t_2 + (x * y)) / t_1
	t_6 = (x / (1.0 - z)) + t_4
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6
	elif t_5 <= -2e-263:
		tmp = t_3
	elif t_5 <= 0.0:
		tmp = t_4
	elif t_5 <= 2e+298:
		tmp = t_3
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(Float64(t_2 + Float64(x * y)) / t_1)
	t_6 = Float64(Float64(x / Float64(1.0 - z)) + t_4)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = t_3;
	elseif (t_5 <= 0.0)
		tmp = t_4;
	elseif (t_5 <= 2e+298)
		tmp = t_3;
	else
		tmp = t_6;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) / t_1) + (t_2 / t_1);
	t_4 = (t - a) / (b - y);
	t_5 = (t_2 + (x * y)) / t_1;
	t_6 = (x / (1.0 - z)) + t_4;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = t_3;
	elseif (t_5 <= 0.0)
		tmp = t_4;
	elseif (t_5 <= 2e+298)
		tmp = t_3;
	else
		tmp = t_6;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -2e-263], t$95$3, If[LessEqual[t$95$5, 0.0], t$95$4, If[LessEqual[t$95$5, 2e+298], t$95$3, t$95$6]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.9999999999999999e298 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   2. Taylor expanded in x around 0 17.8%

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

   3. Taylor expanded in z around inf 61.9%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. sub-neg 92.4%

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

   6. Simplified 92.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-263 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e298

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

   if -2e-263 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 14.8%

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

   2. Taylor expanded in z around inf 79.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y}{t_1}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{t_3 + x \cdot y}{t_1}\\ t_6 := \frac{x}{1 - z} + t_4\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{z \cdot t}{t_1} + t_2\right) - \frac{z \cdot a}{t_1}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_2 + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (* x y) t_1))
        (t_3 (* z (- t a)))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ (+ t_3 (* x y)) t_1))
        (t_6 (+ (/ x (- 1.0 z)) t_4)))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -2e-263)
       (- (+ (/ (* z t) t_1) t_2) (/ (* z a) t_1))
       (if (<= t_5 0.0) t_4 (if (<= t_5 2e+298) (+ t_2 (/ t_3 t_1)) t_6))))))

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) / t_1;
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	} else if (t_5 <= 0.0) {
		tmp = t_4;
	} else if (t_5 <= 2e+298) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_6;
	}
	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) / t_1;
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double t_5 = (t_3 + (x * y)) / t_1;
	double t_6 = (x / (1.0 - z)) + t_4;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_5 <= -2e-263) {
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	} else if (t_5 <= 0.0) {
		tmp = t_4;
	} else if (t_5 <= 2e+298) {
		tmp = t_2 + (t_3 / t_1);
	} else {
		tmp = t_6;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (x * y) / t_1
	t_3 = z * (t - a)
	t_4 = (t - a) / (b - y)
	t_5 = (t_3 + (x * y)) / t_1
	t_6 = (x / (1.0 - z)) + t_4
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6
	elif t_5 <= -2e-263:
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1)
	elif t_5 <= 0.0:
		tmp = t_4
	elif t_5 <= 2e+298:
		tmp = t_2 + (t_3 / t_1)
	else:
		tmp = t_6
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(x * y) / t_1)
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(Float64(t_3 + Float64(x * y)) / t_1)
	t_6 = Float64(Float64(x / Float64(1.0 - z)) + t_4)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + t_2) - Float64(Float64(z * a) / t_1));
	elseif (t_5 <= 0.0)
		tmp = t_4;
	elseif (t_5 <= 2e+298)
		tmp = Float64(t_2 + Float64(t_3 / t_1));
	else
		tmp = t_6;
	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) / t_1;
	t_3 = z * (t - a);
	t_4 = (t - a) / (b - y);
	t_5 = (t_3 + (x * y)) / t_1;
	t_6 = (x / (1.0 - z)) + t_4;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6;
	elseif (t_5 <= -2e-263)
		tmp = (((z * t) / t_1) + t_2) - ((z * a) / t_1);
	elseif (t_5 <= 0.0)
		tmp = t_4;
	elseif (t_5 <= 2e+298)
		tmp = t_2 + (t_3 / t_1);
	else
		tmp = t_6;
	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[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -2e-263], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$4, If[LessEqual[t$95$5, 2e+298], N[(t$95$2 + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$6]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.9999999999999999e298 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   2. Taylor expanded in x around 0 17.8%

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

   3. Taylor expanded in z around inf 61.9%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. sub-neg 92.4%

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

   6. Simplified 92.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-263

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   if -2e-263 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 14.8%

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

   2. Taylor expanded in z around inf 79.9%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e298

   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 x around 0 99.7%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\left(\frac{z \cdot t}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\right) - \frac{z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z} + t_1\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y)))))
        (t_3 (+ (/ x (- 1.0 z)) t_1)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-263)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 2e+298) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-263) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+298) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-263) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+298) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	t_3 = (x / (1.0 - z)) + t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-263:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+298:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-263)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+298)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	t_3 = (x / (1.0 - z)) + t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-263)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+298)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-263], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+298], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.9999999999999999e298 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 17.8%

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

   2. Taylor expanded in x around 0 17.8%

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

   3. Taylor expanded in z around inf 61.9%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. neg-mul-1 92.4%

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

      2. sub-neg 92.4%

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

   6. Simplified 92.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-263 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e298

   1. Initial program 99.7%

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

   if -2e-263 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 14.8%

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

   2. Taylor expanded in z around inf 79.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-263}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;\frac{t_3 + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{t_1}\\ \mathbf{elif}\;z \leq 0.00021:\\ \;\;\;\;x + \frac{t_3}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y))))
        (t_3 (* z (- t a))))
   (if (<= z -1.2e-16)
     t_2
     (if (<= z -1.15e-76)
       (/ (+ t_3 (* x y)) (* z b))
       (if (<= z -2.3e-120)
         (/ (- (* x y) (* z a)) t_1)
         (if (<= z 0.00021) (+ x (/ t_3 t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -1.2e-16) {
		tmp = t_2;
	} else if (z <= -1.15e-76) {
		tmp = (t_3 + (x * y)) / (z * b);
	} else if (z <= -2.3e-120) {
		tmp = ((x * y) - (z * a)) / t_1;
	} else if (z <= 0.00021) {
		tmp = x + (t_3 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    t_3 = z * (t - a)
    if (z <= (-1.2d-16)) then
        tmp = t_2
    else if (z <= (-1.15d-76)) then
        tmp = (t_3 + (x * y)) / (z * b)
    else if (z <= (-2.3d-120)) then
        tmp = ((x * y) - (z * a)) / t_1
    else if (z <= 0.00021d0) then
        tmp = x + (t_3 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -1.2e-16) {
		tmp = t_2;
	} else if (z <= -1.15e-76) {
		tmp = (t_3 + (x * y)) / (z * b);
	} else if (z <= -2.3e-120) {
		tmp = ((x * y) - (z * a)) / t_1;
	} else if (z <= 0.00021) {
		tmp = x + (t_3 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y))
	t_3 = z * (t - a)
	tmp = 0
	if z <= -1.2e-16:
		tmp = t_2
	elif z <= -1.15e-76:
		tmp = (t_3 + (x * y)) / (z * b)
	elif z <= -2.3e-120:
		tmp = ((x * y) - (z * a)) / t_1
	elif z <= 0.00021:
		tmp = x + (t_3 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -1.2e-16)
		tmp = t_2;
	elseif (z <= -1.15e-76)
		tmp = Float64(Float64(t_3 + Float64(x * y)) / Float64(z * b));
	elseif (z <= -2.3e-120)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * a)) / t_1);
	elseif (z <= 0.00021)
		tmp = Float64(x + Float64(t_3 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	t_3 = z * (t - a);
	tmp = 0.0;
	if (z <= -1.2e-16)
		tmp = t_2;
	elseif (z <= -1.15e-76)
		tmp = (t_3 + (x * y)) / (z * b);
	elseif (z <= -2.3e-120)
		tmp = ((x * y) - (z * a)) / t_1;
	elseif (z <= 0.00021)
		tmp = x + (t_3 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-16], t$95$2, If[LessEqual[z, -1.15e-76], N[(N[(t$95$3 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-120], N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 0.00021], N[(x + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.20000000000000002e-16 or 2.1000000000000001e-4 < z

   1. Initial program 43.6%

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

   2. Taylor expanded in x around 0 43.7%

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

   3. Taylor expanded in z around inf 83.0%

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

   4. Taylor expanded in y around inf 87.7%

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

      1. neg-mul-1 87.7%

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

      2. sub-neg 87.7%

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

   6. Simplified 87.7%

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

   if -1.20000000000000002e-16 < z < -1.15000000000000003e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 90.0%

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

   if -1.15000000000000003e-76 < z < -2.29999999999999986e-120

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. mul-1-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. *-commutative 89.9%

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

      5. *-commutative 89.9%

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

   4. Simplified 89.9%

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

   if -2.29999999999999986e-120 < z < 2.1000000000000001e-4

   1. Initial program 86.9%

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

   2. Taylor expanded in x around 0 86.9%

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

   3. Taylor expanded in z around 0 92.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 0.00021:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{x}{\frac{z}{y}}}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-122}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= z -5.3e-14)
     t_1
     (if (<= z -8.4e-85)
       (/ (+ (- t a) (/ x (/ z y))) b)
       (if (<= z 4.4e-122)
         (- x (/ (* z a) y))
         (if (<= z 5e-7) (/ (* z (- t a)) (+ y (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -5.3e-14) {
		tmp = t_1;
	} else if (z <= -8.4e-85) {
		tmp = ((t - a) + (x / (z / y))) / b;
	} else if (z <= 4.4e-122) {
		tmp = x - ((z * a) / y);
	} else if (z <= 5e-7) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    if (z <= (-5.3d-14)) then
        tmp = t_1
    else if (z <= (-8.4d-85)) then
        tmp = ((t - a) + (x / (z / y))) / b
    else if (z <= 4.4d-122) then
        tmp = x - ((z * a) / y)
    else if (z <= 5d-7) then
        tmp = (z * (t - a)) / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (z <= -5.3e-14) {
		tmp = t_1;
	} else if (z <= -8.4e-85) {
		tmp = ((t - a) + (x / (z / y))) / b;
	} else if (z <= 4.4e-122) {
		tmp = x - ((z * a) / y);
	} else if (z <= 5e-7) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if z <= -5.3e-14:
		tmp = t_1
	elif z <= -8.4e-85:
		tmp = ((t - a) + (x / (z / y))) / b
	elif z <= 4.4e-122:
		tmp = x - ((z * a) / y)
	elif z <= 5e-7:
		tmp = (z * (t - a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -5.3e-14)
		tmp = t_1;
	elseif (z <= -8.4e-85)
		tmp = Float64(Float64(Float64(t - a) + Float64(x / Float64(z / y))) / b);
	elseif (z <= 4.4e-122)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 5e-7)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -5.3e-14)
		tmp = t_1;
	elseif (z <= -8.4e-85)
		tmp = ((t - a) + (x / (z / y))) / b;
	elseif (z <= 4.4e-122)
		tmp = x - ((z * a) / y);
	elseif (z <= 5e-7)
		tmp = (z * (t - a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e-14], t$95$1, If[LessEqual[z, -8.4e-85], N[(N[(N[(t - a), $MachinePrecision] + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 4.4e-122], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-7], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3000000000000001e-14 or 4.99999999999999977e-7 < z

   1. Initial program 43.6%

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

   2. Taylor expanded in x around 0 43.7%

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

   3. Taylor expanded in z around inf 83.0%

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

   4. Taylor expanded in y around inf 87.7%

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

      1. neg-mul-1 87.7%

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

      2. sub-neg 87.7%

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

   6. Simplified 87.7%

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

   if -5.3000000000000001e-14 < z < -8.3999999999999999e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in b around inf 90.5%

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

      1. associate--l+ 90.5%

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

      2. sub-neg 90.5%

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

      3. +-commutative 90.5%

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

      4. associate-+r+ 90.5%

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

      5. sub-neg 90.5%

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

      6. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

   if -8.3999999999999999e-85 < z < 4.4e-122

   1. Initial program 86.2%

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

   2. Taylor expanded in t around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

      5. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. associate-*r/ 68.9%

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

      2. neg-mul-1 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

   8. Simplified 68.9%

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

   if 4.4e-122 < z < 4.99999999999999977e-7

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 82.9%

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

   3. Taylor expanded in b around inf 82.9%

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

      1. *-commutative 50.0%

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

   5. Simplified 82.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{\left(t - a\right) + \frac{x}{\frac{z}{y}}}{b}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-122}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-86}:\\ \;\;\;\;\frac{t_2 + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-120}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.000105:\\ \;\;\;\;\frac{t_2}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))) (t_2 (* z (- t a))))
   (if (<= z -6.2e-17)
     t_1
     (if (<= z -6e-86)
       (/ (+ t_2 (* x y)) (* z b))
       (if (<= z 1.2e-120)
         (- x (/ (* z a) y))
         (if (<= z 0.000105) (/ t_2 (+ y (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -6.2e-17) {
		tmp = t_1;
	} else if (z <= -6e-86) {
		tmp = (t_2 + (x * y)) / (z * b);
	} else if (z <= 1.2e-120) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.000105) {
		tmp = t_2 / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    if (z <= (-6.2d-17)) then
        tmp = t_1
    else if (z <= (-6d-86)) then
        tmp = (t_2 + (x * y)) / (z * b)
    else if (z <= 1.2d-120) then
        tmp = x - ((z * a) / y)
    else if (z <= 0.000105d0) then
        tmp = t_2 / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double tmp;
	if (z <= -6.2e-17) {
		tmp = t_1;
	} else if (z <= -6e-86) {
		tmp = (t_2 + (x * y)) / (z * b);
	} else if (z <= 1.2e-120) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.000105) {
		tmp = t_2 / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	tmp = 0
	if z <= -6.2e-17:
		tmp = t_1
	elif z <= -6e-86:
		tmp = (t_2 + (x * y)) / (z * b)
	elif z <= 1.2e-120:
		tmp = x - ((z * a) / y)
	elif z <= 0.000105:
		tmp = t_2 / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -6.2e-17)
		tmp = t_1;
	elseif (z <= -6e-86)
		tmp = Float64(Float64(t_2 + Float64(x * y)) / Float64(z * b));
	elseif (z <= 1.2e-120)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 0.000105)
		tmp = Float64(t_2 / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (1.0 - z)) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	tmp = 0.0;
	if (z <= -6.2e-17)
		tmp = t_1;
	elseif (z <= -6e-86)
		tmp = (t_2 + (x * y)) / (z * b);
	elseif (z <= 1.2e-120)
		tmp = x - ((z * a) / y);
	elseif (z <= 0.000105)
		tmp = t_2 / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-17], t$95$1, If[LessEqual[z, -6e-86], N[(N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-120], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000105], N[(t$95$2 / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1999999999999997e-17 or 1.05e-4 < z

   1. Initial program 43.6%

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

   2. Taylor expanded in x around 0 43.7%

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

   3. Taylor expanded in z around inf 83.0%

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

   4. Taylor expanded in y around inf 87.7%

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

      1. neg-mul-1 87.7%

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

      2. sub-neg 87.7%

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

   6. Simplified 87.7%

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

   if -6.1999999999999997e-17 < z < -6.0000000000000002e-86

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 90.9%

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

   if -6.0000000000000002e-86 < z < 1.2e-120

   1. Initial program 86.2%

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

   2. Taylor expanded in t around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

      5. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. associate-*r/ 68.9%

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

      2. neg-mul-1 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

   8. Simplified 68.9%

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

   if 1.2e-120 < z < 1.05e-4

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 82.9%

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

   3. Taylor expanded in b around inf 82.9%

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

      1. *-commutative 50.0%

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

   5. Simplified 82.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-86}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{z \cdot b}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-120}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.000105:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.75e-85)
     t_1
     (if (<= z 2.4e-70)
       (- x (/ (* z a) y))
       (if (<= z 8.5e+21)
         (/ (* z t) (+ y (* z b)))
         (if (<= z 4.8e+148) (- (/ x (- 1.0 z)) (/ (- t a) 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 <= -1.75e-85) {
		tmp = t_1;
	} else if (z <= 2.4e-70) {
		tmp = x - ((z * a) / y);
	} else if (z <= 8.5e+21) {
		tmp = (z * t) / (y + (z * b));
	} else if (z <= 4.8e+148) {
		tmp = (x / (1.0 - z)) - ((t - a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.75d-85)) then
        tmp = t_1
    else if (z <= 2.4d-70) then
        tmp = x - ((z * a) / y)
    else if (z <= 8.5d+21) then
        tmp = (z * t) / (y + (z * b))
    else if (z <= 4.8d+148) then
        tmp = (x / (1.0d0 - z)) - ((t - a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.75e-85) {
		tmp = t_1;
	} else if (z <= 2.4e-70) {
		tmp = x - ((z * a) / y);
	} else if (z <= 8.5e+21) {
		tmp = (z * t) / (y + (z * b));
	} else if (z <= 4.8e+148) {
		tmp = (x / (1.0 - z)) - ((t - a) / 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 <= -1.75e-85:
		tmp = t_1
	elif z <= 2.4e-70:
		tmp = x - ((z * a) / y)
	elif z <= 8.5e+21:
		tmp = (z * t) / (y + (z * b))
	elif z <= 4.8e+148:
		tmp = (x / (1.0 - z)) - ((t - a) / 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 <= -1.75e-85)
		tmp = t_1;
	elseif (z <= 2.4e-70)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 8.5e+21)
		tmp = Float64(Float64(z * t) / Float64(y + Float64(z * b)));
	elseif (z <= 4.8e+148)
		tmp = Float64(Float64(x / Float64(1.0 - z)) - Float64(Float64(t - a) / 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 <= -1.75e-85)
		tmp = t_1;
	elseif (z <= 2.4e-70)
		tmp = x - ((z * a) / y);
	elseif (z <= 8.5e+21)
		tmp = (z * t) / (y + (z * b));
	elseif (z <= 4.8e+148)
		tmp = (x / (1.0 - z)) - ((t - a) / 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, -1.75e-85], t$95$1, If[LessEqual[z, 2.4e-70], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+21], N[(N[(z * t), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+148], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.74999999999999989e-85 or 4.79999999999999989e148 < z

   1. Initial program 40.0%

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

   2. Taylor expanded in z around inf 81.1%

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

   if -1.74999999999999989e-85 < z < 2.4000000000000001e-70

   1. Initial program 87.1%

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

   2. Taylor expanded in t around 0 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in z around 0 57.1%

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

   6. Taylor expanded in y around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

   8. Simplified 68.8%

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

   if 2.4000000000000001e-70 < z < 8.5e21

   1. Initial program 85.5%

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

   2. Taylor expanded in t around inf 60.3%

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

      1. *-commutative 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in b around inf 60.3%

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

      1. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   if 8.5e21 < z < 4.79999999999999989e148

   1. Initial program 77.2%

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

   2. Taylor expanded in x around 0 77.2%

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

   3. Taylor expanded in z around inf 80.6%

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

   4. Taylor expanded in y around inf 87.3%

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

      1. neg-mul-1 87.3%

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

      2. sub-neg 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in y around -inf 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

   9. Simplified 72.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-85}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 - z} - \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 82.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-51} \lor \neg \left(z \leq 1.4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-51) (not (<= z 1.4e-5)))
   (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))
   (+ x (/ (* 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 <= -6e-51) || !(z <= 1.4e-5)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} else {
		tmp = x + ((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 <= (-6d-51)) .or. (.not. (z <= 1.4d-5))) then
        tmp = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    else
        tmp = x + ((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 <= -6e-51) || !(z <= 1.4e-5)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-51) or not (z <= 1.4e-5):
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y))
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-51) || !(z <= 1.4e-5))
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(x + Float64(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 <= -6e-51) || ~((z <= 1.4e-5)))
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-51], N[Not[LessEqual[z, 1.4e-5]], $MachinePrecision]], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000005e-51 or 1.39999999999999998e-5 < z

   1. Initial program 46.1%

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

   2. Taylor expanded in x around 0 46.1%

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

   3. Taylor expanded in z around inf 83.7%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. neg-mul-1 85.9%

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

      2. sub-neg 85.9%

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

   6. Simplified 85.9%

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

   if -6.00000000000000005e-51 < z < 1.39999999999999998e-5

   1. Initial program 87.9%

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

   2. Taylor expanded in x around 0 88.0%

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

   3. Taylor expanded in z around 0 87.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-51} \lor \neg \left(z \leq 1.4 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 10: 42.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)) (t_3 (/ x (- 1.0 z))))
   (if (<= y -1.2e+94)
     t_3
     (if (<= y -9.2e-144)
       t_1
       (if (<= y 2.5e-275)
         t_2
         (if (<= y 2.2e-190)
           t_1
           (if (<= y 1.6e-122) t_2 (if (<= y 6.8e+24) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -1.2e+94) {
		tmp = t_3;
	} else if (y <= -9.2e-144) {
		tmp = t_1;
	} else if (y <= 2.5e-275) {
		tmp = t_2;
	} else if (y <= 2.2e-190) {
		tmp = t_1;
	} else if (y <= 1.6e-122) {
		tmp = t_2;
	} else if (y <= 6.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = -a / b
    t_3 = x / (1.0d0 - z)
    if (y <= (-1.2d+94)) then
        tmp = t_3
    else if (y <= (-9.2d-144)) then
        tmp = t_1
    else if (y <= 2.5d-275) then
        tmp = t_2
    else if (y <= 2.2d-190) then
        tmp = t_1
    else if (y <= 1.6d-122) then
        tmp = t_2
    else if (y <= 6.8d+24) then
        tmp = t_1
    else
        tmp = t_3
    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 / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -1.2e+94) {
		tmp = t_3;
	} else if (y <= -9.2e-144) {
		tmp = t_1;
	} else if (y <= 2.5e-275) {
		tmp = t_2;
	} else if (y <= 2.2e-190) {
		tmp = t_1;
	} else if (y <= 1.6e-122) {
		tmp = t_2;
	} else if (y <= 6.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	t_3 = x / (1.0 - z)
	tmp = 0
	if y <= -1.2e+94:
		tmp = t_3
	elif y <= -9.2e-144:
		tmp = t_1
	elif y <= 2.5e-275:
		tmp = t_2
	elif y <= 2.2e-190:
		tmp = t_1
	elif y <= 1.6e-122:
		tmp = t_2
	elif y <= 6.8e+24:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.2e+94)
		tmp = t_3;
	elseif (y <= -9.2e-144)
		tmp = t_1;
	elseif (y <= 2.5e-275)
		tmp = t_2;
	elseif (y <= 2.2e-190)
		tmp = t_1;
	elseif (y <= 1.6e-122)
		tmp = t_2;
	elseif (y <= 6.8e+24)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = -a / b;
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.2e+94)
		tmp = t_3;
	elseif (y <= -9.2e-144)
		tmp = t_1;
	elseif (y <= 2.5e-275)
		tmp = t_2;
	elseif (y <= 2.2e-190)
		tmp = t_1;
	elseif (y <= 1.6e-122)
		tmp = t_2;
	elseif (y <= 6.8e+24)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+94], t$95$3, If[LessEqual[y, -9.2e-144], t$95$1, If[LessEqual[y, 2.5e-275], t$95$2, If[LessEqual[y, 2.2e-190], t$95$1, If[LessEqual[y, 1.6e-122], t$95$2, If[LessEqual[y, 6.8e+24], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999991e94 or 6.8000000000000001e24 < y

   1. Initial program 50.8%

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

   2. Taylor expanded in y around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

   4. Simplified 64.6%

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

   if -1.19999999999999991e94 < y < -9.2e-144 or 2.49999999999999992e-275 < y < 2.20000000000000004e-190 or 1.6000000000000001e-122 < y < 6.8000000000000001e24

   1. Initial program 72.2%

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

   2. Taylor expanded in t around inf 35.6%

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

      1. *-commutative 35.6%

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

   4. Simplified 35.6%

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

   5. Taylor expanded in z around inf 39.7%

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

   if -9.2e-144 < y < 2.49999999999999992e-275 or 2.20000000000000004e-190 < y < 1.6000000000000001e-122

   1. Initial program 78.0%

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

   2. Taylor expanded in t around 0 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. *-commutative 52.8%

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

      5. *-commutative 52.8%

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

   4. Simplified 52.8%

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

   5. Taylor expanded in y around 0 46.0%

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

      1. associate-*r/ 46.0%

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

      2. neg-mul-1 46.0%

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

   7. Simplified 46.0%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-190}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-122}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.2e-88)
     t_1
     (if (<= z 3.2e-119)
       (- x (/ (* z a) y))
       (if (<= z 0.00024) (/ (* z (- t a)) (+ y (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e-88) {
		tmp = t_1;
	} else if (z <= 3.2e-119) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.00024) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.2d-88)) then
        tmp = t_1
    else if (z <= 3.2d-119) then
        tmp = x - ((z * a) / y)
    else if (z <= 0.00024d0) then
        tmp = (z * (t - a)) / (y + (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e-88) {
		tmp = t_1;
	} else if (z <= 3.2e-119) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.00024) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.2e-88:
		tmp = t_1
	elif z <= 3.2e-119:
		tmp = x - ((z * a) / y)
	elif z <= 0.00024:
		tmp = (z * (t - a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.2e-88)
		tmp = t_1;
	elseif (z <= 3.2e-119)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 0.00024)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.2e-88)
		tmp = t_1;
	elseif (z <= 3.2e-119)
		tmp = x - ((z * a) / y);
	elseif (z <= 0.00024)
		tmp = (z * (t - a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-88], t$95$1, If[LessEqual[z, 3.2e-119], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00024], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999999e-88 or 2.40000000000000006e-4 < z

   1. Initial program 47.9%

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

   2. Taylor expanded in z around inf 76.8%

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

   if -7.1999999999999999e-88 < z < 3.19999999999999993e-119

   1. Initial program 86.2%

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

   2. Taylor expanded in t around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

      5. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in z around 0 56.4%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. associate-*r/ 68.9%

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

      2. neg-mul-1 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

   8. Simplified 68.9%

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

   if 3.19999999999999993e-119 < z < 2.40000000000000006e-4

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 82.9%

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

   3. Taylor expanded in b around inf 82.9%

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

      1. *-commutative 50.0%

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

   5. Simplified 82.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.00024:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+214} \lor \neg \left(z \leq 9 \cdot 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.75e-78)
     t_1
     (if (<= z 1.95e-67)
       x
       (if (or (<= z 9.5e+214) (not (<= z 9e+256))) t_1 (/ (- a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.75e-78) {
		tmp = t_1;
	} else if (z <= 1.95e-67) {
		tmp = x;
	} else if ((z <= 9.5e+214) || !(z <= 9e+256)) {
		tmp = t_1;
	} else {
		tmp = -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 = t / (b - y)
    if (z <= (-1.75d-78)) then
        tmp = t_1
    else if (z <= 1.95d-67) then
        tmp = x
    else if ((z <= 9.5d+214) .or. (.not. (z <= 9d+256))) then
        tmp = t_1
    else
        tmp = -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 = t / (b - y);
	double tmp;
	if (z <= -1.75e-78) {
		tmp = t_1;
	} else if (z <= 1.95e-67) {
		tmp = x;
	} else if ((z <= 9.5e+214) || !(z <= 9e+256)) {
		tmp = t_1;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1.75e-78:
		tmp = t_1
	elif z <= 1.95e-67:
		tmp = x
	elif (z <= 9.5e+214) or not (z <= 9e+256):
		tmp = t_1
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.75e-78)
		tmp = t_1;
	elseif (z <= 1.95e-67)
		tmp = x;
	elseif ((z <= 9.5e+214) || !(z <= 9e+256))
		tmp = t_1;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.75e-78)
		tmp = t_1;
	elseif (z <= 1.95e-67)
		tmp = x;
	elseif ((z <= 9.5e+214) || ~((z <= 9e+256)))
		tmp = t_1;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e-78], t$95$1, If[LessEqual[z, 1.95e-67], x, If[Or[LessEqual[z, 9.5e+214], N[Not[LessEqual[z, 9e+256]], $MachinePrecision]], t$95$1, N[((-a) / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e-78 or 1.9499999999999999e-67 < z < 9.49999999999999921e214 or 8.9999999999999996e256 < z

   1. Initial program 53.6%

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

   2. Taylor expanded in t around inf 29.4%

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

      1. *-commutative 29.4%

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

   4. Simplified 29.4%

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

   5. Taylor expanded in z around inf 41.5%

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

   if -1.75e-78 < z < 1.9499999999999999e-67

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 50.6%

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

   if 9.49999999999999921e214 < z < 8.9999999999999996e256

   1. Initial program 21.3%

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

   2. Taylor expanded in t around 0 21.0%

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

      1. +-commutative 21.0%

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

      2. mul-1-neg 21.0%

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

      3. unsub-neg 21.0%

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

      4. *-commutative 21.0%

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

      5. *-commutative 21.0%

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

   4. Simplified 21.0%

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

   5. Taylor expanded in y around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-78}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+214} \lor \neg \left(z \leq 9 \cdot 10^{+256}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 13: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00076:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -7.5e+136)
     t_1
     (if (<= z -7.5e+36)
       (- (/ x z))
       (if (<= z -6e-79) (/ t b) (if (<= z 0.00076) (+ x (* x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -7.5e+136) {
		tmp = t_1;
	} else if (z <= -7.5e+36) {
		tmp = -(x / z);
	} else if (z <= -6e-79) {
		tmp = t / b;
	} else if (z <= 0.00076) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-7.5d+136)) then
        tmp = t_1
    else if (z <= (-7.5d+36)) then
        tmp = -(x / z)
    else if (z <= (-6d-79)) then
        tmp = t / b
    else if (z <= 0.00076d0) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -7.5e+136) {
		tmp = t_1;
	} else if (z <= -7.5e+36) {
		tmp = -(x / z);
	} else if (z <= -6e-79) {
		tmp = t / b;
	} else if (z <= 0.00076) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -7.5e+136:
		tmp = t_1
	elif z <= -7.5e+36:
		tmp = -(x / z)
	elif z <= -6e-79:
		tmp = t / b
	elif z <= 0.00076:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -7.5e+136)
		tmp = t_1;
	elseif (z <= -7.5e+36)
		tmp = Float64(-Float64(x / z));
	elseif (z <= -6e-79)
		tmp = Float64(t / b);
	elseif (z <= 0.00076)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -7.5e+136)
		tmp = t_1;
	elseif (z <= -7.5e+36)
		tmp = -(x / z);
	elseif (z <= -6e-79)
		tmp = t / b;
	elseif (z <= 0.00076)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -7.5e+136], t$95$1, If[LessEqual[z, -7.5e+36], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, -6e-79], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.00076], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000002e136 or 7.6000000000000004e-4 < z

   1. Initial program 40.1%

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

   2. Taylor expanded in t around 0 24.3%

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

      1. +-commutative 24.3%

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

      2. mul-1-neg 24.3%

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

      3. unsub-neg 24.3%

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

      4. *-commutative 24.3%

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

      5. *-commutative 24.3%

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

   4. Simplified 24.3%

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

   5. Taylor expanded in y around 0 30.7%

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

      1. associate-*r/ 30.7%

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

      2. neg-mul-1 30.7%

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

   7. Simplified 30.7%

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

   if -7.5000000000000002e136 < z < -7.50000000000000054e36

   1. Initial program 48.1%

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

   2. Taylor expanded in y around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. unsub-neg 44.0%

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

   4. Simplified 44.0%

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

   5. Taylor expanded in z around inf 44.0%

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

      1. associate-*r/ 44.0%

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

      2. mul-1-neg 44.0%

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

   7. Simplified 44.0%

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

   if -7.50000000000000054e36 < z < -5.99999999999999999e-79

   1. Initial program 80.2%

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

   2. Taylor expanded in t around inf 42.9%

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

      1. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in y around 0 43.8%

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

   if -5.99999999999999999e-79 < z < 7.6000000000000004e-4

   1. Initial program 86.8%

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

   2. Taylor expanded in y around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. unsub-neg 47.3%

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

   4. Simplified 47.3%

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

   5. Taylor expanded in z around 0 46.9%

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

      1. *-commutative 46.9%

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

   7. Simplified 46.9%

      \[\leadsto \color{blue}{x + z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00076:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 36.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+37}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -7.8e+136)
     t_1
     (if (<= z -6e+37)
       (- (/ x z))
       (if (<= z -7e-80) (/ t b) (if (<= z 0.00032) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -7.8e+136) {
		tmp = t_1;
	} else if (z <= -6e+37) {
		tmp = -(x / z);
	} else if (z <= -7e-80) {
		tmp = t / b;
	} else if (z <= 0.00032) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-7.8d+136)) then
        tmp = t_1
    else if (z <= (-6d+37)) then
        tmp = -(x / z)
    else if (z <= (-7d-80)) then
        tmp = t / b
    else if (z <= 0.00032d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -7.8e+136) {
		tmp = t_1;
	} else if (z <= -6e+37) {
		tmp = -(x / z);
	} else if (z <= -7e-80) {
		tmp = t / b;
	} else if (z <= 0.00032) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -7.8e+136:
		tmp = t_1
	elif z <= -6e+37:
		tmp = -(x / z)
	elif z <= -7e-80:
		tmp = t / b
	elif z <= 0.00032:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -7.8e+136)
		tmp = t_1;
	elseif (z <= -6e+37)
		tmp = Float64(-Float64(x / z));
	elseif (z <= -7e-80)
		tmp = Float64(t / b);
	elseif (z <= 0.00032)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -7.8e+136)
		tmp = t_1;
	elseif (z <= -6e+37)
		tmp = -(x / z);
	elseif (z <= -7e-80)
		tmp = t / b;
	elseif (z <= 0.00032)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -7.8e+136], t$95$1, If[LessEqual[z, -6e+37], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, -7e-80], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.00032], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.80000000000000038e136 or 3.20000000000000026e-4 < z

   1. Initial program 40.1%

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

   2. Taylor expanded in t around 0 24.3%

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

      1. +-commutative 24.3%

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

      2. mul-1-neg 24.3%

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

      3. unsub-neg 24.3%

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

      4. *-commutative 24.3%

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

      5. *-commutative 24.3%

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

   4. Simplified 24.3%

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

   5. Taylor expanded in y around 0 30.7%

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

      1. associate-*r/ 30.7%

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

      2. neg-mul-1 30.7%

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

   7. Simplified 30.7%

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

   if -7.80000000000000038e136 < z < -6.00000000000000043e37

   1. Initial program 48.1%

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

   2. Taylor expanded in y around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. unsub-neg 44.0%

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

   4. Simplified 44.0%

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

   5. Taylor expanded in z around inf 44.0%

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

      1. associate-*r/ 44.0%

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

      2. mul-1-neg 44.0%

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

   7. Simplified 44.0%

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

   if -6.00000000000000043e37 < z < -7.00000000000000029e-80

   1. Initial program 80.2%

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

   2. Taylor expanded in t around inf 42.9%

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

      1. *-commutative 42.9%

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

   4. Simplified 42.9%

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

   5. Taylor expanded in y around 0 43.8%

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

   if -7.00000000000000029e-80 < z < 3.20000000000000026e-4

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 46.7%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+37}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.00032:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15: 68.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-84} \lor \neg \left(z \leq 1.35 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e-84) (not (<= z 1.35e-67)))
   (/ (- t a) (- b y))
   (- x (/ a (/ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-84) || !(z <= 1.35e-67)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (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 <= (-2.1d-84)) .or. (.not. (z <= 1.35d-67))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - (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 <= -2.1e-84) || !(z <= 1.35e-67)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (a / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e-84) or not (z <= 1.35e-67):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - (a / (y / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e-84) || !(z <= 1.35e-67))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(a / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e-84) || ~((z <= 1.35e-67)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - (a / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e-84], N[Not[LessEqual[z, 1.35e-67]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999998e-84 or 1.35000000000000008e-67 < z

   1. Initial program 51.7%

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

   2. Taylor expanded in z around inf 73.7%

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

   if -2.09999999999999998e-84 < z < 1.35000000000000008e-67

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. *-commutative 70.3%

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

      5. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in z around 0 56.9%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. *-commutative 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-/l* 67.4%

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

   8. Simplified 67.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-84} \lor \neg \left(z \leq 1.35 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \end{array} \]

Alternative 16: 68.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-84} \lor \neg \left(z \leq 2.1 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-84) (not (<= z 2.1e-67)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-84) || !(z <= 2.1e-67)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6d-84)) .or. (.not. (z <= 2.1d-67))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-84) || !(z <= 2.1e-67)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-84) or not (z <= 2.1e-67):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-84) || !(z <= 2.1e-67))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-84) || ~((z <= 2.1e-67)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-84], N[Not[LessEqual[z, 2.1e-67]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e-84 or 2.1000000000000002e-67 < z

   1. Initial program 51.7%

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

   2. Taylor expanded in z around inf 73.7%

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

   if -6.0000000000000002e-84 < z < 2.1000000000000002e-67

   1. Initial program 87.3%

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

   2. Taylor expanded in t around 0 70.3%

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

      1. +-commutative 70.3%

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

      2. mul-1-neg 70.3%

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

      3. unsub-neg 70.3%

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

      4. *-commutative 70.3%

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

      5. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in z around 0 56.9%

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

   6. Taylor expanded in y around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. neg-mul-1 68.4%

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

      3. distribute-rgt-neg-in 68.4%

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

   8. Simplified 68.4%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-84} \lor \neg \left(z \leq 2.1 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]

Alternative 17: 53.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+111} \lor \neg \left(y \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e+111) (not (<= y 2.5e+39)))
   (/ 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 <= -1.55e+111) || !(y <= 2.5e+39)) {
		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 <= (-1.55d+111)) .or. (.not. (y <= 2.5d+39))) 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 <= -1.55e+111) || !(y <= 2.5e+39)) {
		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 <= -1.55e+111) or not (y <= 2.5e+39):
		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 <= -1.55e+111) || !(y <= 2.5e+39))
		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 <= -1.55e+111) || ~((y <= 2.5e+39)))
		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, -1.55e+111], N[Not[LessEqual[y, 2.5e+39]], $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 < -1.55e111 or 2.50000000000000008e39 < y

   1. Initial program 50.8%

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

   2. Taylor expanded in y around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. unsub-neg 66.2%

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

   4. Simplified 66.2%

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

   if -1.55e111 < y < 2.50000000000000008e39

   1. Initial program 73.6%

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

   2. Taylor expanded in y around 0 52.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+111} \lor \neg \left(y \leq 2.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 36.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.000245:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.35e-80) (/ t b) (if (<= z 0.000245) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.35e-80) {
		tmp = t / b;
	} else if (z <= 0.000245) {
		tmp = x;
	} else {
		tmp = -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 (z <= (-2.35d-80)) then
        tmp = t / b
    else if (z <= 0.000245d0) then
        tmp = x
    else
        tmp = -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 (z <= -2.35e-80) {
		tmp = t / b;
	} else if (z <= 0.000245) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.35e-80:
		tmp = t / b
	elif z <= 0.000245:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.35e-80)
		tmp = Float64(t / b);
	elseif (z <= 0.000245)
		tmp = x;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.35e-80)
		tmp = t / b;
	elseif (z <= 0.000245)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.35e-80], N[(t / b), $MachinePrecision], If[LessEqual[z, 0.000245], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.34999999999999986e-80

   1. Initial program 50.0%

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

   2. Taylor expanded in t around inf 30.0%

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

      1. *-commutative 30.0%

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

   4. Simplified 30.0%

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

   5. Taylor expanded in y around 0 34.6%

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

   if -2.34999999999999986e-80 < z < 2.4499999999999999e-4

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 46.7%

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

   if 2.4499999999999999e-4 < z

   1. Initial program 45.2%

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

   2. Taylor expanded in t around 0 30.4%

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

      1. +-commutative 30.4%

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

      2. mul-1-neg 30.4%

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

      3. unsub-neg 30.4%

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

      4. *-commutative 30.4%

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

      5. *-commutative 30.4%

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

   4. Simplified 30.4%

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

   5. Taylor expanded in y around 0 26.8%

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

      1. associate-*r/ 26.8%

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

      2. neg-mul-1 26.8%

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

   7. Simplified 26.8%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-80}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 0.000245:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 19: 36.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e-79) (/ t b) (if (<= z 2e-67) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e-79) {
		tmp = t / b;
	} else if (z <= 2e-67) {
		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 <= (-2.05d-79)) then
        tmp = t / b
    else if (z <= 2d-67) 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 <= -2.05e-79) {
		tmp = t / b;
	} else if (z <= 2e-67) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.05e-79:
		tmp = t / b
	elif z <= 2e-67:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e-79)
		tmp = Float64(t / b);
	elseif (z <= 2e-67)
		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 <= -2.05e-79)
		tmp = t / b;
	elseif (z <= 2e-67)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e-79], N[(t / b), $MachinePrecision], If[LessEqual[z, 2e-67], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999997e-79 or 1.99999999999999989e-67 < z

   1. Initial program 51.4%

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

   2. Taylor expanded in t around inf 27.6%

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

      1. *-commutative 27.6%

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

   4. Simplified 27.6%

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

   5. Taylor expanded in y around 0 28.8%

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

   if -2.04999999999999997e-79 < z < 1.99999999999999989e-67

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 50.6%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-79}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20: 25.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.2%

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

2. Taylor expanded in z around 0 23.0%

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

3. Final simplification 23.0%

   \[\leadsto x \]

Developer target: 74.1% 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 2023290 
(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)))))