Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.9% → 87.7%

Time: 16.1s

Alternatives: 13

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: 65.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+307}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-273} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* y x) (* z (- t a))) (- y (* z (- y b))))))
   (if (<= t_1 -4e+307)
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (or (<= t_1 -1e-273) (and (not (<= t_1 0.0)) (<= t_1 5e+305)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) + (z * (t - a))) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -4e+307) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -1e-273) || (!(t_1 <= 0.0) && (t_1 <= 5e+305))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (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) :: t_1
    real(8) :: tmp
    t_1 = ((y * x) + (z * (t - a))) / (y - (z * (y - b)))
    if (t_1 <= (-4d+307)) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    else if ((t_1 <= (-1d-273)) .or. (.not. (t_1 <= 0.0d0)) .and. (t_1 <= 5d+305)) then
        tmp = t_1
    else
        tmp = (t - a) / (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 t_1 = ((y * x) + (z * (t - a))) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -4e+307) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -1e-273) || (!(t_1 <= 0.0) && (t_1 <= 5e+305))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) + (z * (t - a))) / (y - (z * (y - b)))
	tmp = 0
	if t_1 <= -4e+307:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif (t_1 <= -1e-273) or (not (t_1 <= 0.0) and (t_1 <= 5e+305)):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y - Float64(z * Float64(y - b))))
	tmp = 0.0
	if (t_1 <= -4e+307)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -1e-273) || (!(t_1 <= 0.0) && (t_1 <= 5e+305)))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) + (z * (t - a))) / (y - (z * (y - b)));
	tmp = 0.0;
	if (t_1 <= -4e+307)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -1e-273) || (~((t_1 <= 0.0)) && (t_1 <= 5e+305)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+307], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-273], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 5e+305]]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

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)))) < -3.99999999999999994e307

   1. Initial program 49.1%

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

   2. Taylor expanded in y around -inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. unsub-neg 55.3%

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

      3. associate-*r/ 55.3%

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

      4. neg-mul-1 55.3%

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

      5. sub-neg 55.3%

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

      6. metadata-eval 55.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in z around inf 70.9%

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

   if -3.99999999999999994e307 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e-273 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000009e305

   1. Initial program 99.2%

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

   if -1e-273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 5.00000000000000009e305 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 14.2%

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

   2. Taylor expanded in z around inf 76.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -4 \cdot 10^{+307}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -1 \cdot 10^{-273} \lor \neg \left(\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 0\right) \land \frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{z \cdot t}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{z \cdot a}{t_1}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-45}:\\ \;\;\;\;\left(t_2 + \frac{x}{z} \cdot \frac{y}{b - y}\right) - t_4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;\left(t_2 + \frac{y \cdot x}{t_1}\right) - t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (/ (* z t) t_1))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ (* z a) t_1)))
   (if (<= z -2e+131)
     t_3
     (if (<= z -4.15e-45)
       (- (+ t_2 (* (/ x z) (/ y (- b y)))) t_4)
       (if (<= z 4.2e+41) (- (+ t_2 (/ (* y x) t_1)) t_4) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (z * t) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = (z * a) / t_1;
	double tmp;
	if (z <= -2e+131) {
		tmp = t_3;
	} else if (z <= -4.15e-45) {
		tmp = (t_2 + ((x / z) * (y / (b - y)))) - t_4;
	} else if (z <= 4.2e+41) {
		tmp = (t_2 + ((y * x) / t_1)) - t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (z * t) / t_1
    t_3 = (t - a) / (b - y)
    t_4 = (z * a) / t_1
    if (z <= (-2d+131)) then
        tmp = t_3
    else if (z <= (-4.15d-45)) then
        tmp = (t_2 + ((x / z) * (y / (b - y)))) - t_4
    else if (z <= 4.2d+41) then
        tmp = (t_2 + ((y * x) / t_1)) - t_4
    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 = y - (z * (y - b));
	double t_2 = (z * t) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = (z * a) / t_1;
	double tmp;
	if (z <= -2e+131) {
		tmp = t_3;
	} else if (z <= -4.15e-45) {
		tmp = (t_2 + ((x / z) * (y / (b - y)))) - t_4;
	} else if (z <= 4.2e+41) {
		tmp = (t_2 + ((y * x) / t_1)) - t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (z * t) / t_1
	t_3 = (t - a) / (b - y)
	t_4 = (z * a) / t_1
	tmp = 0
	if z <= -2e+131:
		tmp = t_3
	elif z <= -4.15e-45:
		tmp = (t_2 + ((x / z) * (y / (b - y)))) - t_4
	elif z <= 4.2e+41:
		tmp = (t_2 + ((y * x) / t_1)) - t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(z * t) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(z * a) / t_1)
	tmp = 0.0
	if (z <= -2e+131)
		tmp = t_3;
	elseif (z <= -4.15e-45)
		tmp = Float64(Float64(t_2 + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) - t_4);
	elseif (z <= 4.2e+41)
		tmp = Float64(Float64(t_2 + Float64(Float64(y * x) / t_1)) - t_4);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (z * t) / t_1;
	t_3 = (t - a) / (b - y);
	t_4 = (z * a) / t_1;
	tmp = 0.0;
	if (z <= -2e+131)
		tmp = t_3;
	elseif (z <= -4.15e-45)
		tmp = (t_2 + ((x / z) * (y / (b - y)))) - t_4;
	elseif (z <= 4.2e+41)
		tmp = (t_2 + ((y * x) / t_1)) - t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[z, -2e+131], t$95$3, If[LessEqual[z, -4.15e-45], N[(N[(t$95$2 + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[z, 4.2e+41], N[(N[(t$95$2 + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999998e131 or 4.1999999999999999e41 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 87.7%

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

   if -1.9999999999999998e131 < z < -4.1500000000000002e-45

   1. Initial program 74.0%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. times-frac 88.6%

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

   5. Simplified 88.6%

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

   if -4.1500000000000002e-45 < z < 4.1999999999999999e41

   1. Initial program 88.6%

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

   2. Taylor expanded in t around 0 88.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+131}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-45}:\\ \;\;\;\;\left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} + \frac{x}{z} \cdot \frac{y}{b - y}\right) - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+41}:\\ \;\;\;\;\left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} + \frac{y \cdot x}{y - z \cdot \left(y - b\right)}\right) - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-45}:\\ \;\;\;\;\left(\frac{z \cdot t}{t_1} + \frac{x}{z} \cdot \frac{y}{b - y}\right) - \frac{z \cdot a}{t_1}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1e+131)
     t_2
     (if (<= z -4.15e-45)
       (- (+ (/ (* z t) t_1) (* (/ x z) (/ y (- b y)))) (/ (* z a) t_1))
       (if (<= z 3.8e+41) (/ (+ (* y x) (* z (- t a))) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1e+131) {
		tmp = t_2;
	} else if (z <= -4.15e-45) {
		tmp = (((z * t) / t_1) + ((x / z) * (y / (b - y)))) - ((z * a) / t_1);
	} else if (z <= 3.8e+41) {
		tmp = ((y * x) + (z * (t - a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1d+131)) then
        tmp = t_2
    else if (z <= (-4.15d-45)) then
        tmp = (((z * t) / t_1) + ((x / z) * (y / (b - y)))) - ((z * a) / t_1)
    else if (z <= 3.8d+41) then
        tmp = ((y * x) + (z * (t - a))) / 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 * (y - b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1e+131) {
		tmp = t_2;
	} else if (z <= -4.15e-45) {
		tmp = (((z * t) / t_1) + ((x / z) * (y / (b - y)))) - ((z * a) / t_1);
	} else if (z <= 3.8e+41) {
		tmp = ((y * x) + (z * (t - a))) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1e+131:
		tmp = t_2
	elif z <= -4.15e-45:
		tmp = (((z * t) / t_1) + ((x / z) * (y / (b - y)))) - ((z * a) / t_1)
	elif z <= 3.8e+41:
		tmp = ((y * x) + (z * (t - a))) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1e+131)
		tmp = t_2;
	elseif (z <= -4.15e-45)
		tmp = Float64(Float64(Float64(Float64(z * t) / t_1) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) - Float64(Float64(z * a) / t_1));
	elseif (z <= 3.8e+41)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / 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 * (y - b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1e+131)
		tmp = t_2;
	elseif (z <= -4.15e-45)
		tmp = (((z * t) / t_1) + ((x / z) * (y / (b - y)))) - ((z * a) / t_1);
	elseif (z <= 3.8e+41)
		tmp = ((y * x) + (z * (t - a))) / 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[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+131], t$95$2, If[LessEqual[z, -4.15e-45], N[(N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+41], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999991e130 or 3.8000000000000001e41 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 87.7%

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

   if -9.9999999999999991e130 < z < -4.1500000000000002e-45

   1. Initial program 74.0%

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

   2. Taylor expanded in t around 0 74.0%

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

   3. Taylor expanded in z around inf 74.0%

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

      1. times-frac 88.6%

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

   5. Simplified 88.6%

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

   if -4.1500000000000002e-45 < z < 3.8000000000000001e41

   1. Initial program 88.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.15 \cdot 10^{-45}:\\ \;\;\;\;\left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} + \frac{x}{z} \cdot \frac{y}{b - y}\right) - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-230}:\\ \;\;\;\;x + z \cdot \left(t_1 - \frac{x}{\frac{y}{b - y}}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -3.5e-31)
     t_2
     (if (<= z -9.5e-230)
       (+ x (* z (- t_1 (/ x (/ y (- b y))))))
       (if (<= z 9.5e-270)
         (/ (+ (* y x) (* z (- t a))) y)
         (if (<= z 1.1e-14) (+ x (* z t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-31) {
		tmp = t_2;
	} else if (z <= -9.5e-230) {
		tmp = x + (z * (t_1 - (x / (y / (b - y)))));
	} else if (z <= 9.5e-270) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 1.1e-14) {
		tmp = x + (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-3.5d-31)) then
        tmp = t_2
    else if (z <= (-9.5d-230)) then
        tmp = x + (z * (t_1 - (x / (y / (b - y)))))
    else if (z <= 9.5d-270) then
        tmp = ((y * x) + (z * (t - a))) / y
    else if (z <= 1.1d-14) then
        tmp = x + (z * 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 = (t - a) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-31) {
		tmp = t_2;
	} else if (z <= -9.5e-230) {
		tmp = x + (z * (t_1 - (x / (y / (b - y)))));
	} else if (z <= 9.5e-270) {
		tmp = ((y * x) + (z * (t - a))) / y;
	} else if (z <= 1.1e-14) {
		tmp = x + (z * t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.5e-31:
		tmp = t_2
	elif z <= -9.5e-230:
		tmp = x + (z * (t_1 - (x / (y / (b - y)))))
	elif z <= 9.5e-270:
		tmp = ((y * x) + (z * (t - a))) / y
	elif z <= 1.1e-14:
		tmp = x + (z * t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e-31)
		tmp = t_2;
	elseif (z <= -9.5e-230)
		tmp = Float64(x + Float64(z * Float64(t_1 - Float64(x / Float64(y / Float64(b - y))))));
	elseif (z <= 9.5e-270)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1.1e-14)
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.5e-31)
		tmp = t_2;
	elseif (z <= -9.5e-230)
		tmp = x + (z * (t_1 - (x / (y / (b - y)))));
	elseif (z <= 9.5e-270)
		tmp = ((y * x) + (z * (t - a))) / y;
	elseif (z <= 1.1e-14)
		tmp = x + (z * t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-31], t$95$2, If[LessEqual[z, -9.5e-230], N[(x + N[(z * N[(t$95$1 - N[(x / N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-270], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.1e-14], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999985e-31 or 1.1e-14 < z

   1. Initial program 50.7%

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

   2. Taylor expanded in z around inf 82.0%

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

   if -3.49999999999999985e-31 < z < -9.5000000000000004e-230

   1. Initial program 77.9%

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

   2. Taylor expanded in t around 0 77.9%

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

   3. Taylor expanded in z around 0 66.9%

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

      1. +-commutative 66.9%

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

      2. mul-1-neg 66.9%

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

      3. sub-neg 66.9%

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

      4. div-sub 67.0%

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

      5. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   if -9.5000000000000004e-230 < z < 9.5000000000000006e-270

   1. Initial program 95.9%

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

   2. Taylor expanded in z around 0 84.3%

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

   if 9.5000000000000006e-270 < z < 1.1e-14

   1. Initial program 88.5%

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

   2. Taylor expanded in y around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in z around 0 67.6%

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

      1. associate--r+ 67.6%

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

      2. cancel-sign-sub-inv 67.6%

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

      3. metadata-eval 67.6%

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

      4. *-lft-identity 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in x around 0 67.6%

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

      1. div-sub 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-230}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{x}{\frac{y}{b - y}}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-270}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 72.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-31} \lor \neg \left(z \leq 3.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e-31) (not (<= z 3.6e-15)))
   (/ (- t a) (- b y))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e-31) || !(z <= 3.6e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.5d-31)) .or. (.not. (z <= 3.6d-15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e-31) || !(z <= 3.6e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e-31) or not (z <= 3.6e-15):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e-31) || !(z <= 3.6e-15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e-31) || ~((z <= 3.6e-15)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e-31], N[Not[LessEqual[z, 3.6e-15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999985e-31 or 3.6000000000000001e-15 < z

   1. Initial program 50.7%

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

   2. Taylor expanded in z around inf 82.0%

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

   if -3.49999999999999985e-31 < z < 3.6000000000000001e-15

   1. Initial program 87.4%

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

   2. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. associate--r+ 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. metadata-eval 71.6%

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

      4. *-lft-identity 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in x around 0 71.6%

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

      1. div-sub 71.7%

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

   10. Simplified 71.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-31} \lor \neg \left(z \leq 3.6 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]

Alternative 6: 41.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-240}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.2e-72)
     t_1
     (if (<= y 4.1e-240) (/ t b) (if (<= y 2.5e-78) (/ (- a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.2e-72) {
		tmp = t_1;
	} else if (y <= 4.1e-240) {
		tmp = t / b;
	} else if (y <= 2.5e-78) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.2d-72)) then
        tmp = t_1
    else if (y <= 4.1d-240) then
        tmp = t / b
    else if (y <= 2.5d-78) then
        tmp = -a / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.2e-72) {
		tmp = t_1;
	} else if (y <= 4.1e-240) {
		tmp = t / b;
	} else if (y <= 2.5e-78) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -2.2e-72:
		tmp = t_1
	elif y <= 4.1e-240:
		tmp = t / b
	elif y <= 2.5e-78:
		tmp = -a / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.2e-72)
		tmp = t_1;
	elseif (y <= 4.1e-240)
		tmp = Float64(t / b);
	elseif (y <= 2.5e-78)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.2e-72)
		tmp = t_1;
	elseif (y <= 4.1e-240)
		tmp = t / b;
	elseif (y <= 2.5e-78)
		tmp = -a / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-72], t$95$1, If[LessEqual[y, 4.1e-240], N[(t / b), $MachinePrecision], If[LessEqual[y, 2.5e-78], N[((-a) / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000002e-72 or 2.4999999999999998e-78 < y

   1. Initial program 58.3%

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

   2. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

   4. Simplified 48.6%

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

   if -2.20000000000000002e-72 < y < 4.1000000000000001e-240

   1. Initial program 81.9%

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

   2. Taylor expanded in t around 0 81.8%

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

   3. Taylor expanded in b around inf 76.0%

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

      1. mul-1-neg 76.0%

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

      2. associate-+r+ 76.0%

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

      3. sub-neg 76.0%

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

      4. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in t around inf 47.0%

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

   if 4.1000000000000001e-240 < y < 2.4999999999999998e-78

   1. Initial program 81.5%

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

   2. Taylor expanded in t around 0 78.3%

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

   3. Taylor expanded in b around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-+r+ 66.5%

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

      3. sub-neg 66.5%

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

      4. associate-/l* 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in a around inf 48.1%

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

      1. associate-*r/ 48.1%

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

      2. mul-1-neg 48.1%

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

   8. Simplified 48.1%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-240}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 7: 65.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-77} \lor \neg \left(z \leq 4.4 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.28e-77) (not (<= z 4.4e-15)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e-77) || !(z <= 4.4e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.28d-77)) .or. (.not. (z <= 4.4d-15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.28e-77) || !(z <= 4.4e-15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.28e-77) or not (z <= 4.4e-15):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.28e-77) || !(z <= 4.4e-15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.28e-77) || ~((z <= 4.4e-15)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.28e-77], N[Not[LessEqual[z, 4.4e-15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-77 or 4.39999999999999971e-15 < 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 80.0%

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

   if -1.28e-77 < z < 4.39999999999999971e-15

   1. Initial program 87.7%

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

   2. Taylor expanded in y around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   4. Simplified 60.1%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-77} \lor \neg \left(z \leq 4.4 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 8: 69.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-32} \lor \neg \left(z \leq 1.45 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e-32) (not (<= z 1.45e-15)))
   (/ (- 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 <= -9e-32) || !(z <= 1.45e-15)) {
		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 <= (-9d-32)) .or. (.not. (z <= 1.45d-15))) 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 <= -9e-32) || !(z <= 1.45e-15)) {
		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 <= -9e-32) or not (z <= 1.45e-15):
		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 <= -9e-32) || !(z <= 1.45e-15))
		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 <= -9e-32) || ~((z <= 1.45e-15)))
		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, -9e-32], N[Not[LessEqual[z, 1.45e-15]], $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 < -9.00000000000000009e-32 or 1.45000000000000009e-15 < z

   1. Initial program 50.7%

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

   2. Taylor expanded in z around inf 82.0%

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

   if -9.00000000000000009e-32 < z < 1.45000000000000009e-15

   1. Initial program 87.4%

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

   2. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. associate--r+ 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. metadata-eval 71.6%

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

      4. *-lft-identity 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in a around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/l* 69.5%

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

      3. distribute-neg-frac 69.5%

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

   10. Simplified 69.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-32} \lor \neg \left(z \leq 1.45 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{y}{z}}\\ \end{array} \]

Alternative 9: 53.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+55} \lor \neg \left(y \leq 1.48 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.05e+55) (not (<= y 1.48e-77)))
   (/ x (- 1.0 z))
   (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+55) || !(y <= 1.48e-77)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.05d+55)) .or. (.not. (y <= 1.48d-77))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+55) || !(y <= 1.48e-77)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.05e+55) or not (y <= 1.48e-77):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.05e+55) || !(y <= 1.48e-77))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.05e+55) || ~((y <= 1.48e-77)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.05e+55], N[Not[LessEqual[y, 1.48e-77]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999991e55 or 1.48000000000000002e-77 < y

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   4. Simplified 51.7%

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

   if -2.04999999999999991e55 < y < 1.48000000000000002e-77

   1. Initial program 81.7%

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

   2. Taylor expanded in y around 0 59.0%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+55} \lor \neg \left(y \leq 1.48 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 10: 36.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.3e-72) (/ t b) (if (<= z 1.3e-15) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.3e-72) {
		tmp = t / b;
	} else if (z <= 1.3e-15) {
		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 <= (-4.3d-72)) then
        tmp = t / b
    else if (z <= 1.3d-15) 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 <= -4.3e-72) {
		tmp = t / b;
	} else if (z <= 1.3e-15) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.3e-72:
		tmp = t / b
	elif z <= 1.3e-15:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.3e-72)
		tmp = Float64(t / b);
	elseif (z <= 1.3e-15)
		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 <= -4.3e-72)
		tmp = t / b;
	elseif (z <= 1.3e-15)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.3e-72], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.3e-15], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2999999999999999e-72

   1. Initial program 59.4%

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

   2. Taylor expanded in t around 0 59.4%

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

   3. Taylor expanded in b around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-+r+ 55.4%

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

      3. sub-neg 55.4%

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

      4. associate-/l* 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in t around inf 32.6%

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

   if -4.2999999999999999e-72 < z < 1.30000000000000002e-15

   1. Initial program 87.7%

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

   2. Taylor expanded in z around 0 60.1%

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

   if 1.30000000000000002e-15 < 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 38.2%

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

   3. Taylor expanded in b around inf 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate-+r+ 42.7%

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

      3. sub-neg 42.7%

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

      4. associate-/l* 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in a around inf 20.7%

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

      1. associate-*r/ 20.7%

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

      2. mul-1-neg 20.7%

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

   8. Simplified 20.7%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 11: 35.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.96e-72) (/ t b) (if (<= z 1.0) x (/ (- t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.96e-72) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -t / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.96d-72)) then
        tmp = t / b
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = -t / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.96e-72) {
		tmp = t / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -t / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.96e-72:
		tmp = t / b
	elif z <= 1.0:
		tmp = x
	else:
		tmp = -t / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.96e-72)
		tmp = Float64(t / b);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(Float64(-t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.96e-72)
		tmp = t / b;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = -t / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.96e-72], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.0], x, N[((-t) / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.96000000000000011e-72

   1. Initial program 59.4%

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

   2. Taylor expanded in t around 0 59.4%

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

   3. Taylor expanded in b around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-+r+ 55.4%

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

      3. sub-neg 55.4%

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

      4. associate-/l* 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in t around inf 32.6%

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

   if -1.96000000000000011e-72 < z < 1

   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 z around 0 59.2%

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

   if 1 < z

   1. Initial program 38.0%

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

   2. Taylor expanded in y around inf 20.6%

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

      1. mul-1-neg 20.6%

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

      2. unsub-neg 20.6%

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

   4. Simplified 20.6%

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

   5. Taylor expanded in x around 0 17.3%

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

      1. times-frac 43.9%

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

   7. Simplified 43.9%

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

   8. Taylor expanded in t around inf 33.2%

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

   9. Taylor expanded in z around inf 33.2%

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

       1. associate-*r/ 33.2%

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

       2. mul-1-neg 33.2%

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

   11. Simplified 33.2%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{-72}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{y}\\ \end{array} \]

Alternative 12: 36.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-72} \lor \neg \left(z \leq 62\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.3e-72) (not (<= z 62.0))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.3e-72) || !(z <= 62.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.3d-72)) .or. (.not. (z <= 62.0d0))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.3e-72) || !(z <= 62.0)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.3e-72) or not (z <= 62.0):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.3e-72) || !(z <= 62.0))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.3e-72) || ~((z <= 62.0)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.3e-72], N[Not[LessEqual[z, 62.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.2999999999999999e-72 or 62 < z

   1. Initial program 50.7%

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

   2. Taylor expanded in t around 0 49.9%

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

   3. Taylor expanded in b around inf 50.0%

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

      1. mul-1-neg 50.0%

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

      2. associate-+r+ 50.0%

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

      3. sub-neg 50.0%

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

      4. associate-/l* 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in t around inf 28.2%

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

   if -4.2999999999999999e-72 < z < 62

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 58.7%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-72} \lor \neg \left(z \leq 62\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 24.4% 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 67.6%

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

2. Taylor expanded in z around 0 28.8%

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

3. Final simplification 28.8%

   \[\leadsto x \]

Developer target: 73.2% 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 2023320 
(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)))))