Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.0% → 83.9%

Time: 16.2s

Alternatives: 17

Speedup: 0.9×

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: 66.0% 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: 83.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{y} + -1\\ t_2 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;\frac{t - a}{y \cdot t\_1} + \frac{\frac{\frac{a - t}{y}}{{\left(1 - \frac{b}{y}\right)}^{2}} + \frac{x}{t\_1}}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ b y) -1.0)) (t_2 (+ y (* z (- b y)))))
   (if (<= z -480000000.0)
     (+
      (/ (- t a) (* y t_1))
      (/ (+ (/ (/ (- a t) y) (pow (- 1.0 (/ b y)) 2.0)) (/ x t_1)) z))
     (if (<= z 6.5e+89)
       (* x (+ (/ y t_2) (/ (* z (- t a)) (* x t_2))))
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b / y) + -1.0;
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -480000000.0) {
		tmp = ((t - a) / (y * t_1)) + (((((a - t) / y) / pow((1.0 - (b / y)), 2.0)) + (x / t_1)) / z);
	} else if (z <= 6.5e+89) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (b / y) + (-1.0d0)
    t_2 = y + (z * (b - y))
    if (z <= (-480000000.0d0)) then
        tmp = ((t - a) / (y * t_1)) + (((((a - t) / y) / ((1.0d0 - (b / y)) ** 2.0d0)) + (x / t_1)) / z)
    else if (z <= 6.5d+89) then
        tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
    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 = (b / y) + -1.0;
	double t_2 = y + (z * (b - y));
	double tmp;
	if (z <= -480000000.0) {
		tmp = ((t - a) / (y * t_1)) + (((((a - t) / y) / Math.pow((1.0 - (b / y)), 2.0)) + (x / t_1)) / z);
	} else if (z <= 6.5e+89) {
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b / y) + -1.0
	t_2 = y + (z * (b - y))
	tmp = 0
	if z <= -480000000.0:
		tmp = ((t - a) / (y * t_1)) + (((((a - t) / y) / math.pow((1.0 - (b / y)), 2.0)) + (x / t_1)) / z)
	elif z <= 6.5e+89:
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)))
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b / y) + -1.0)
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if (z <= -480000000.0)
		tmp = Float64(Float64(Float64(t - a) / Float64(y * t_1)) + Float64(Float64(Float64(Float64(Float64(a - t) / y) / (Float64(1.0 - Float64(b / y)) ^ 2.0)) + Float64(x / t_1)) / z));
	elseif (z <= 6.5e+89)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_2))));
	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 = (b / y) + -1.0;
	t_2 = y + (z * (b - y));
	tmp = 0.0;
	if (z <= -480000000.0)
		tmp = ((t - a) / (y * t_1)) + (((((a - t) / y) / ((1.0 - (b / y)) ^ 2.0)) + (x / t_1)) / z);
	elseif (z <= 6.5e+89)
		tmp = x * ((y / t_2) + ((z * (t - a)) / (x * t_2)));
	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[(b / y), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -480000000.0], N[(N[(N[(t - a), $MachinePrecision] / N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[Power[N[(1.0 - N[(b / y), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+89], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e8

   1. Initial program 34.8%

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

   3. Taylor expanded in y around inf 28.5%

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

      1. +-commutative 28.5%

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

      2. mul-1-neg 28.5%

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

      3. unsub-neg 28.5%

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

      4. associate-/l* 24.0%

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

   5. Simplified 24.0%

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

   6. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. unsub-neg 91.8%

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

      3. mul-1-neg 91.8%

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

      4. mul-1-neg 91.8%

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

      5. sub-neg 91.8%

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

   8. Simplified 83.9%

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

   if -4.8e8 < z < 6.4999999999999996e89

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf 95.2%

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

   if 6.4999999999999996e89 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in z around inf 100.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480000000:\\ \;\;\;\;\frac{t - a}{y \cdot \left(\frac{b}{y} + -1\right)} + \frac{\frac{\frac{a - t}{y}}{{\left(1 - \frac{b}{y}\right)}^{2}} + \frac{x}{\frac{b}{y} + -1}}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+54}:\\ \;\;\;\;t\_2 + \frac{\frac{y \cdot x}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.6e+54)
     (+ t_2 (/ (+ (/ (* y x) (- b y)) (* y (/ (- a t) (pow (- b y) 2.0)))) z))
     (if (<= z 2.25e+91)
       (* x (+ (/ y t_1) (/ (* z (- t a)) (* x 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 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.6e+54) {
		tmp = t_2 + ((((y * x) / (b - y)) + (y * ((a - t) / pow((b - y), 2.0)))) / z);
	} else if (z <= 2.25e+91) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 * (b - y))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.6d+54)) then
        tmp = t_2 + ((((y * x) / (b - y)) + (y * ((a - t) / ((b - y) ** 2.0d0)))) / z)
    else if (z <= 2.25d+91) then
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.6e+54) {
		tmp = t_2 + ((((y * x) / (b - y)) + (y * ((a - t) / Math.pow((b - y), 2.0)))) / z);
	} else if (z <= 2.25e+91) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.6e+54:
		tmp = t_2 + ((((y * x) / (b - y)) + (y * ((a - t) / math.pow((b - y), 2.0)))) / z)
	elif z <= 2.25e+91:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.6e+54)
		tmp = Float64(t_2 + Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) + Float64(y * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0)))) / z));
	elseif (z <= 2.25e+91)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * 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 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.6e+54)
		tmp = t_2 + ((((y * x) / (b - y)) + (y * ((a - t) / ((b - y) ^ 2.0)))) / z);
	elseif (z <= 2.25e+91)
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+54], N[(t$95$2 + N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+91], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e54

   1. Initial program 27.9%

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

   3. Taylor expanded in z around -inf 66.4%

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

      1. associate--l+ 66.4%

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

      2. mul-1-neg 66.4%

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

      3. distribute-lft-out-- 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-/l* 77.4%

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

      6. div-sub 77.4%

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

   5. Simplified 77.4%

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

   if -1.6e54 < z < 2.25e91

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 93.6%

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

   if 2.25e91 < z

   1. Initial program 42.1%

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

   3. Taylor expanded in z around inf 100.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+54}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y \cdot x}{b - y} + y \cdot \frac{a - t}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{z \cdot \left(t - a\right) + y \cdot x}{t\_1}\\ t_4 := \frac{y}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(t\_4 + \frac{t - a}{y \cdot \left(\frac{x}{z} - x\right)}\right)\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-268}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;x \cdot \left(t\_4 + \frac{\frac{a - t}{x}}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ (* z (- t a)) (* y x)) t_1))
        (t_4 (/ y t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ t_4 (/ (- t a) (* y (- (/ x z) x)))))
     (if (<= t_3 -1e-268)
       t_3
       (if (<= t_3 0.0)
         t_2
         (if (<= t_3 2e+256)
           t_3
           (if (<= t_3 INFINITY)
             (* x (+ t_4 (/ (/ (- a t) x) (- y b))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((z * (t - a)) + (y * x)) / t_1;
	double t_4 = y / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * (t_4 + ((t - a) / (y * ((x / z) - x))));
	} else if (t_3 <= -1e-268) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+256) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x * (t_4 + (((a - t) / x) / (y - b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = ((z * (t - a)) + (y * x)) / t_1;
	double t_4 = y / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * (t_4 + ((t - a) / (y * ((x / z) - x))));
	} else if (t_3 <= -1e-268) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = t_2;
	} else if (t_3 <= 2e+256) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = x * (t_4 + (((a - t) / x) / (y - b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = ((z * (t - a)) + (y * x)) / t_1
	t_4 = y / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * (t_4 + ((t - a) / (y * ((x / z) - x))))
	elif t_3 <= -1e-268:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = t_2
	elif t_3 <= 2e+256:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = x * (t_4 + (((a - t) / x) / (y - b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / t_1)
	t_4 = Float64(y / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(t_4 + Float64(Float64(t - a) / Float64(y * Float64(Float64(x / z) - x)))));
	elseif (t_3 <= -1e-268)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+256)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(x * Float64(t_4 + Float64(Float64(Float64(a - t) / x) / Float64(y - b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = ((z * (t - a)) + (y * x)) / t_1;
	t_4 = y / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * (t_4 + ((t - a) / (y * ((x / z) - x))));
	elseif (t_3 <= -1e-268)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = t_2;
	elseif (t_3 <= 2e+256)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = x * (t_4 + (((a - t) / x) / (y - b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(y / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(t$95$4 + N[(N[(t - a), $MachinePrecision] / N[(y * N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-268], t$95$3, If[LessEqual[t$95$3, 0.0], t$95$2, If[LessEqual[t$95$3, 2e+256], t$95$3, If[LessEqual[t$95$3, Infinity], N[(x * N[(t$95$4 + N[(N[(N[(a - t), $MachinePrecision] / x), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 40.5%

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

   3. Taylor expanded in x around inf 65.4%

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

   4. Taylor expanded in z around inf 41.5%

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

   5. Taylor expanded in y around inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

   7. Simplified 81.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99999999999999958e-269 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e256

   1. Initial program 99.6%

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

   if -9.99999999999999958e-269 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.5%

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

   3. Taylor expanded in z around inf 78.1%

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

   if 2.0000000000000001e256 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 26.3%

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

   3. Taylor expanded in x around inf 75.0%

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

   4. Taylor expanded in z around inf 40.4%

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

   5. Taylor expanded in z around inf 95.4%

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

      1. associate-/r* 91.5%

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

   7. Simplified 91.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{y \cdot \left(\frac{x}{z} - x\right)}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-268}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{\frac{a - t}{x}}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := x \cdot \left(\frac{y}{t\_1} + \frac{\frac{a - t}{x}}{y - b}\right)\\ t_4 := \frac{z \cdot \left(t - a\right) + y \cdot x}{t\_1}\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-268}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* x (+ (/ y t_1) (/ (/ (- a t) x) (- y b)))))
        (t_4 (/ (+ (* z (- t a)) (* y x)) t_1)))
   (if (<= t_4 -5e+302)
     t_3
     (if (<= t_4 -1e-268)
       t_4
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 2e+256) t_4 (if (<= t_4 INFINITY) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = x * ((y / t_1) + (((a - t) / x) / (y - b)));
	double t_4 = ((z * (t - a)) + (y * x)) / t_1;
	double tmp;
	if (t_4 <= -5e+302) {
		tmp = t_3;
	} else if (t_4 <= -1e-268) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+256) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = x * ((y / t_1) + (((a - t) / x) / (y - b)));
	double t_4 = ((z * (t - a)) + (y * x)) / t_1;
	double tmp;
	if (t_4 <= -5e+302) {
		tmp = t_3;
	} else if (t_4 <= -1e-268) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 2e+256) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = x * ((y / t_1) + (((a - t) / x) / (y - b)))
	t_4 = ((z * (t - a)) + (y * x)) / t_1
	tmp = 0
	if t_4 <= -5e+302:
		tmp = t_3
	elif t_4 <= -1e-268:
		tmp = t_4
	elif t_4 <= 0.0:
		tmp = t_2
	elif t_4 <= 2e+256:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(Float64(a - t) / x) / Float64(y - b))))
	t_4 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / t_1)
	tmp = 0.0
	if (t_4 <= -5e+302)
		tmp = t_3;
	elseif (t_4 <= -1e-268)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+256)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = x * ((y / t_1) + (((a - t) / x) / (y - b)));
	t_4 = ((z * (t - a)) + (y * x)) / t_1;
	tmp = 0.0;
	if (t_4 <= -5e+302)
		tmp = t_3;
	elseif (t_4 <= -1e-268)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 2e+256)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(N[(a - t), $MachinePrecision] / x), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+302], t$95$3, If[LessEqual[t$95$4, -1e-268], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 2e+256], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5e302 or 2.0000000000000001e256 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 36.3%

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

   3. Taylor expanded in x around inf 71.2%

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

   4. Taylor expanded in z around inf 43.3%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-/r* 82.5%

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

   7. Simplified 82.5%

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

   if -5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -9.99999999999999958e-269 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e256

   1. Initial program 99.6%

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

   if -9.99999999999999958e-269 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.5%

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

   3. Taylor expanded in z around inf 78.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{\frac{a - t}{x}}{y - b}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-268}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{\frac{a - t}{x}}{y - b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+56} \lor \neg \left(z \leq 1.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3.55e+56) (not (<= z 1.6e+89)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.55e+56) || !(z <= 1.6e+89)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y))
    if ((z <= (-3.55d+56)) .or. (.not. (z <= 1.6d+89))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.55e+56) || !(z <= 1.6e+89)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -3.55e+56) or not (z <= 1.6e+89):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -3.55e+56) || !(z <= 1.6e+89))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -3.55e+56) || ~((z <= 1.6e+89)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.55e+56], N[Not[LessEqual[z, 1.6e+89]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.55e56 or 1.59999999999999994e89 < z

   1. Initial program 33.6%

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

   3. Taylor expanded in z around inf 84.7%

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

   if -3.55e56 < z < 1.59999999999999994e89

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 93.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+56} \lor \neg \left(z \leq 1.6 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+54} \lor \neg \left(z \leq 2.6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e+54) (not (<= z 2.6e+90)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e+54) || !(z <= 2.6e+90)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (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 <= (-2.4d+54)) .or. (.not. (z <= 2.6d+90))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (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 <= -2.4e+54) || !(z <= 2.6e+90)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e+54) or not (z <= 2.6e+90):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e+54) || !(z <= 2.6e+90))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / 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 <= -2.4e+54) || ~((z <= 2.6e+90)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e+54], N[Not[LessEqual[z, 2.6e+90]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999998e54 or 2.5999999999999998e90 < z

   1. Initial program 34.0%

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

   3. Taylor expanded in z around inf 84.0%

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

   if -2.39999999999999998e54 < z < 2.5999999999999998e90

   1. Initial program 86.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+54} \lor \neg \left(z \leq 2.6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-161}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.65e-31)
     t_1
     (if (<= z 1e-161)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 4.8e-42) (/ (* y x) (+ y (* z (- b 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 <= -1.65e-31) {
		tmp = t_1;
	} else if (z <= 1e-161) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 4.8e-42) {
		tmp = (y * x) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.65d-31)) then
        tmp = t_1
    else if (z <= 1d-161) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 4.8d-42) then
        tmp = (y * x) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.65e-31) {
		tmp = t_1;
	} else if (z <= 1e-161) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 4.8e-42) {
		tmp = (y * x) / (y + (z * (b - 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 <= -1.65e-31:
		tmp = t_1
	elif z <= 1e-161:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 4.8e-42:
		tmp = (y * x) / (y + (z * (b - 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 <= -1.65e-31)
		tmp = t_1;
	elseif (z <= 1e-161)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 4.8e-42)
		tmp = Float64(Float64(y * x) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.65e-31)
		tmp = t_1;
	elseif (z <= 1e-161)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 4.8e-42)
		tmp = (y * x) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-31], t$95$1, If[LessEqual[z, 1e-161], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-42], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e-31 or 4.80000000000000005e-42 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around inf 75.9%

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

   if -1.65e-31 < z < 1.00000000000000003e-161

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 66.7%

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

   4. Taylor expanded in x around 0 80.9%

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

   if 1.00000000000000003e-161 < z < 4.80000000000000005e-42

   1. Initial program 99.7%

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

      1. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 68.2%

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

      1. *-commutative 68.2%

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

   7. Simplified 68.2%

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

Alternative 8: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-161}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-33}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5e-32)
     t_1
     (if (<= z 1e-161)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 1.02e-33) (/ (* y x) (+ 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 <= -5e-32) {
		tmp = t_1;
	} else if (z <= 1e-161) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.02e-33) {
		tmp = (y * x) / (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 <= (-5d-32)) then
        tmp = t_1
    else if (z <= 1d-161) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.02d-33) then
        tmp = (y * x) / (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 <= -5e-32) {
		tmp = t_1;
	} else if (z <= 1e-161) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.02e-33) {
		tmp = (y * x) / (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 <= -5e-32:
		tmp = t_1
	elif z <= 1e-161:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.02e-33:
		tmp = (y * x) / (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 <= -5e-32)
		tmp = t_1;
	elseif (z <= 1e-161)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.02e-33)
		tmp = Float64(Float64(y * x) / 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 <= -5e-32)
		tmp = t_1;
	elseif (z <= 1e-161)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.02e-33)
		tmp = (y * x) / (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, -5e-32], t$95$1, If[LessEqual[z, 1e-161], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-33], N[(N[(y * x), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e-32 or 1.02e-33 < z

   1. Initial program 46.6%

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

   3. Taylor expanded in z around inf 75.9%

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

   if -5e-32 < z < 1.00000000000000003e-161

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0 66.7%

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

   4. Taylor expanded in x around 0 80.9%

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

   if 1.00000000000000003e-161 < z < 1.02e-33

   1. Initial program 99.7%

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

      1. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 68.2%

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

      1. *-commutative 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in b around inf 68.2%

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

Alternative 9: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-44} \lor \neg \left(z \leq 3.5 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-44) (not (<= z 3.5e-50)))
   (/ (- 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 <= -5.5e-44) || !(z <= 3.5e-50)) {
		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 <= (-5.5d-44)) .or. (.not. (z <= 3.5d-50))) 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 <= -5.5e-44) || !(z <= 3.5e-50)) {
		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 <= -5.5e-44) or not (z <= 3.5e-50):
		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 <= -5.5e-44) || !(z <= 3.5e-50))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.5e-44) || ~((z <= 3.5e-50)))
		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, -5.5e-44], N[Not[LessEqual[z, 3.5e-50]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999993e-44 or 3.49999999999999997e-50 < z

   1. Initial program 47.8%

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

   3. Taylor expanded in z around inf 75.0%

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

   if -5.49999999999999993e-44 < z < 3.49999999999999997e-50

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 64.1%

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

   4. Taylor expanded in x around 0 76.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-44} \lor \neg \left(z \leq 3.5 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-58} \lor \neg \left(z \leq 3.8 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.35e-58) (not (<= z 3.8e-51))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e-58) || !(z <= 3.8e-51)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.35d-58)) .or. (.not. (z <= 3.8d-51))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.35e-58) || !(z <= 3.8e-51)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.35e-58) or not (z <= 3.8e-51):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.35e-58) || !(z <= 3.8e-51))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.35e-58) || ~((z <= 3.8e-51)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.35e-58], N[Not[LessEqual[z, 3.8e-51]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-58 or 3.80000000000000003e-51 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in z around inf 74.2%

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

   if -1.3499999999999999e-58 < z < 3.80000000000000003e-51

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 56.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-58} \lor \neg \left(z \leq 3.8 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-46} \lor \neg \left(y \leq 1.26 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e-46) (not (<= y 1.26e+53))) (/ 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 <= -9.5e-46) || !(y <= 1.26e+53)) {
		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 <= (-9.5d-46)) .or. (.not. (y <= 1.26d+53))) 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 <= -9.5e-46) || !(y <= 1.26e+53)) {
		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 <= -9.5e-46) or not (y <= 1.26e+53):
		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 <= -9.5e-46) || !(y <= 1.26e+53))
		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 <= -9.5e-46) || ~((y <= 1.26e+53)))
		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, -9.5e-46], N[Not[LessEqual[y, 1.26e+53]], $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 < -9.49999999999999993e-46 or 1.25999999999999999e53 < y

   1. Initial program 53.8%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

   5. Simplified 60.3%

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

   if -9.49999999999999993e-46 < y < 1.25999999999999999e53

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 52.9%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-46} \lor \neg \left(y \leq 1.26 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{+71} \lor \neg \left(z \leq 1.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.96e+71) (not (<= z 1.2e-50))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.96e+71) || !(z <= 1.2e-50)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.96d+71)) .or. (.not. (z <= 1.2d-50))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.96e+71) || !(z <= 1.2e-50)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.96e+71) or not (z <= 1.2e-50):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.96e+71) || !(z <= 1.2e-50))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.96e+71) || ~((z <= 1.2e-50)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.96e+71], N[Not[LessEqual[z, 1.2e-50]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.96000000000000011e71 or 1.20000000000000001e-50 < z

   1. Initial program 42.4%

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

   3. Taylor expanded in x around inf 43.8%

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

   4. Taylor expanded in z around inf 43.1%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. associate-/r* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in t around inf 47.2%

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

   if -1.96000000000000011e71 < z < 1.20000000000000001e-50

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

   5. Simplified 54.5%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.96 \cdot 10^{+71} \lor \neg \left(z \leq 1.2 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.1 \lor \neg \left(z \leq 5.4 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.1) (not (<= z 5.4e-51))) (/ t (- b y)) (+ x (* z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.1) || !(z <= 5.4e-51)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.1d0)) .or. (.not. (z <= 5.4d-51))) then
        tmp = t / (b - y)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.1) || !(z <= 5.4e-51)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.1) or not (z <= 5.4e-51):
		tmp = t / (b - y)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.1) || !(z <= 5.4e-51))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.1) || ~((z <= 5.4e-51)))
		tmp = t / (b - y);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.1], N[Not[LessEqual[z, 5.4e-51]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.10000000000000001 or 5.3999999999999994e-51 < z

   1. Initial program 44.6%

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

   3. Taylor expanded in x around inf 45.8%

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

   4. Taylor expanded in z around inf 46.0%

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

   5. Taylor expanded in z around inf 72.2%

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

      1. associate-/r* 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in t around inf 45.8%

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

   if -0.10000000000000001 < z < 5.3999999999999994e-51

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in z around 0 54.6%

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

      1. *-commutative 54.6%

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

   8. Simplified 54.6%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.1 \lor \neg \left(z \leq 5.4 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.76:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.76) (- (/ x z)) (if (<= z 18000.0) (+ x (* z x)) (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.76) {
		tmp = -(x / z);
	} else if (z <= 18000.0) {
		tmp = x + (z * x);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.76d0)) then
        tmp = -(x / z)
    else if (z <= 18000.0d0) then
        tmp = x + (z * x)
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.76) {
		tmp = -(x / z);
	} else if (z <= 18000.0) {
		tmp = x + (z * x);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.76:
		tmp = -(x / z)
	elif z <= 18000.0:
		tmp = x + (z * x)
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.76)
		tmp = Float64(-Float64(x / z));
	elseif (z <= 18000.0)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.76)
		tmp = -(x / z);
	elseif (z <= 18000.0)
		tmp = x + (z * x);
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.76], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, 18000.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.76000000000000001

   1. Initial program 35.8%

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

   3. Taylor expanded in y around inf 27.1%

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

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in z around inf 25.6%

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

      1. associate-*r/ 25.6%

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

      2. mul-1-neg 25.6%

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

   8. Simplified 25.6%

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

   if -0.76000000000000001 < z < 18000

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. unsub-neg 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around 0 52.0%

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

      1. *-commutative 52.0%

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

   8. Simplified 52.0%

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

   if 18000 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in b around 0 29.9%

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

      1. mul-1-neg 29.9%

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

      2. *-commutative 29.9%

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

      3. distribute-lft-neg-in 29.9%

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

   5. Simplified 29.9%

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

   6. Taylor expanded in t around 0 19.9%

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

      1. mul-1-neg 19.9%

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

      2. distribute-lft-neg-out 19.9%

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

      3. *-commutative 19.9%

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

   8. Simplified 19.9%

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

   9. Taylor expanded in z around inf 25.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.76:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+54} \lor \neg \left(z \leq 18000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+54) (not (<= z 18000.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+54) || !(z <= 18000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.4d+54)) .or. (.not. (z <= 18000.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+54) || !(z <= 18000.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.4e+54) or not (z <= 18000.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+54) || !(z <= 18000.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.4e+54) || ~((z <= 18000.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+54], N[Not[LessEqual[z, 18000.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000001e54 or 18000 < z

   1. Initial program 38.3%

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

   3. Taylor expanded in b around 0 23.9%

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

      1. mul-1-neg 23.9%

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

      2. *-commutative 23.9%

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

      3. distribute-lft-neg-in 23.9%

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

   5. Simplified 23.9%

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

   6. Taylor expanded in t around 0 17.4%

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

      1. mul-1-neg 17.4%

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

      2. distribute-lft-neg-out 17.4%

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

      3. *-commutative 17.4%

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

   8. Simplified 17.4%

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

   9. Taylor expanded in z around inf 24.2%

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

   if -3.4000000000000001e54 < z < 18000

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 48.3%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+54} \lor \neg \left(z \leq 18000\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.0) (- (/ x z)) (if (<= z 18000.0) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -(x / z);
	} else if (z <= 18000.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -(x / z)
    else if (z <= 18000.0d0) then
        tmp = x
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -(x / z);
	} else if (z <= 18000.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.0:
		tmp = -(x / z)
	elif z <= 18000.0:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-Float64(x / z));
	elseif (z <= 18000.0)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -(x / z);
	elseif (z <= 18000.0)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.0], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, 18000.0], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 35.8%

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

   3. Taylor expanded in y around inf 27.1%

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

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in z around inf 25.6%

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

      1. associate-*r/ 25.6%

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

      2. mul-1-neg 25.6%

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

   8. Simplified 25.6%

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

   if -1 < z < 18000

   1. Initial program 88.1%

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

   3. Taylor expanded in z around 0 51.7%

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

   if 18000 < z

   1. Initial program 48.7%

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

   3. Taylor expanded in b around 0 29.9%

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

      1. mul-1-neg 29.9%

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

      2. *-commutative 29.9%

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

      3. distribute-lft-neg-in 29.9%

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

   5. Simplified 29.9%

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

   6. Taylor expanded in t around 0 19.9%

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

      1. mul-1-neg 19.9%

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

      2. distribute-lft-neg-out 19.9%

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

      3. *-commutative 19.9%

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

   8. Simplified 19.9%

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

   9. Taylor expanded in z around inf 25.4%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 18000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 24.8% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.5%

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

3. Taylor expanded in z around 0 29.4%

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

Developer Target 1: 73.5% 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 2024146 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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