Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.3% → 84.9%

Time: 16.1s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.3% 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: 84.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, y \cdot x\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -1.2e+52)
     t_3
     (if (<= z -7.6e-104)
       t_2
       (if (<= z 5.6e-196)
         (/ (fma z (- t a) (* y x)) (fma z (- b y) y))
         (if (<= z 1.02e+27) t_2 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 = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e+52) {
		tmp = t_3;
	} else if (z <= -7.6e-104) {
		tmp = t_2;
	} else if (z <= 5.6e-196) {
		tmp = fma(z, (t - a), (y * x)) / fma(z, (b - y), y);
	} else if (z <= 1.02e+27) {
		tmp = t_2;
	} 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(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.2e+52)
		tmp = t_3;
	elseif (z <= -7.6e-104)
		tmp = t_2;
	elseif (z <= 5.6e-196)
		tmp = Float64(fma(z, Float64(t - a), Float64(y * x)) / fma(z, Float64(b - y), y));
	elseif (z <= 1.02e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return 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[(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]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+52], t$95$3, If[LessEqual[z, -7.6e-104], t$95$2, If[LessEqual[z, 5.6e-196], N[(N[(z * N[(t - a), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+27], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e52 or 1.0199999999999999e27 < z

   1. Initial program 37.7%

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

   3. Taylor expanded in z around inf 86.6%

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

   if -1.2e52 < z < -7.6000000000000001e-104 or 5.5999999999999997e-196 < z < 1.0199999999999999e27

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 91.7%

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

   if -7.6000000000000001e-104 < z < 5.5999999999999997e-196

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. fma-define 95.6%

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

      3. +-commutative 95.6%

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

      4. fma-define 95.7%

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

   3. Simplified 95.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-196}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t - a, y \cdot x\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-104}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{t\_3 + y \cdot x}{t\_1}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+24}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= z -9e+51)
     t_2
     (if (<= z -6.2e-104)
       t_4
       (if (<= z 2.9e-199)
         (/ (+ t_3 (* y x)) t_1)
         (if (<= z 5.6e+24) t_4 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 t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -9e+51) {
		tmp = t_2;
	} else if (z <= -6.2e-104) {
		tmp = t_4;
	} else if (z <= 2.9e-199) {
		tmp = (t_3 + (y * x)) / t_1;
	} else if (z <= 5.6e+24) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (t - a) / (b - y)
    t_3 = z * (t - a)
    t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
    if (z <= (-9d+51)) then
        tmp = t_2
    else if (z <= (-6.2d-104)) then
        tmp = t_4
    else if (z <= 2.9d-199) then
        tmp = (t_3 + (y * x)) / t_1
    else if (z <= 5.6d+24) then
        tmp = t_4
    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 t_3 = z * (t - a);
	double t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (z <= -9e+51) {
		tmp = t_2;
	} else if (z <= -6.2e-104) {
		tmp = t_4;
	} else if (z <= 2.9e-199) {
		tmp = (t_3 + (y * x)) / t_1;
	} else if (z <= 5.6e+24) {
		tmp = t_4;
	} 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)
	t_3 = z * (t - a)
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)))
	tmp = 0
	if z <= -9e+51:
		tmp = t_2
	elif z <= -6.2e-104:
		tmp = t_4
	elif z <= 2.9e-199:
		tmp = (t_3 + (y * x)) / t_1
	elif z <= 5.6e+24:
		tmp = t_4
	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))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (z <= -9e+51)
		tmp = t_2;
	elseif (z <= -6.2e-104)
		tmp = t_4;
	elseif (z <= 2.9e-199)
		tmp = Float64(Float64(t_3 + Float64(y * x)) / t_1);
	elseif (z <= 5.6e+24)
		tmp = t_4;
	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);
	t_3 = z * (t - a);
	t_4 = x * ((y / t_1) + (t_3 / (x * t_1)));
	tmp = 0.0;
	if (z <= -9e+51)
		tmp = t_2;
	elseif (z <= -6.2e-104)
		tmp = t_4;
	elseif (z <= 2.9e-199)
		tmp = (t_3 + (y * x)) / t_1;
	elseif (z <= 5.6e+24)
		tmp = t_4;
	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]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+51], t$95$2, If[LessEqual[z, -6.2e-104], t$95$4, If[LessEqual[z, 2.9e-199], N[(N[(t$95$3 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 5.6e+24], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e51 or 5.6000000000000003e24 < z

   1. Initial program 37.7%

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

   3. Taylor expanded in z around inf 86.6%

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

   if -8.9999999999999999e51 < z < -6.19999999999999951e-104 or 2.9e-199 < z < 5.6000000000000003e24

   1. Initial program 78.6%

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

   3. Taylor expanded in x around inf 91.7%

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

   if -6.19999999999999951e-104 < z < 2.9e-199

   1. Initial program 95.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+51}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\frac{y}{y - z \cdot \left(y - b\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y - z \cdot \left(y - b\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.00195:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* y x) (* z t)) (- y (* z (- y b)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.6e+18)
     t_2
     (if (<= z 5.5e-71)
       t_1
       (if (<= z 2.6e-38) (- x (/ (* z a) y)) (if (<= z 0.00195) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * x) + (z * t)) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.6e+18) {
		tmp = t_2;
	} else if (z <= 5.5e-71) {
		tmp = t_1;
	} else if (z <= 2.6e-38) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.00195) {
		tmp = 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 * x) + (z * t)) / (y - (z * (y - b)))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.6d+18)) then
        tmp = t_2
    else if (z <= 5.5d-71) then
        tmp = t_1
    else if (z <= 2.6d-38) then
        tmp = x - ((z * a) / y)
    else if (z <= 0.00195d0) then
        tmp = 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 * x) + (z * t)) / (y - (z * (y - b)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.6e+18) {
		tmp = t_2;
	} else if (z <= 5.5e-71) {
		tmp = t_1;
	} else if (z <= 2.6e-38) {
		tmp = x - ((z * a) / y);
	} else if (z <= 0.00195) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * x) + (z * t)) / (y - (z * (y - b)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.6e+18:
		tmp = t_2
	elif z <= 5.5e-71:
		tmp = t_1
	elif z <= 2.6e-38:
		tmp = x - ((z * a) / y)
	elif z <= 0.00195:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * x) + Float64(z * t)) / Float64(y - Float64(z * Float64(y - b))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.6e+18)
		tmp = t_2;
	elseif (z <= 5.5e-71)
		tmp = t_1;
	elseif (z <= 2.6e-38)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 0.00195)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * x) + (z * t)) / (y - (z * (y - b)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.6e+18)
		tmp = t_2;
	elseif (z <= 5.5e-71)
		tmp = t_1;
	elseif (z <= 2.6e-38)
		tmp = x - ((z * a) / y);
	elseif (z <= 0.00195)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+18], t$95$2, If[LessEqual[z, 5.5e-71], t$95$1, If[LessEqual[z, 2.6e-38], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00195], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e18 or 0.0019499999999999999 < z

   1. Initial program 42.8%

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

   3. Taylor expanded in z around inf 85.1%

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

   if -1.6e18 < z < 5.4999999999999997e-71 or 2.60000000000000011e-38 < z < 0.0019499999999999999

   1. Initial program 88.8%

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

   3. Taylor expanded in a around 0 74.0%

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

   if 5.4999999999999997e-71 < z < 2.60000000000000011e-38

   1. Initial program 54.4%

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

   3. Taylor expanded in z around 0 37.4%

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

   4. Taylor expanded in a around inf 100.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-71}:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-38}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 0.00195:\\ \;\;\;\;\frac{y \cdot x + z \cdot t}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right) + y \cdot x\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-211}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{t\_1}{z \cdot b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- t a)) (* y x))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.6e-79)
     t_2
     (if (<= z 5.6e-211)
       (/ t_1 y)
       (if (<= z 3.3e-175)
         (/ t_1 (* z b))
         (if (<= z 9.2e-7) (+ x (* z (/ t y))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (t - a)) + (y * x);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e-79) {
		tmp = t_2;
	} else if (z <= 5.6e-211) {
		tmp = t_1 / y;
	} else if (z <= 3.3e-175) {
		tmp = t_1 / (z * b);
	} else if (z <= 9.2e-7) {
		tmp = x + (z * (t / y));
	} 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 = (z * (t - a)) + (y * x)
    t_2 = (t - a) / (b - y)
    if (z <= (-2.6d-79)) then
        tmp = t_2
    else if (z <= 5.6d-211) then
        tmp = t_1 / y
    else if (z <= 3.3d-175) then
        tmp = t_1 / (z * b)
    else if (z <= 9.2d-7) then
        tmp = x + (z * (t / y))
    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 = (z * (t - a)) + (y * x);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e-79) {
		tmp = t_2;
	} else if (z <= 5.6e-211) {
		tmp = t_1 / y;
	} else if (z <= 3.3e-175) {
		tmp = t_1 / (z * b);
	} else if (z <= 9.2e-7) {
		tmp = x + (z * (t / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) + (y * x)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e-79:
		tmp = t_2
	elif z <= 5.6e-211:
		tmp = t_1 / y
	elif z <= 3.3e-175:
		tmp = t_1 / (z * b)
	elif z <= 9.2e-7:
		tmp = x + (z * (t / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) + Float64(y * x))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e-79)
		tmp = t_2;
	elseif (z <= 5.6e-211)
		tmp = Float64(t_1 / y);
	elseif (z <= 3.3e-175)
		tmp = Float64(t_1 / Float64(z * b));
	elseif (z <= 9.2e-7)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (t - a)) + (y * x);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e-79)
		tmp = t_2;
	elseif (z <= 5.6e-211)
		tmp = t_1 / y;
	elseif (z <= 3.3e-175)
		tmp = t_1 / (z * b);
	elseif (z <= 9.2e-7)
		tmp = x + (z * (t / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-79], t$95$2, If[LessEqual[z, 5.6e-211], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[z, 3.3e-175], N[(t$95$1 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-7], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.59999999999999994e-79 or 9.1999999999999998e-7 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -2.59999999999999994e-79 < z < 5.5999999999999996e-211

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 70.3%

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

   if 5.5999999999999996e-211 < z < 3.29999999999999999e-175

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if 3.29999999999999999e-175 < z < 9.1999999999999998e-7

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in t around inf 65.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-211}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{z \cdot b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(\frac{x}{z \cdot b} - \frac{a}{b \cdot y}\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e-79)
     t_1
     (if (<= z 1.3e-206)
       (/ (+ (* z (- t a)) (* y x)) y)
       (if (<= z 3.3e-175)
         (* y (- (/ x (* z b)) (/ a (* b y))))
         (if (<= z 1.7e-8) (+ x (* z (/ t 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 <= -4e-79) {
		tmp = t_1;
	} else if (z <= 1.3e-206) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 3.3e-175) {
		tmp = y * ((x / (z * b)) - (a / (b * y)));
	} else if (z <= 1.7e-8) {
		tmp = x + (z * (t / 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 <= (-4d-79)) then
        tmp = t_1
    else if (z <= 1.3d-206) then
        tmp = ((z * (t - a)) + (y * x)) / y
    else if (z <= 3.3d-175) then
        tmp = y * ((x / (z * b)) - (a / (b * y)))
    else if (z <= 1.7d-8) then
        tmp = x + (z * (t / 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 <= -4e-79) {
		tmp = t_1;
	} else if (z <= 1.3e-206) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 3.3e-175) {
		tmp = y * ((x / (z * b)) - (a / (b * y)));
	} else if (z <= 1.7e-8) {
		tmp = x + (z * (t / 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 <= -4e-79:
		tmp = t_1
	elif z <= 1.3e-206:
		tmp = ((z * (t - a)) + (y * x)) / y
	elif z <= 3.3e-175:
		tmp = y * ((x / (z * b)) - (a / (b * y)))
	elif z <= 1.7e-8:
		tmp = x + (z * (t / 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 <= -4e-79)
		tmp = t_1;
	elseif (z <= 1.3e-206)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	elseif (z <= 3.3e-175)
		tmp = Float64(y * Float64(Float64(x / Float64(z * b)) - Float64(a / Float64(b * y))));
	elseif (z <= 1.7e-8)
		tmp = Float64(x + Float64(z * Float64(t / 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 <= -4e-79)
		tmp = t_1;
	elseif (z <= 1.3e-206)
		tmp = ((z * (t - a)) + (y * x)) / y;
	elseif (z <= 3.3e-175)
		tmp = y * ((x / (z * b)) - (a / (b * y)));
	elseif (z <= 1.7e-8)
		tmp = x + (z * (t / 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, -4e-79], t$95$1, If[LessEqual[z, 1.3e-206], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.3e-175], N[(y * N[(N[(x / N[(z * b), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-8], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e-79 or 1.7e-8 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -4e-79 < z < 1.3e-206

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 69.3%

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

   if 1.3e-206 < z < 3.29999999999999999e-175

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 87.8%

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

   4. Taylor expanded in b around inf 51.2%

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

   5. Taylor expanded in t around 0 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. associate-/l* 51.8%

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

   7. Simplified 51.8%

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

   8. Taylor expanded in y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   10. Simplified 76.1%

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

   if 3.29999999999999999e-175 < z < 1.7e-8

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in t around inf 65.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(\frac{x}{z \cdot b} - \frac{a}{b \cdot y}\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-173}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-6}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -4e-79)
     t_1
     (if (<= z 9.5e-220)
       (/ (+ (* z (- t a)) (* y x)) y)
       (if (<= z 1.08e-173)
         (/ (* y x) (- y (* z (- y b))))
         (if (<= z 2.25e-6) (+ x (* z (/ t 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 <= -4e-79) {
		tmp = t_1;
	} else if (z <= 9.5e-220) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 1.08e-173) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 2.25e-6) {
		tmp = x + (z * (t / 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 <= (-4d-79)) then
        tmp = t_1
    else if (z <= 9.5d-220) then
        tmp = ((z * (t - a)) + (y * x)) / y
    else if (z <= 1.08d-173) then
        tmp = (y * x) / (y - (z * (y - b)))
    else if (z <= 2.25d-6) then
        tmp = x + (z * (t / 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 <= -4e-79) {
		tmp = t_1;
	} else if (z <= 9.5e-220) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 1.08e-173) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 2.25e-6) {
		tmp = x + (z * (t / 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 <= -4e-79:
		tmp = t_1
	elif z <= 9.5e-220:
		tmp = ((z * (t - a)) + (y * x)) / y
	elif z <= 1.08e-173:
		tmp = (y * x) / (y - (z * (y - b)))
	elif z <= 2.25e-6:
		tmp = x + (z * (t / 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 <= -4e-79)
		tmp = t_1;
	elseif (z <= 9.5e-220)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	elseif (z <= 1.08e-173)
		tmp = Float64(Float64(y * x) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 2.25e-6)
		tmp = Float64(x + Float64(z * Float64(t / 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 <= -4e-79)
		tmp = t_1;
	elseif (z <= 9.5e-220)
		tmp = ((z * (t - a)) + (y * x)) / y;
	elseif (z <= 1.08e-173)
		tmp = (y * x) / (y - (z * (y - b)));
	elseif (z <= 2.25e-6)
		tmp = x + (z * (t / 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, -4e-79], t$95$1, If[LessEqual[z, 9.5e-220], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.08e-173], N[(N[(y * x), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e-6], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e-79 or 2.25000000000000006e-6 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -4e-79 < z < 9.50000000000000062e-220

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0 70.8%

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

   if 9.50000000000000062e-220 < z < 1.07999999999999995e-173

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 64.7%

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

      1. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if 1.07999999999999995e-173 < z < 2.25000000000000006e-6

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in t around inf 65.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-173}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-6}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.2e-35)
     t_1
     (if (<= z 1.05e-226)
       (- x (/ (* z a) y))
       (if (<= z 8.4e-172)
         (/ (* y x) (- y (* z (- y b))))
         (if (<= z 1.6e-8) (+ x (* z (/ t 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 <= -7.2e-35) {
		tmp = t_1;
	} else if (z <= 1.05e-226) {
		tmp = x - ((z * a) / y);
	} else if (z <= 8.4e-172) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.6e-8) {
		tmp = x + (z * (t / 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 <= (-7.2d-35)) then
        tmp = t_1
    else if (z <= 1.05d-226) then
        tmp = x - ((z * a) / y)
    else if (z <= 8.4d-172) then
        tmp = (y * x) / (y - (z * (y - b)))
    else if (z <= 1.6d-8) then
        tmp = x + (z * (t / 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 <= -7.2e-35) {
		tmp = t_1;
	} else if (z <= 1.05e-226) {
		tmp = x - ((z * a) / y);
	} else if (z <= 8.4e-172) {
		tmp = (y * x) / (y - (z * (y - b)));
	} else if (z <= 1.6e-8) {
		tmp = x + (z * (t / 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 <= -7.2e-35:
		tmp = t_1
	elif z <= 1.05e-226:
		tmp = x - ((z * a) / y)
	elif z <= 8.4e-172:
		tmp = (y * x) / (y - (z * (y - b)))
	elif z <= 1.6e-8:
		tmp = x + (z * (t / 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 <= -7.2e-35)
		tmp = t_1;
	elseif (z <= 1.05e-226)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 8.4e-172)
		tmp = Float64(Float64(y * x) / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 1.6e-8)
		tmp = Float64(x + Float64(z * Float64(t / 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 <= -7.2e-35)
		tmp = t_1;
	elseif (z <= 1.05e-226)
		tmp = x - ((z * a) / y);
	elseif (z <= 8.4e-172)
		tmp = (y * x) / (y - (z * (y - b)));
	elseif (z <= 1.6e-8)
		tmp = x + (z * (t / 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, -7.2e-35], t$95$1, If[LessEqual[z, 1.05e-226], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.4e-172], N[(N[(y * x), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-8], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000038e-35 or 1.6000000000000001e-8 < z

   1. Initial program 46.5%

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

   3. Taylor expanded in z around inf 82.1%

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

   if -7.20000000000000038e-35 < z < 1.0500000000000001e-226

   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 z around 0 51.9%

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

   4. Taylor expanded in a around inf 63.4%

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

   if 1.0500000000000001e-226 < z < 8.3999999999999998e-172

   1. Initial program 93.1%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 8.3999999999999998e-172 < z < 1.6000000000000001e-8

   1. Initial program 82.5%

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

   3. Taylor expanded in z around 0 57.8%

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

   4. Taylor expanded in t around inf 65.2%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y}\\ t_2 := \frac{t - a}{b}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -40000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) y)) (t_2 (/ (- t a) b)))
   (if (<= z -2e+61)
     t_2
     (if (<= z -40000000000000.0)
       t_1
       (if (<= z -4.2e-79) t_2 (if (<= z 1.0) (+ x (* z (/ t y))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = (t - a) / b;
	double tmp;
	if (z <= -2e+61) {
		tmp = t_2;
	} else if (z <= -40000000000000.0) {
		tmp = t_1;
	} else if (z <= -4.2e-79) {
		tmp = t_2;
	} else if (z <= 1.0) {
		tmp = x + (z * (t / 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) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / y
    t_2 = (t - a) / b
    if (z <= (-2d+61)) then
        tmp = t_2
    else if (z <= (-40000000000000.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-79)) then
        tmp = t_2
    else if (z <= 1.0d0) then
        tmp = x + (z * (t / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / y;
	double t_2 = (t - a) / b;
	double tmp;
	if (z <= -2e+61) {
		tmp = t_2;
	} else if (z <= -40000000000000.0) {
		tmp = t_1;
	} else if (z <= -4.2e-79) {
		tmp = t_2;
	} else if (z <= 1.0) {
		tmp = x + (z * (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / y
	t_2 = (t - a) / b
	tmp = 0
	if z <= -2e+61:
		tmp = t_2
	elif z <= -40000000000000.0:
		tmp = t_1
	elif z <= -4.2e-79:
		tmp = t_2
	elif z <= 1.0:
		tmp = x + (z * (t / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / y)
	t_2 = Float64(Float64(t - a) / b)
	tmp = 0.0
	if (z <= -2e+61)
		tmp = t_2;
	elseif (z <= -40000000000000.0)
		tmp = t_1;
	elseif (z <= -4.2e-79)
		tmp = t_2;
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / y;
	t_2 = (t - a) / b;
	tmp = 0.0;
	if (z <= -2e+61)
		tmp = t_2;
	elseif (z <= -40000000000000.0)
		tmp = t_1;
	elseif (z <= -4.2e-79)
		tmp = t_2;
	elseif (z <= 1.0)
		tmp = x + (z * (t / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[z, -2e+61], t$95$2, If[LessEqual[z, -40000000000000.0], t$95$1, If[LessEqual[z, -4.2e-79], t$95$2, If[LessEqual[z, 1.0], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e61 or -4e13 < z < -4.1999999999999999e-79

   1. Initial program 56.8%

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

   3. Taylor expanded in y around 0 55.4%

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

   if -1.9999999999999999e61 < z < -4e13 or 1 < z

   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 z around inf 83.4%

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

   4. Taylor expanded in b around 0 58.2%

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

      1. associate-*r/ 58.2%

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

      2. neg-mul-1 58.2%

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

   6. Simplified 58.2%

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

   if -4.1999999999999999e-79 < z < 1

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 54.0%

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

   4. Taylor expanded in t around inf 59.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -40000000000000:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+30} \lor \neg \left(z \leq 8.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e+30) (not (<= z 8.5e+27)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (- y (* z (- y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e+30) || !(z <= 8.5e+27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - 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 <= (-6.5d+30)) .or. (.not. (z <= 8.5d+27))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - 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 <= -6.5e+30) || !(z <= 8.5e+27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.5e+30) or not (z <= 8.5e+27):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.5e+30) || !(z <= 8.5e+27))
		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(y - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.5e+30) || ~((z <= 8.5e+27)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.5e+30], N[Not[LessEqual[z, 8.5e+27]], $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[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e30 or 8.5e27 < z

   1. Initial program 39.6%

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

   3. Taylor expanded in z around inf 85.9%

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

   if -6.5e30 < z < 8.5e27

   1. Initial program 87.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+30} \lor \neg \left(z \leq 8.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.2e+97)
     t_1
     (if (<= y -8.5e+15)
       (/ t (- b y))
       (if (<= y -2.3e-35)
         (/ a (- y b))
         (if (<= y 4.5e+18) (/ (- t 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 <= -3.2e+97) {
		tmp = t_1;
	} else if (y <= -8.5e+15) {
		tmp = t / (b - y);
	} else if (y <= -2.3e-35) {
		tmp = a / (y - b);
	} else if (y <= 4.5e+18) {
		tmp = (t - 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 <= (-3.2d+97)) then
        tmp = t_1
    else if (y <= (-8.5d+15)) then
        tmp = t / (b - y)
    else if (y <= (-2.3d-35)) then
        tmp = a / (y - b)
    else if (y <= 4.5d+18) then
        tmp = (t - 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 <= -3.2e+97) {
		tmp = t_1;
	} else if (y <= -8.5e+15) {
		tmp = t / (b - y);
	} else if (y <= -2.3e-35) {
		tmp = a / (y - b);
	} else if (y <= 4.5e+18) {
		tmp = (t - 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 <= -3.2e+97:
		tmp = t_1
	elif y <= -8.5e+15:
		tmp = t / (b - y)
	elif y <= -2.3e-35:
		tmp = a / (y - b)
	elif y <= 4.5e+18:
		tmp = (t - 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 <= -3.2e+97)
		tmp = t_1;
	elseif (y <= -8.5e+15)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -2.3e-35)
		tmp = Float64(a / Float64(y - b));
	elseif (y <= 4.5e+18)
		tmp = Float64(Float64(t - 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 <= -3.2e+97)
		tmp = t_1;
	elseif (y <= -8.5e+15)
		tmp = t / (b - y);
	elseif (y <= -2.3e-35)
		tmp = a / (y - b);
	elseif (y <= 4.5e+18)
		tmp = (t - 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, -3.2e+97], t$95$1, If[LessEqual[y, -8.5e+15], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-35], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000016e97 or 4.5e18 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -3.20000000000000016e97 < y < -8.5e15

   1. Initial program 68.0%

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

   3. Taylor expanded in t around inf 38.7%

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

      1. *-commutative 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in z around inf 49.9%

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

   if -8.5e15 < y < -2.2999999999999999e-35

   1. Initial program 81.2%

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

   3. Taylor expanded in z around inf 44.6%

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

   4. Taylor expanded in t around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. mul-1-neg 35.1%

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

   6. Simplified 35.1%

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

   if -2.2999999999999999e-35 < y < 4.5e18

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 59.6%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e+97)
     t_1
     (if (<= y -1.45e+14)
       (/ t (- b y))
       (if (<= y -2.35e-35) x (if (<= y 2.7e+18) (/ (- t 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 <= -7.8e+97) {
		tmp = t_1;
	} else if (y <= -1.45e+14) {
		tmp = t / (b - y);
	} else if (y <= -2.35e-35) {
		tmp = x;
	} else if (y <= 2.7e+18) {
		tmp = (t - 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 <= (-7.8d+97)) then
        tmp = t_1
    else if (y <= (-1.45d+14)) then
        tmp = t / (b - y)
    else if (y <= (-2.35d-35)) then
        tmp = x
    else if (y <= 2.7d+18) then
        tmp = (t - 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 <= -7.8e+97) {
		tmp = t_1;
	} else if (y <= -1.45e+14) {
		tmp = t / (b - y);
	} else if (y <= -2.35e-35) {
		tmp = x;
	} else if (y <= 2.7e+18) {
		tmp = (t - 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 <= -7.8e+97:
		tmp = t_1
	elif y <= -1.45e+14:
		tmp = t / (b - y)
	elif y <= -2.35e-35:
		tmp = x
	elif y <= 2.7e+18:
		tmp = (t - 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 <= -7.8e+97)
		tmp = t_1;
	elseif (y <= -1.45e+14)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -2.35e-35)
		tmp = x;
	elseif (y <= 2.7e+18)
		tmp = Float64(Float64(t - 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 <= -7.8e+97)
		tmp = t_1;
	elseif (y <= -1.45e+14)
		tmp = t / (b - y);
	elseif (y <= -2.35e-35)
		tmp = x;
	elseif (y <= 2.7e+18)
		tmp = (t - 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, -7.8e+97], t$95$1, If[LessEqual[y, -1.45e+14], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.35e-35], x, If[LessEqual[y, 2.7e+18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.7999999999999999e97 or 2.7e18 < y

   1. Initial program 52.1%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -7.7999999999999999e97 < y < -1.45e14

   1. Initial program 69.9%

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

   3. Taylor expanded in t around inf 36.5%

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

      1. *-commutative 36.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in z around inf 47.1%

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

   if -1.45e14 < y < -2.35e-35

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 31.9%

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

   if -2.35e-35 < y < 2.7e18

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 59.6%

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

Alternative 12: 42.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -5.5e+97)
     t_2
     (if (<= y -1.95e-278)
       t_1
       (if (<= y 1.8e-148) (/ a (- b)) (if (<= y 2.25e+60) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_2;
	} else if (y <= -1.95e-278) {
		tmp = t_1;
	} else if (y <= 1.8e-148) {
		tmp = a / -b;
	} else if (y <= 2.25e+60) {
		tmp = 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 / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-5.5d+97)) then
        tmp = t_2
    else if (y <= (-1.95d-278)) then
        tmp = t_1
    else if (y <= 1.8d-148) then
        tmp = a / -b
    else if (y <= 2.25d+60) then
        tmp = 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 / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e+97) {
		tmp = t_2;
	} else if (y <= -1.95e-278) {
		tmp = t_1;
	} else if (y <= 1.8e-148) {
		tmp = a / -b;
	} else if (y <= 2.25e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -5.5e+97:
		tmp = t_2
	elif y <= -1.95e-278:
		tmp = t_1
	elif y <= 1.8e-148:
		tmp = a / -b
	elif y <= 2.25e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.5e+97)
		tmp = t_2;
	elseif (y <= -1.95e-278)
		tmp = t_1;
	elseif (y <= 1.8e-148)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 2.25e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.5e+97)
		tmp = t_2;
	elseif (y <= -1.95e-278)
		tmp = t_1;
	elseif (y <= 1.8e-148)
		tmp = a / -b;
	elseif (y <= 2.25e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+97], t$95$2, If[LessEqual[y, -1.95e-278], t$95$1, If[LessEqual[y, 1.8e-148], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 2.25e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000021e97 or 2.25000000000000006e60 < y

   1. Initial program 50.2%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. unsub-neg 63.0%

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

   5. Simplified 63.0%

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

   if -5.50000000000000021e97 < y < -1.9500000000000001e-278 or 1.7999999999999999e-148 < y < 2.25000000000000006e60

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 33.5%

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

      1. *-commutative 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in z around inf 32.9%

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

   if -1.9500000000000001e-278 < y < 1.7999999999999999e-148

   1. Initial program 67.7%

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

   3. Taylor expanded in t around inf 61.7%

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

   4. Taylor expanded in b around inf 71.6%

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

   5. Taylor expanded in a around inf 55.9%

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

      1. mul-1-neg 55.9%

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

   7. Simplified 55.9%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3e+97)
     t_1
     (if (<= y -4.4e-35) (/ (- a t) y) (if (<= y 8e+18) (/ (- t 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 <= -3e+97) {
		tmp = t_1;
	} else if (y <= -4.4e-35) {
		tmp = (a - t) / y;
	} else if (y <= 8e+18) {
		tmp = (t - 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 <= (-3d+97)) then
        tmp = t_1
    else if (y <= (-4.4d-35)) then
        tmp = (a - t) / y
    else if (y <= 8d+18) then
        tmp = (t - 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 <= -3e+97) {
		tmp = t_1;
	} else if (y <= -4.4e-35) {
		tmp = (a - t) / y;
	} else if (y <= 8e+18) {
		tmp = (t - 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 <= -3e+97:
		tmp = t_1
	elif y <= -4.4e-35:
		tmp = (a - t) / y
	elif y <= 8e+18:
		tmp = (t - 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 <= -3e+97)
		tmp = t_1;
	elseif (y <= -4.4e-35)
		tmp = Float64(Float64(a - t) / y);
	elseif (y <= 8e+18)
		tmp = Float64(Float64(t - 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 <= -3e+97)
		tmp = t_1;
	elseif (y <= -4.4e-35)
		tmp = (a - t) / y;
	elseif (y <= 8e+18)
		tmp = (t - 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, -3e+97], t$95$1, If[LessEqual[y, -4.4e-35], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8e+18], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9999999999999998e97 or 8e18 < y

   1. Initial program 52.3%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   5. Simplified 57.9%

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

   if -2.9999999999999998e97 < y < -4.39999999999999987e-35

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf 56.4%

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

   4. Taylor expanded in b around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

   6. Simplified 41.5%

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

   if -4.39999999999999987e-35 < y < 8e18

   1. Initial program 77.9%

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

   3. Taylor expanded in y around 0 59.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-28}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -1.2e+50)
     t_1
     (if (<= z -8e-41) (/ t b) (if (<= z 8.2e-28) (+ x (* z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.2e+50) {
		tmp = t_1;
	} else if (z <= -8e-41) {
		tmp = t / b;
	} else if (z <= 8.2e-28) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-1.2d+50)) then
        tmp = t_1
    else if (z <= (-8d-41)) then
        tmp = t / b
    else if (z <= 8.2d-28) then
        tmp = x + (z * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.2e+50) {
		tmp = t_1;
	} else if (z <= -8e-41) {
		tmp = t / b;
	} else if (z <= 8.2e-28) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -1.2e+50:
		tmp = t_1
	elif z <= -8e-41:
		tmp = t / b
	elif z <= 8.2e-28:
		tmp = x + (z * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -1.2e+50)
		tmp = t_1;
	elseif (z <= -8e-41)
		tmp = Float64(t / b);
	elseif (z <= 8.2e-28)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -1.2e+50)
		tmp = t_1;
	elseif (z <= -8e-41)
		tmp = t / b;
	elseif (z <= 8.2e-28)
		tmp = x + (z * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -1.2e+50], t$95$1, If[LessEqual[z, -8e-41], N[(t / b), $MachinePrecision], If[LessEqual[z, 8.2e-28], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2000000000000001e50 or 8.2000000000000005e-28 < z

   1. Initial program 40.4%

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

   3. Taylor expanded in t around inf 43.3%

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

   4. Taylor expanded in b around inf 39.0%

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

   5. Taylor expanded in a around inf 29.5%

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

      1. mul-1-neg 29.5%

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

   7. Simplified 29.5%

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

   if -1.2000000000000001e50 < z < -8.00000000000000005e-41

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 34.3%

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

      1. *-commutative 34.3%

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

   5. Simplified 34.3%

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

   6. Taylor expanded in y around 0 38.5%

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

   if -8.00000000000000005e-41 < z < 8.2000000000000005e-28

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 50.9%

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

   4. Taylor expanded in y around inf 48.3%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-28}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{-b}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- b))))
   (if (<= z -1.05e+51)
     t_1
     (if (<= z -1.15e-29) (/ t b) (if (<= z 9.2e-28) x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.05e+51) {
		tmp = t_1;
	} else if (z <= -1.15e-29) {
		tmp = t / b;
	} else if (z <= 9.2e-28) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / -b
    if (z <= (-1.05d+51)) then
        tmp = t_1
    else if (z <= (-1.15d-29)) then
        tmp = t / b
    else if (z <= 9.2d-28) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / -b;
	double tmp;
	if (z <= -1.05e+51) {
		tmp = t_1;
	} else if (z <= -1.15e-29) {
		tmp = t / b;
	} else if (z <= 9.2e-28) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / -b
	tmp = 0
	if z <= -1.05e+51:
		tmp = t_1
	elif z <= -1.15e-29:
		tmp = t / b
	elif z <= 9.2e-28:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(-b))
	tmp = 0.0
	if (z <= -1.05e+51)
		tmp = t_1;
	elseif (z <= -1.15e-29)
		tmp = Float64(t / b);
	elseif (z <= 9.2e-28)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / -b;
	tmp = 0.0;
	if (z <= -1.05e+51)
		tmp = t_1;
	elseif (z <= -1.15e-29)
		tmp = t / b;
	elseif (z <= 9.2e-28)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / (-b)), $MachinePrecision]}, If[LessEqual[z, -1.05e+51], t$95$1, If[LessEqual[z, -1.15e-29], N[(t / b), $MachinePrecision], If[LessEqual[z, 9.2e-28], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e51 or 9.19999999999999942e-28 < z

   1. Initial program 40.4%

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

   3. Taylor expanded in t around inf 43.3%

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

   4. Taylor expanded in b around inf 39.0%

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

   5. Taylor expanded in a around inf 29.5%

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

      1. mul-1-neg 29.5%

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

   7. Simplified 29.5%

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

   if -1.0500000000000001e51 < z < -1.14999999999999996e-29

   1. Initial program 82.9%

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

   3. Taylor expanded in t around inf 34.3%

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

      1. *-commutative 34.3%

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

   5. Simplified 34.3%

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

   6. Taylor expanded in y around 0 38.5%

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

   if -1.14999999999999996e-29 < z < 9.19999999999999942e-28

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 48.3%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-30} \lor \neg \left(z \leq 4.8 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e-30) (not (<= z 4.8e-27)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-30) || !(z <= 4.8e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.1d-30)) .or. (.not. (z <= 4.8d-27))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e-30) || !(z <= 4.8e-27)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e-30) or not (z <= 4.8e-27):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e-30) || !(z <= 4.8e-27))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e-30) || ~((z <= 4.8e-27)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e-30], N[Not[LessEqual[z, 4.8e-27]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000002e-30 or 4.80000000000000004e-27 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in z around inf 80.9%

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

   if -2.1000000000000002e-30 < z < 4.80000000000000004e-27

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 50.9%

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

   4. Taylor expanded in a around inf 59.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-30} \lor \neg \left(z \leq 4.8 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-79} \lor \neg \left(z \leq 3.8 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.1e-79) (not (<= z 3.8e-10)))
   (/ (- t a) (- b y))
   (+ x (* z (/ t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e-79) || !(z <= 3.8e-10)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.1d-79)) .or. (.not. (z <= 3.8d-10))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e-79) || !(z <= 3.8e-10)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.1e-79) or not (z <= 3.8e-10):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.1e-79) || !(z <= 3.8e-10))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.1e-79) || ~((z <= 3.8e-10)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.1e-79], N[Not[LessEqual[z, 3.8e-10]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999994e-79 or 3.7999999999999998e-10 < z

   1. Initial program 48.1%

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

   3. Taylor expanded in z around inf 79.4%

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

   if -4.09999999999999994e-79 < z < 3.7999999999999998e-10

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 53.6%

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

   4. Taylor expanded in t around inf 59.5%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-79} \lor \neg \left(z \leq 3.8 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 45.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-50} \lor \neg \left(z \leq 4.7 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e-50) (not (<= z 4.7e-27))) (/ 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 <= -2.5e-50) || !(z <= 4.7e-27)) {
		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 <= (-2.5d-50)) .or. (.not. (z <= 4.7d-27))) 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 <= -2.5e-50) || !(z <= 4.7e-27)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e-50) or not (z <= 4.7e-27):
		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 <= -2.5e-50) || !(z <= 4.7e-27))
		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 <= -2.5e-50) || ~((z <= 4.7e-27)))
		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, -2.5e-50], N[Not[LessEqual[z, 4.7e-27]], $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 < -2.49999999999999984e-50 or 4.70000000000000032e-27 < z

   1. Initial program 47.2%

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

   3. Taylor expanded in t around inf 22.3%

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

      1. *-commutative 22.3%

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

   5. Simplified 22.3%

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

   6. Taylor expanded in z around inf 37.3%

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

   if -2.49999999999999984e-50 < z < 4.70000000000000032e-27

   1. Initial program 87.4%

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

   3. Taylor expanded in z around 0 50.9%

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

   4. Taylor expanded in y around inf 48.3%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-50} \lor \neg \left(z \leq 4.7 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-36} \lor \neg \left(y \leq 2.7 \cdot 10^{+18}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.16e-36) (not (<= y 2.7e+18))) x (/ t b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.16e-36) || !(y <= 2.7e+18)) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.16d-36)) .or. (.not. (y <= 2.7d+18))) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.16e-36) || !(y <= 2.7e+18)) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.16e-36) or not (y <= 2.7e+18):
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.16e-36) || !(y <= 2.7e+18))
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.16e-36) || ~((y <= 2.7e+18)))
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.16e-36], N[Not[LessEqual[y, 2.7e+18]], $MachinePrecision]], x, N[(t / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.16000000000000002e-36 or 2.7e18 < y

   1. Initial program 57.1%

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

   3. Taylor expanded in z around 0 37.9%

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

   if -1.16000000000000002e-36 < y < 2.7e18

   1. Initial program 77.5%

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

   3. Taylor expanded in t around inf 35.4%

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

      1. *-commutative 35.4%

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

   5. Simplified 35.4%

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

   6. Taylor expanded in y around 0 34.9%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-36} \lor \neg \left(y \leq 2.7 \cdot 10^{+18}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 25.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.9%

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

3. Taylor expanded in z around 0 24.8%

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

Developer target: 73.3% 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 2024096 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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