Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 93.4%

Time: 22.6s

Alternatives: 21

Speedup: 0.8×

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: 66.4% 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: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3}{t_2}\\ \mathbf{if}\;z \leq -600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y}{t_2} + t_4\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-226}:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;z \leq 1650000:\\ \;\;\;\;\frac{x \cdot y + t_3}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y))))
        (t_2 (+ y (* z (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ t_3 t_2)))
   (if (<= z -600000000000.0)
     t_1
     (if (<= z -2.3e-228)
       (+ (/ (* x y) t_2) t_4)
       (if (<= z 5e-226)
         (+ x t_4)
         (if (<= z 1650000.0) (/ (+ (* x y) t_3) t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = y + (z * (b - y));
	double t_3 = z * (t - a);
	double t_4 = t_3 / t_2;
	double tmp;
	if (z <= -600000000000.0) {
		tmp = t_1;
	} else if (z <= -2.3e-228) {
		tmp = ((x * y) / t_2) + t_4;
	} else if (z <= 5e-226) {
		tmp = x + t_4;
	} else if (z <= 1650000.0) {
		tmp = ((x * y) + t_3) / t_2;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    t_2 = y + (z * (b - y))
    t_3 = z * (t - a)
    t_4 = t_3 / t_2
    if (z <= (-600000000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.3d-228)) then
        tmp = ((x * y) / t_2) + t_4
    else if (z <= 5d-226) then
        tmp = x + t_4
    else if (z <= 1650000.0d0) then
        tmp = ((x * y) + t_3) / t_2
    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 / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = y + (z * (b - y));
	double t_3 = z * (t - a);
	double t_4 = t_3 / t_2;
	double tmp;
	if (z <= -600000000000.0) {
		tmp = t_1;
	} else if (z <= -2.3e-228) {
		tmp = ((x * y) / t_2) + t_4;
	} else if (z <= 5e-226) {
		tmp = x + t_4;
	} else if (z <= 1650000.0) {
		tmp = ((x * y) + t_3) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	t_2 = y + (z * (b - y))
	t_3 = z * (t - a)
	t_4 = t_3 / t_2
	tmp = 0
	if z <= -600000000000.0:
		tmp = t_1
	elif z <= -2.3e-228:
		tmp = ((x * y) / t_2) + t_4
	elif z <= 5e-226:
		tmp = x + t_4
	elif z <= 1650000.0:
		tmp = ((x * y) + t_3) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(t_3 / t_2)
	tmp = 0.0
	if (z <= -600000000000.0)
		tmp = t_1;
	elseif (z <= -2.3e-228)
		tmp = Float64(Float64(Float64(x * y) / t_2) + t_4);
	elseif (z <= 5e-226)
		tmp = Float64(x + t_4);
	elseif (z <= 1650000.0)
		tmp = Float64(Float64(Float64(x * y) + t_3) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	t_2 = y + (z * (b - y));
	t_3 = z * (t - a);
	t_4 = t_3 / t_2;
	tmp = 0.0;
	if (z <= -600000000000.0)
		tmp = t_1;
	elseif (z <= -2.3e-228)
		tmp = ((x * y) / t_2) + t_4;
	elseif (z <= 5e-226)
		tmp = x + t_4;
	elseif (z <= 1650000.0)
		tmp = ((x * y) + t_3) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / t$95$2), $MachinePrecision]}, If[LessEqual[z, -600000000000.0], t$95$1, If[LessEqual[z, -2.3e-228], N[(N[(N[(x * y), $MachinePrecision] / t$95$2), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[z, 5e-226], N[(x + t$95$4), $MachinePrecision], If[LessEqual[z, 1650000.0], N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e11 or 1.65e6 < z

   1. Initial program 37.8%

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

   3. Taylor expanded in x around 0 37.8%

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

   4. Taylor expanded in z around inf 37.8%

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

      1. times-frac 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in z around inf 99.5%

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

   if -6e11 < z < -2.2999999999999999e-228

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 88.7%

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

   if -2.2999999999999999e-228 < z < 4.9999999999999998e-226

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 72.2%

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

   4. Taylor expanded in z around 0 99.9%

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

   if 4.9999999999999998e-226 < z < 1.65e6

   1. Initial program 95.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -600000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1650000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := x + \frac{t_2}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{x \cdot y + t_2}{y + z \cdot b}\\ \mathbf{if}\;z \leq -400000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ x (/ t_2 (+ y (* z (- b y))))))
        (t_4 (/ (+ (* x y) t_2) (+ y (* z b)))))
   (if (<= z -400000.0)
     t_1
     (if (<= z -2.2e-227)
       t_4
       (if (<= z 3.2e-227)
         t_3
         (if (<= z 1.5e-14) t_4 (if (<= z 0.75) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = x + (t_2 / (y + (z * (b - y))));
	double t_4 = ((x * y) + t_2) / (y + (z * b));
	double tmp;
	if (z <= -400000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-227) {
		tmp = t_4;
	} else if (z <= 3.2e-227) {
		tmp = t_3;
	} else if (z <= 1.5e-14) {
		tmp = t_4;
	} else if (z <= 0.75) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    t_3 = x + (t_2 / (y + (z * (b - y))))
    t_4 = ((x * y) + t_2) / (y + (z * b))
    if (z <= (-400000.0d0)) then
        tmp = t_1
    else if (z <= (-2.2d-227)) then
        tmp = t_4
    else if (z <= 3.2d-227) then
        tmp = t_3
    else if (z <= 1.5d-14) then
        tmp = t_4
    else if (z <= 0.75d0) then
        tmp = t_3
    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 / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = x + (t_2 / (y + (z * (b - y))));
	double t_4 = ((x * y) + t_2) / (y + (z * b));
	double tmp;
	if (z <= -400000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-227) {
		tmp = t_4;
	} else if (z <= 3.2e-227) {
		tmp = t_3;
	} else if (z <= 1.5e-14) {
		tmp = t_4;
	} else if (z <= 0.75) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	t_3 = x + (t_2 / (y + (z * (b - y))))
	t_4 = ((x * y) + t_2) / (y + (z * b))
	tmp = 0
	if z <= -400000.0:
		tmp = t_1
	elif z <= -2.2e-227:
		tmp = t_4
	elif z <= 3.2e-227:
		tmp = t_3
	elif z <= 1.5e-14:
		tmp = t_4
	elif z <= 0.75:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(x + Float64(t_2 / Float64(y + Float64(z * Float64(b - y)))))
	t_4 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -400000.0)
		tmp = t_1;
	elseif (z <= -2.2e-227)
		tmp = t_4;
	elseif (z <= 3.2e-227)
		tmp = t_3;
	elseif (z <= 1.5e-14)
		tmp = t_4;
	elseif (z <= 0.75)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	t_3 = x + (t_2 / (y + (z * (b - y))));
	t_4 = ((x * y) + t_2) / (y + (z * b));
	tmp = 0.0;
	if (z <= -400000.0)
		tmp = t_1;
	elseif (z <= -2.2e-227)
		tmp = t_4;
	elseif (z <= 3.2e-227)
		tmp = t_3;
	elseif (z <= 1.5e-14)
		tmp = t_4;
	elseif (z <= 0.75)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -400000.0], t$95$1, If[LessEqual[z, -2.2e-227], t$95$4, If[LessEqual[z, 3.2e-227], t$95$3, If[LessEqual[z, 1.5e-14], t$95$4, If[LessEqual[z, 0.75], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4e5 or 0.75 < z

   1. Initial program 38.3%

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

   3. Taylor expanded in x around 0 38.3%

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

   4. Taylor expanded in z around inf 38.3%

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

      1. times-frac 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around inf 99.3%

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

   if -4e5 < z < -2.19999999999999981e-227 or 3.2000000000000001e-227 < z < 1.4999999999999999e-14

   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 b around inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   if -2.19999999999999981e-227 < z < 3.2000000000000001e-227 or 1.4999999999999999e-14 < z < 0.75

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0 77.8%

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

   4. Taylor expanded in z around 0 96.2%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-227}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{y + z \cdot b}\\ \mathbf{if}\;z \leq -400000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2050000:\\ \;\;\;\;\frac{a}{y} \cdot \frac{z}{z + -1} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) (+ y (* z b)))))
   (if (<= z -400000.0)
     t_1
     (if (<= z -2.2e-227)
       t_3
       (if (<= z 9.5e-225)
         (+ x (/ t_2 (+ y (* z (- b y)))))
         (if (<= z 6.6e-5)
           t_3
           (if (<= z 2050000.0)
             (- (* (/ a y) (/ z (+ z -1.0))) (/ x (+ z -1.0)))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / (y + (z * b));
	double tmp;
	if (z <= -400000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-227) {
		tmp = t_3;
	} else if (z <= 9.5e-225) {
		tmp = x + (t_2 / (y + (z * (b - y))));
	} else if (z <= 6.6e-5) {
		tmp = t_3;
	} else if (z <= 2050000.0) {
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    t_3 = ((x * y) + t_2) / (y + (z * b))
    if (z <= (-400000.0d0)) then
        tmp = t_1
    else if (z <= (-2.2d-227)) then
        tmp = t_3
    else if (z <= 9.5d-225) then
        tmp = x + (t_2 / (y + (z * (b - y))))
    else if (z <= 6.6d-5) then
        tmp = t_3
    else if (z <= 2050000.0d0) then
        tmp = ((a / y) * (z / (z + (-1.0d0)))) - (x / (z + (-1.0d0)))
    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 / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / (y + (z * b));
	double tmp;
	if (z <= -400000.0) {
		tmp = t_1;
	} else if (z <= -2.2e-227) {
		tmp = t_3;
	} else if (z <= 9.5e-225) {
		tmp = x + (t_2 / (y + (z * (b - y))));
	} else if (z <= 6.6e-5) {
		tmp = t_3;
	} else if (z <= 2050000.0) {
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / (y + (z * b))
	tmp = 0
	if z <= -400000.0:
		tmp = t_1
	elif z <= -2.2e-227:
		tmp = t_3
	elif z <= 9.5e-225:
		tmp = x + (t_2 / (y + (z * (b - y))))
	elif z <= 6.6e-5:
		tmp = t_3
	elif z <= 2050000.0:
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -400000.0)
		tmp = t_1;
	elseif (z <= -2.2e-227)
		tmp = t_3;
	elseif (z <= 9.5e-225)
		tmp = Float64(x + Float64(t_2 / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 6.6e-5)
		tmp = t_3;
	elseif (z <= 2050000.0)
		tmp = Float64(Float64(Float64(a / y) * Float64(z / Float64(z + -1.0))) - Float64(x / Float64(z + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / (y + (z * b));
	tmp = 0.0;
	if (z <= -400000.0)
		tmp = t_1;
	elseif (z <= -2.2e-227)
		tmp = t_3;
	elseif (z <= 9.5e-225)
		tmp = x + (t_2 / (y + (z * (b - y))));
	elseif (z <= 6.6e-5)
		tmp = t_3;
	elseif (z <= 2050000.0)
		tmp = ((a / y) * (z / (z + -1.0))) - (x / (z + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -400000.0], t$95$1, If[LessEqual[z, -2.2e-227], t$95$3, If[LessEqual[z, 9.5e-225], N[(x + N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-5], t$95$3, If[LessEqual[z, 2050000.0], N[(N[(N[(a / y), $MachinePrecision] * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e5 or 2.05e6 < z

   1. Initial program 38.5%

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

   3. Taylor expanded in x around 0 38.5%

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

   4. Taylor expanded in z around inf 38.5%

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

      1. times-frac 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around inf 99.7%

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

   if -4e5 < z < -2.19999999999999981e-227 or 9.50000000000000006e-225 < z < 6.6000000000000005e-5

   1. Initial program 92.1%

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

   3. Taylor expanded in b around inf 89.9%

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

      1. *-commutative 89.9%

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

   5. Simplified 89.9%

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

   if -2.19999999999999981e-227 < z < 9.50000000000000006e-225

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 72.2%

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

   4. Taylor expanded in z around 0 99.9%

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

   if 6.6000000000000005e-5 < z < 2.05e6

   1. Initial program 68.4%

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

   3. Taylor expanded in y around -inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. unsub-neg 99.0%

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

      3. associate-*r/ 99.0%

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

      4. neg-mul-1 99.0%

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

      5. sub-neg 99.0%

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

      6. metadata-eval 99.0%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf 99.0%

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

      1. mul-1-neg 99.0%

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

      2. times-frac 99.5%

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

      3. distribute-lft-neg-in 99.5%

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

      4. sub-neg 99.5%

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

      5. metadata-eval 99.5%

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

   8. Simplified 99.5%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\left(-\frac{a}{y}\right) \cdot \frac{z}{z + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2050000:\\ \;\;\;\;\frac{a}{y} \cdot \frac{z}{z + -1} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x + \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x \cdot y + t_1}{y + z \cdot b}\\ t_4 := \frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{if}\;z \leq -0.24:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ x (/ t_1 (+ y (* z (- b y))))))
        (t_3 (/ (+ (* x y) t_1) (+ y (* z b))))
        (t_4 (- (/ t (- b y)) (/ a (- b y)))))
   (if (<= z -0.24)
     t_4
     (if (<= z -1.05e-228)
       t_3
       (if (<= z 2.6e-226)
         t_2
         (if (<= z 6e-14) t_3 (if (<= z 280.0) t_2 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / (y + (z * (b - y))));
	double t_3 = ((x * y) + t_1) / (y + (z * b));
	double t_4 = (t / (b - y)) - (a / (b - y));
	double tmp;
	if (z <= -0.24) {
		tmp = t_4;
	} else if (z <= -1.05e-228) {
		tmp = t_3;
	} else if (z <= 2.6e-226) {
		tmp = t_2;
	} else if (z <= 6e-14) {
		tmp = t_3;
	} else if (z <= 280.0) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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 = z * (t - a)
    t_2 = x + (t_1 / (y + (z * (b - y))))
    t_3 = ((x * y) + t_1) / (y + (z * b))
    t_4 = (t / (b - y)) - (a / (b - y))
    if (z <= (-0.24d0)) then
        tmp = t_4
    else if (z <= (-1.05d-228)) then
        tmp = t_3
    else if (z <= 2.6d-226) then
        tmp = t_2
    else if (z <= 6d-14) then
        tmp = t_3
    else if (z <= 280.0d0) then
        tmp = t_2
    else
        tmp = t_4
    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);
	double t_2 = x + (t_1 / (y + (z * (b - y))));
	double t_3 = ((x * y) + t_1) / (y + (z * b));
	double t_4 = (t / (b - y)) - (a / (b - y));
	double tmp;
	if (z <= -0.24) {
		tmp = t_4;
	} else if (z <= -1.05e-228) {
		tmp = t_3;
	} else if (z <= 2.6e-226) {
		tmp = t_2;
	} else if (z <= 6e-14) {
		tmp = t_3;
	} else if (z <= 280.0) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = x + (t_1 / (y + (z * (b - y))))
	t_3 = ((x * y) + t_1) / (y + (z * b))
	t_4 = (t / (b - y)) - (a / (b - y))
	tmp = 0
	if z <= -0.24:
		tmp = t_4
	elif z <= -1.05e-228:
		tmp = t_3
	elif z <= 2.6e-226:
		tmp = t_2
	elif z <= 6e-14:
		tmp = t_3
	elif z <= 280.0:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(x + Float64(t_1 / Float64(y + Float64(z * Float64(b - y)))))
	t_3 = Float64(Float64(Float64(x * y) + t_1) / Float64(y + Float64(z * b)))
	t_4 = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)))
	tmp = 0.0
	if (z <= -0.24)
		tmp = t_4;
	elseif (z <= -1.05e-228)
		tmp = t_3;
	elseif (z <= 2.6e-226)
		tmp = t_2;
	elseif (z <= 6e-14)
		tmp = t_3;
	elseif (z <= 280.0)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = x + (t_1 / (y + (z * (b - y))));
	t_3 = ((x * y) + t_1) / (y + (z * b));
	t_4 = (t / (b - y)) - (a / (b - y));
	tmp = 0.0;
	if (z <= -0.24)
		tmp = t_4;
	elseif (z <= -1.05e-228)
		tmp = t_3;
	elseif (z <= 2.6e-226)
		tmp = t_2;
	elseif (z <= 6e-14)
		tmp = t_3;
	elseif (z <= 280.0)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.24], t$95$4, If[LessEqual[z, -1.05e-228], t$95$3, If[LessEqual[z, 2.6e-226], t$95$2, If[LessEqual[z, 6e-14], t$95$3, If[LessEqual[z, 280.0], t$95$2, t$95$4]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.23999999999999999 or 280 < z

   1. Initial program 39.2%

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

   3. Taylor expanded in x around 0 39.2%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -0.23999999999999999 < z < -1.04999999999999995e-228 or 2.5999999999999998e-226 < z < 5.9999999999999997e-14

   1. Initial program 91.6%

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

   3. Taylor expanded in b around inf 91.5%

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

      1. *-commutative 91.5%

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

   5. Simplified 91.5%

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

   if -1.04999999999999995e-228 < z < 2.5999999999999998e-226 or 5.9999999999999997e-14 < z < 280

   1. Initial program 77.8%

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

   3. Taylor expanded in x around 0 77.8%

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

   4. Taylor expanded in z around 0 96.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.24:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := y + z \cdot \left(b - y\right)\\ t_4 := \frac{x \cdot y + t_2}{t_3}\\ \mathbf{if}\;z \leq -54000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{t_2}{t_3}\\ \mathbf{elif}\;z \leq 1550000:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ y (* z (- b y))))
        (t_4 (/ (+ (* x y) t_2) t_3)))
   (if (<= z -54000000000.0)
     t_1
     (if (<= z -2.5e-229)
       t_4
       (if (<= z 1.05e-226)
         (+ x (/ t_2 t_3))
         (if (<= z 1550000.0) t_4 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = ((x * y) + t_2) / t_3;
	double tmp;
	if (z <= -54000000000.0) {
		tmp = t_1;
	} else if (z <= -2.5e-229) {
		tmp = t_4;
	} else if (z <= 1.05e-226) {
		tmp = x + (t_2 / t_3);
	} else if (z <= 1550000.0) {
		tmp = t_4;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    t_3 = y + (z * (b - y))
    t_4 = ((x * y) + t_2) / t_3
    if (z <= (-54000000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.5d-229)) then
        tmp = t_4
    else if (z <= 1.05d-226) then
        tmp = x + (t_2 / t_3)
    else if (z <= 1550000.0d0) then
        tmp = t_4
    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 / z) * (y / (b - y))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = ((x * y) + t_2) / t_3;
	double tmp;
	if (z <= -54000000000.0) {
		tmp = t_1;
	} else if (z <= -2.5e-229) {
		tmp = t_4;
	} else if (z <= 1.05e-226) {
		tmp = x + (t_2 / t_3);
	} else if (z <= 1550000.0) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	t_3 = y + (z * (b - y))
	t_4 = ((x * y) + t_2) / t_3
	tmp = 0
	if z <= -54000000000.0:
		tmp = t_1
	elif z <= -2.5e-229:
		tmp = t_4
	elif z <= 1.05e-226:
		tmp = x + (t_2 / t_3)
	elif z <= 1550000.0:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	t_4 = Float64(Float64(Float64(x * y) + t_2) / t_3)
	tmp = 0.0
	if (z <= -54000000000.0)
		tmp = t_1;
	elseif (z <= -2.5e-229)
		tmp = t_4;
	elseif (z <= 1.05e-226)
		tmp = Float64(x + Float64(t_2 / t_3));
	elseif (z <= 1550000.0)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x / z) * (y / (b - y))) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	t_3 = y + (z * (b - y));
	t_4 = ((x * y) + t_2) / t_3;
	tmp = 0.0;
	if (z <= -54000000000.0)
		tmp = t_1;
	elseif (z <= -2.5e-229)
		tmp = t_4;
	elseif (z <= 1.05e-226)
		tmp = x + (t_2 / t_3);
	elseif (z <= 1550000.0)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[z, -54000000000.0], t$95$1, If[LessEqual[z, -2.5e-229], t$95$4, If[LessEqual[z, 1.05e-226], N[(x + N[(t$95$2 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1550000.0], t$95$4, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4e10 or 1.55e6 < z

   1. Initial program 37.8%

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

   3. Taylor expanded in x around 0 37.8%

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

   4. Taylor expanded in z around inf 37.8%

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

      1. times-frac 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in z around inf 99.5%

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

   if -5.4e10 < z < -2.50000000000000008e-229 or 1.0500000000000001e-226 < z < 1.55e6

   1. Initial program 92.4%

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

   if -2.50000000000000008e-229 < z < 1.0500000000000001e-226

   1. Initial program 72.2%

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

   3. Taylor expanded in x around 0 72.2%

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

   4. Taylor expanded in z around 0 99.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1550000:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -10600000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+66}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+178} \lor \neg \left(y \leq 9.8 \cdot 10^{+244}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5.2e+115)
     t_1
     (if (<= y -10600000000.0)
       (/ (- a) (- b y))
       (if (<= y -8e-79)
         x
         (if (<= y 1.66e+66)
           (/ (- t a) b)
           (if (or (<= y 2.3e+178) (not (<= y 9.8e+244)))
             t_1
             (/ (- a t) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e+115) {
		tmp = t_1;
	} else if (y <= -10600000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -8e-79) {
		tmp = x;
	} else if (y <= 1.66e+66) {
		tmp = (t - a) / b;
	} else if ((y <= 2.3e+178) || !(y <= 9.8e+244)) {
		tmp = t_1;
	} else {
		tmp = (a - 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-5.2d+115)) then
        tmp = t_1
    else if (y <= (-10600000000.0d0)) then
        tmp = -a / (b - y)
    else if (y <= (-8d-79)) then
        tmp = x
    else if (y <= 1.66d+66) then
        tmp = (t - a) / b
    else if ((y <= 2.3d+178) .or. (.not. (y <= 9.8d+244))) then
        tmp = t_1
    else
        tmp = (a - 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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.2e+115) {
		tmp = t_1;
	} else if (y <= -10600000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -8e-79) {
		tmp = x;
	} else if (y <= 1.66e+66) {
		tmp = (t - a) / b;
	} else if ((y <= 2.3e+178) || !(y <= 9.8e+244)) {
		tmp = t_1;
	} else {
		tmp = (a - t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -5.2e+115:
		tmp = t_1
	elif y <= -10600000000.0:
		tmp = -a / (b - y)
	elif y <= -8e-79:
		tmp = x
	elif y <= 1.66e+66:
		tmp = (t - a) / b
	elif (y <= 2.3e+178) or not (y <= 9.8e+244):
		tmp = t_1
	else:
		tmp = (a - t) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.2e+115)
		tmp = t_1;
	elseif (y <= -10600000000.0)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif (y <= -8e-79)
		tmp = x;
	elseif (y <= 1.66e+66)
		tmp = Float64(Float64(t - a) / b);
	elseif ((y <= 2.3e+178) || !(y <= 9.8e+244))
		tmp = t_1;
	else
		tmp = Float64(Float64(a - t) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.2e+115)
		tmp = t_1;
	elseif (y <= -10600000000.0)
		tmp = -a / (b - y);
	elseif (y <= -8e-79)
		tmp = x;
	elseif (y <= 1.66e+66)
		tmp = (t - a) / b;
	elseif ((y <= 2.3e+178) || ~((y <= 9.8e+244)))
		tmp = t_1;
	else
		tmp = (a - t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+115], t$95$1, If[LessEqual[y, -10600000000.0], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-79], x, If[LessEqual[y, 1.66e+66], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[Or[LessEqual[y, 2.3e+178], N[Not[LessEqual[y, 9.8e+244]], $MachinePrecision]], t$95$1, N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.2000000000000001e115 or 1.6600000000000001e66 < y < 2.3000000000000001e178 or 9.8e244 < y

   1. Initial program 50.9%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -5.2000000000000001e115 < y < -1.06e10

   1. Initial program 47.3%

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

   3. Taylor expanded in a around inf 15.4%

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

      1. mul-1-neg 15.4%

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

      2. distribute-lft-neg-out 15.4%

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

      3. *-commutative 15.4%

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

   5. Simplified 15.4%

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

   6. Taylor expanded in z around inf 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

   if -1.06e10 < y < -8e-79

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 54.4%

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

   if -8e-79 < y < 1.6600000000000001e66

   1. Initial program 76.7%

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

   3. Taylor expanded in y around 0 60.5%

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

   if 2.3000000000000001e178 < y < 9.8e244

   1. Initial program 27.6%

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

   3. Taylor expanded in x around 0 27.6%

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

   4. Taylor expanded in z around inf 62.7%

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

   5. Taylor expanded in b around 0 59.6%

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

      1. distribute-lft-out-- 59.6%

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

      2. div-sub 59.6%

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

      3. mul-1-neg 59.6%

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

      4. distribute-frac-neg 59.6%

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

   7. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -10600000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+66}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+178} \lor \neg \left(y \leq 9.8 \cdot 10^{+244}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -12000000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+178} \lor \neg \left(y \leq 4 \cdot 10^{+244}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -6e+113)
     t_1
     (if (<= y -12000000000.0)
       (/ (- a) (- b y))
       (if (<= y -2.2e-78)
         x
         (if (<= y 4.9e+66)
           (- (/ t b) (/ a b))
           (if (or (<= y 1.15e+178) (not (<= y 4e+244)))
             t_1
             (/ (- a t) y))))))))

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 <= -6e+113) {
		tmp = t_1;
	} else if (y <= -12000000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -2.2e-78) {
		tmp = x;
	} else if (y <= 4.9e+66) {
		tmp = (t / b) - (a / b);
	} else if ((y <= 1.15e+178) || !(y <= 4e+244)) {
		tmp = t_1;
	} else {
		tmp = (a - 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-6d+113)) then
        tmp = t_1
    else if (y <= (-12000000000.0d0)) then
        tmp = -a / (b - y)
    else if (y <= (-2.2d-78)) then
        tmp = x
    else if (y <= 4.9d+66) then
        tmp = (t / b) - (a / b)
    else if ((y <= 1.15d+178) .or. (.not. (y <= 4d+244))) then
        tmp = t_1
    else
        tmp = (a - 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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -6e+113) {
		tmp = t_1;
	} else if (y <= -12000000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -2.2e-78) {
		tmp = x;
	} else if (y <= 4.9e+66) {
		tmp = (t / b) - (a / b);
	} else if ((y <= 1.15e+178) || !(y <= 4e+244)) {
		tmp = t_1;
	} else {
		tmp = (a - t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -6e+113:
		tmp = t_1
	elif y <= -12000000000.0:
		tmp = -a / (b - y)
	elif y <= -2.2e-78:
		tmp = x
	elif y <= 4.9e+66:
		tmp = (t / b) - (a / b)
	elif (y <= 1.15e+178) or not (y <= 4e+244):
		tmp = t_1
	else:
		tmp = (a - t) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -6e+113)
		tmp = t_1;
	elseif (y <= -12000000000.0)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif (y <= -2.2e-78)
		tmp = x;
	elseif (y <= 4.9e+66)
		tmp = Float64(Float64(t / b) - Float64(a / b));
	elseif ((y <= 1.15e+178) || !(y <= 4e+244))
		tmp = t_1;
	else
		tmp = Float64(Float64(a - t) / y);
	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 <= -6e+113)
		tmp = t_1;
	elseif (y <= -12000000000.0)
		tmp = -a / (b - y);
	elseif (y <= -2.2e-78)
		tmp = x;
	elseif (y <= 4.9e+66)
		tmp = (t / b) - (a / b);
	elseif ((y <= 1.15e+178) || ~((y <= 4e+244)))
		tmp = t_1;
	else
		tmp = (a - t) / y;
	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, -6e+113], t$95$1, If[LessEqual[y, -12000000000.0], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-78], x, If[LessEqual[y, 4.9e+66], N[(N[(t / b), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.15e+178], N[Not[LessEqual[y, 4e+244]], $MachinePrecision]], t$95$1, N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6e113 or 4.89999999999999975e66 < y < 1.15e178 or 4.0000000000000003e244 < y

   1. Initial program 50.9%

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

   3. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   if -6e113 < y < -1.2e10

   1. Initial program 47.3%

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

   3. Taylor expanded in a around inf 15.4%

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

      1. mul-1-neg 15.4%

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

      2. distribute-lft-neg-out 15.4%

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

      3. *-commutative 15.4%

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

   5. Simplified 15.4%

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

   6. Taylor expanded in z around inf 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

   if -1.2e10 < y < -2.1999999999999999e-78

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 54.4%

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

   if -2.1999999999999999e-78 < y < 4.89999999999999975e66

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0 76.7%

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

   4. Taylor expanded in y around 0 60.5%

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

   if 1.15e178 < y < 4.0000000000000003e244

   1. Initial program 27.6%

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

   3. Taylor expanded in x around 0 27.6%

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

   4. Taylor expanded in z around inf 62.7%

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

   5. Taylor expanded in b around 0 59.6%

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

      1. distribute-lft-out-- 59.6%

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

      2. div-sub 59.6%

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

      3. mul-1-neg 59.6%

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

      4. distribute-frac-neg 59.6%

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

   7. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{-\left(t - a\right)}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -12000000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+178} \lor \neg \left(y \leq 4 \cdot 10^{+244}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.00094:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+255} \lor \neg \left(z \leq 3.6 \cdot 10^{+282}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.85e-18)
     t_1
     (if (<= z 0.00094)
       (+ x (* z x))
       (if (or (<= z 1.05e+255) (not (<= z 3.6e+282))) t_1 (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.85e-18) {
		tmp = t_1;
	} else if (z <= 0.00094) {
		tmp = x + (z * x);
	} else if ((z <= 1.05e+255) || !(z <= 3.6e+282)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.85d-18)) then
        tmp = t_1
    else if (z <= 0.00094d0) then
        tmp = x + (z * x)
    else if ((z <= 1.05d+255) .or. (.not. (z <= 3.6d+282))) then
        tmp = t_1
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.85e-18) {
		tmp = t_1;
	} else if (z <= 0.00094) {
		tmp = x + (z * x);
	} else if ((z <= 1.05e+255) || !(z <= 3.6e+282)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.85e-18:
		tmp = t_1
	elif z <= 0.00094:
		tmp = x + (z * x)
	elif (z <= 1.05e+255) or not (z <= 3.6e+282):
		tmp = t_1
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.85e-18)
		tmp = t_1;
	elseif (z <= 0.00094)
		tmp = Float64(x + Float64(z * x));
	elseif ((z <= 1.05e+255) || !(z <= 3.6e+282))
		tmp = t_1;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -2.85e-18)
		tmp = t_1;
	elseif (z <= 0.00094)
		tmp = x + (z * x);
	elseif ((z <= 1.05e+255) || ~((z <= 3.6e+282)))
		tmp = t_1;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.85e-18], t$95$1, If[LessEqual[z, 0.00094], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.05e+255], N[Not[LessEqual[z, 3.6e+282]], $MachinePrecision]], t$95$1, N[(a / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.84999999999999986e-18 or 9.39999999999999972e-4 < z < 1.05e255 or 3.59999999999999986e282 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in t around inf 18.8%

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

      1. associate-/l* 26.1%

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

      2. +-commutative 26.1%

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

      3. fma-udef 26.1%

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

      4. associate-/r/ 25.6%

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

   5. Simplified 25.6%

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

   6. Taylor expanded in z around inf 44.1%

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

   if -2.84999999999999986e-18 < z < 9.39999999999999972e-4

   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. Taylor expanded in y around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around 0 51.3%

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

      1. *-commutative 51.3%

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

   8. Simplified 51.3%

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

   if 1.05e255 < z < 3.59999999999999986e282

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 0.3%

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

      1. mul-1-neg 0.3%

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

      2. distribute-lft-neg-out 0.3%

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

      3. *-commutative 0.3%

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

   5. Simplified 0.3%

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

   6. Taylor expanded in z around inf 87.9%

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

      1. associate-*r/ 87.9%

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

      2. neg-mul-1 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in b around 0 64.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 0.00094:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+255} \lor \neg \left(z \leq 3.6 \cdot 10^{+282}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+252} \lor \neg \left(z \leq 3.8 \cdot 10^{+282}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -2.55e-18)
     t_1
     (if (<= z 3.6e+50)
       (/ x (- 1.0 z))
       (if (or (<= z 3.5e+252) (not (<= z 3.8e+282))) t_1 (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.55e-18) {
		tmp = t_1;
	} else if (z <= 3.6e+50) {
		tmp = x / (1.0 - z);
	} else if ((z <= 3.5e+252) || !(z <= 3.8e+282)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-2.55d-18)) then
        tmp = t_1
    else if (z <= 3.6d+50) then
        tmp = x / (1.0d0 - z)
    else if ((z <= 3.5d+252) .or. (.not. (z <= 3.8d+282))) then
        tmp = t_1
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -2.55e-18) {
		tmp = t_1;
	} else if (z <= 3.6e+50) {
		tmp = x / (1.0 - z);
	} else if ((z <= 3.5e+252) || !(z <= 3.8e+282)) {
		tmp = t_1;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -2.55e-18:
		tmp = t_1
	elif z <= 3.6e+50:
		tmp = x / (1.0 - z)
	elif (z <= 3.5e+252) or not (z <= 3.8e+282):
		tmp = t_1
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -2.55e-18)
		tmp = t_1;
	elseif (z <= 3.6e+50)
		tmp = Float64(x / Float64(1.0 - z));
	elseif ((z <= 3.5e+252) || !(z <= 3.8e+282))
		tmp = t_1;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -2.55e-18)
		tmp = t_1;
	elseif (z <= 3.6e+50)
		tmp = x / (1.0 - z);
	elseif ((z <= 3.5e+252) || ~((z <= 3.8e+282)))
		tmp = t_1;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e-18], t$95$1, If[LessEqual[z, 3.6e+50], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.5e+252], N[Not[LessEqual[z, 3.8e+282]], $MachinePrecision]], t$95$1, N[(a / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.54999999999999991e-18 or 3.59999999999999986e50 < z < 3.4999999999999999e252 or 3.8e282 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in t around inf 19.1%

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

      1. associate-/l* 26.1%

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

      2. +-commutative 26.1%

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

      3. fma-udef 26.1%

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

      4. associate-/r/ 25.6%

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

   5. Simplified 25.6%

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

   6. Taylor expanded in z around inf 45.5%

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

   if -2.54999999999999991e-18 < z < 3.59999999999999986e50

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

   if 3.4999999999999999e252 < z < 3.8e282

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 0.3%

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

      1. mul-1-neg 0.3%

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

      2. distribute-lft-neg-out 0.3%

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

      3. *-commutative 0.3%

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

   5. Simplified 0.3%

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

   6. Taylor expanded in z around inf 87.9%

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

      1. associate-*r/ 87.9%

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

      2. neg-mul-1 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in b around 0 64.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+252} \lor \neg \left(z \leq 3.8 \cdot 10^{+282}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -16000000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.25e+120)
     t_1
     (if (<= y -16000000000.0)
       (/ (- a) (- b y))
       (if (<= y -2.4e-78) x (if (<= y 2.75e+66) (/ (- 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 <= -1.25e+120) {
		tmp = t_1;
	} else if (y <= -16000000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -2.4e-78) {
		tmp = x;
	} else if (y <= 2.75e+66) {
		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 <= (-1.25d+120)) then
        tmp = t_1
    else if (y <= (-16000000000.0d0)) then
        tmp = -a / (b - y)
    else if (y <= (-2.4d-78)) then
        tmp = x
    else if (y <= 2.75d+66) 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 <= -1.25e+120) {
		tmp = t_1;
	} else if (y <= -16000000000.0) {
		tmp = -a / (b - y);
	} else if (y <= -2.4e-78) {
		tmp = x;
	} else if (y <= 2.75e+66) {
		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 <= -1.25e+120:
		tmp = t_1
	elif y <= -16000000000.0:
		tmp = -a / (b - y)
	elif y <= -2.4e-78:
		tmp = x
	elif y <= 2.75e+66:
		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 <= -1.25e+120)
		tmp = t_1;
	elseif (y <= -16000000000.0)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif (y <= -2.4e-78)
		tmp = x;
	elseif (y <= 2.75e+66)
		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 <= -1.25e+120)
		tmp = t_1;
	elseif (y <= -16000000000.0)
		tmp = -a / (b - y);
	elseif (y <= -2.4e-78)
		tmp = x;
	elseif (y <= 2.75e+66)
		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, -1.25e+120], t$95$1, If[LessEqual[y, -16000000000.0], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-78], x, If[LessEqual[y, 2.75e+66], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.25000000000000005e120 or 2.75e66 < y

   1. Initial program 47.5%

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

   3. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if -1.25000000000000005e120 < y < -1.6e10

   1. Initial program 47.3%

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

   3. Taylor expanded in a around inf 15.4%

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

      1. mul-1-neg 15.4%

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

      2. distribute-lft-neg-out 15.4%

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

      3. *-commutative 15.4%

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

   5. Simplified 15.4%

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

   6. Taylor expanded in z around inf 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

   if -1.6e10 < y < -2.4e-78

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 54.4%

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

   if -2.4e-78 < y < 2.75e66

   1. Initial program 76.7%

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

   3. Taylor expanded in y around 0 60.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -16000000000:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+66}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-9} \lor \neg \left(z \leq 3400\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e-9) (not (<= z 3400.0)))
   (- (/ t (- b y)) (/ a (- b y)))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-9) || !(z <= 3400.0)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d-9)) .or. (.not. (z <= 3400.0d0))) then
        tmp = (t / (b - y)) - (a / (b - y))
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-9) || !(z <= 3400.0)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e-9) or not (z <= 3400.0):
		tmp = (t / (b - y)) - (a / (b - y))
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e-9) || !(z <= 3400.0))
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e-9) || ~((z <= 3400.0)))
		tmp = (t / (b - y)) - (a / (b - y));
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e-9], N[Not[LessEqual[z, 3400.0]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999984e-9 or 3400 < 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 x around 0 39.6%

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

   4. Taylor expanded in z around inf 84.2%

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

   if -2.79999999999999984e-9 < z < 3400

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 87.7%

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

   4. Taylor expanded in z around 0 85.8%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-9} \lor \neg \left(z \leq 3400\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 0.000235:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e+106)
   (/ a y)
   (if (<= z -2.5e-18)
     (/ (- a) b)
     (if (<= z 0.000235) x (if (<= z 5.6e+238) (/ t b) (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+106) {
		tmp = a / y;
	} else if (z <= -2.5e-18) {
		tmp = -a / b;
	} else if (z <= 0.000235) {
		tmp = x;
	} else if (z <= 5.6e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.8d+106)) then
        tmp = a / y
    else if (z <= (-2.5d-18)) then
        tmp = -a / b
    else if (z <= 0.000235d0) then
        tmp = x
    else if (z <= 5.6d+238) then
        tmp = t / b
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+106) {
		tmp = a / y;
	} else if (z <= -2.5e-18) {
		tmp = -a / b;
	} else if (z <= 0.000235) {
		tmp = x;
	} else if (z <= 5.6e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.8e+106:
		tmp = a / y
	elif z <= -2.5e-18:
		tmp = -a / b
	elif z <= 0.000235:
		tmp = x
	elif z <= 5.6e+238:
		tmp = t / b
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e+106)
		tmp = Float64(a / y);
	elseif (z <= -2.5e-18)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 0.000235)
		tmp = x;
	elseif (z <= 5.6e+238)
		tmp = Float64(t / b);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.8e+106)
		tmp = a / y;
	elseif (z <= -2.5e-18)
		tmp = -a / b;
	elseif (z <= 0.000235)
		tmp = x;
	elseif (z <= 5.6e+238)
		tmp = t / b;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e+106], N[(a / y), $MachinePrecision], If[LessEqual[z, -2.5e-18], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 0.000235], x, If[LessEqual[z, 5.6e+238], N[(t / b), $MachinePrecision], N[(a / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000001e106 or 5.59999999999999981e238 < z

   1. Initial program 20.6%

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

   3. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. distribute-lft-neg-out 13.2%

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

      3. *-commutative 13.2%

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

   5. Simplified 13.2%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. associate-*r/ 55.8%

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

      2. neg-mul-1 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in b around 0 37.5%

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

   if -4.8000000000000001e106 < z < -2.50000000000000018e-18

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-lft-neg-out 40.2%

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

      3. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in y around 0 36.0%

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

      1. associate-*r/ 36.0%

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

      2. neg-mul-1 36.0%

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

   8. Simplified 36.0%

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

   if -2.50000000000000018e-18 < z < 2.34999999999999993e-4

   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. Taylor expanded in z around 0 50.7%

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

   if 2.34999999999999993e-4 < z < 5.59999999999999981e238

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. associate-/l* 28.4%

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

      2. +-commutative 28.4%

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

      3. fma-udef 28.4%

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

      4. associate-/r/ 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in b around inf 32.7%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 0.000235:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+110}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9e+110)
   (/ a y)
   (if (<= z -3.1e-18)
     (/ (- a) b)
     (if (<= z 0.00017) (+ x (* z x)) (if (<= z 6.8e+238) (/ t b) (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9e+110) {
		tmp = a / y;
	} else if (z <= -3.1e-18) {
		tmp = -a / b;
	} else if (z <= 0.00017) {
		tmp = x + (z * x);
	} else if (z <= 6.8e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9d+110)) then
        tmp = a / y
    else if (z <= (-3.1d-18)) then
        tmp = -a / b
    else if (z <= 0.00017d0) then
        tmp = x + (z * x)
    else if (z <= 6.8d+238) then
        tmp = t / b
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9e+110) {
		tmp = a / y;
	} else if (z <= -3.1e-18) {
		tmp = -a / b;
	} else if (z <= 0.00017) {
		tmp = x + (z * x);
	} else if (z <= 6.8e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9e+110:
		tmp = a / y
	elif z <= -3.1e-18:
		tmp = -a / b
	elif z <= 0.00017:
		tmp = x + (z * x)
	elif z <= 6.8e+238:
		tmp = t / b
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9e+110)
		tmp = Float64(a / y);
	elseif (z <= -3.1e-18)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 0.00017)
		tmp = Float64(x + Float64(z * x));
	elseif (z <= 6.8e+238)
		tmp = Float64(t / b);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9e+110)
		tmp = a / y;
	elseif (z <= -3.1e-18)
		tmp = -a / b;
	elseif (z <= 0.00017)
		tmp = x + (z * x);
	elseif (z <= 6.8e+238)
		tmp = t / b;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9e+110], N[(a / y), $MachinePrecision], If[LessEqual[z, -3.1e-18], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 0.00017], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+238], N[(t / b), $MachinePrecision], N[(a / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.0000000000000005e110 or 6.7999999999999995e238 < z

   1. Initial program 20.6%

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

   3. Taylor expanded in a around inf 13.2%

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

      1. mul-1-neg 13.2%

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

      2. distribute-lft-neg-out 13.2%

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

      3. *-commutative 13.2%

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

   5. Simplified 13.2%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. associate-*r/ 55.8%

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

      2. neg-mul-1 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in b around 0 37.5%

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

   if -9.0000000000000005e110 < z < -3.10000000000000007e-18

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-lft-neg-out 40.2%

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

      3. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in y around 0 36.0%

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

      1. associate-*r/ 36.0%

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

      2. neg-mul-1 36.0%

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

   8. Simplified 36.0%

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

   if -3.10000000000000007e-18 < z < 1.7e-4

   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. Taylor expanded in y around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in z around 0 51.3%

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

      1. *-commutative 51.3%

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

   8. Simplified 51.3%

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

   if 1.7e-4 < z < 6.7999999999999995e238

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. associate-/l* 28.4%

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

      2. +-commutative 28.4%

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

      3. fma-udef 28.4%

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

      4. associate-/r/ 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in b around inf 32.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+110}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 0.00017:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-14} \lor \neg \left(z \leq 0.13\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x \cdot b + \left(a - t\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.15e-14) (not (<= z 0.13)))
   (- (/ t (- b y)) (/ a (- b y)))
   (- x (/ (* z (+ (* x b) (- a t))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.15e-14) || !(z <= 0.13)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = x - ((z * ((x * b) + (a - 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 <= (-2.15d-14)) .or. (.not. (z <= 0.13d0))) then
        tmp = (t / (b - y)) - (a / (b - y))
    else
        tmp = x - ((z * ((x * b) + (a - 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 <= -2.15e-14) || !(z <= 0.13)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = x - ((z * ((x * b) + (a - t))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.15e-14) or not (z <= 0.13):
		tmp = (t / (b - y)) - (a / (b - y))
	else:
		tmp = x - ((z * ((x * b) + (a - t))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.15e-14) || !(z <= 0.13))
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(Float64(x * b) + Float64(a - t))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.15e-14) || ~((z <= 0.13)))
		tmp = (t / (b - y)) - (a / (b - y));
	else
		tmp = x - ((z * ((x * b) + (a - t))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.15e-14], N[Not[LessEqual[z, 0.13]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(N[(x * b), $MachinePrecision] + N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999999e-14 or 0.13 < z

   1. Initial program 40.1%

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

   3. Taylor expanded in x around 0 40.1%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -2.14999999999999999e-14 < z < 0.13

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf 85.4%

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

      1. *-commutative 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in y around -inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. distribute-lft-out-- 75.5%

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

      4. mul-1-neg 75.5%

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

      5. *-commutative 75.5%

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

      6. associate-*r* 71.5%

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

      7. distribute-rgt-out-- 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-14} \lor \neg \left(z \leq 0.13\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(x \cdot b + \left(a - t\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-14} \lor \neg \left(z \leq 0.13\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e-14) (not (<= z 0.13)))
   (- (/ t (- b y)) (/ a (- b y)))
   (/ (+ (* x y) (* z (- t a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-14) || !(z <= 0.13)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = ((x * y) + (z * (t - a))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d-14)) .or. (.not. (z <= 0.13d0))) then
        tmp = (t / (b - y)) - (a / (b - y))
    else
        tmp = ((x * y) + (z * (t - a))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e-14) || !(z <= 0.13)) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else {
		tmp = ((x * y) + (z * (t - a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e-14) or not (z <= 0.13):
		tmp = (t / (b - y)) - (a / (b - y))
	else:
		tmp = ((x * y) + (z * (t - a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e-14) || !(z <= 0.13))
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e-14) || ~((z <= 0.13)))
		tmp = (t / (b - y)) - (a / (b - y));
	else
		tmp = ((x * y) + (z * (t - a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e-14], N[Not[LessEqual[z, 0.13]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e-14 or 0.13 < z

   1. Initial program 40.1%

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

   3. Taylor expanded in x around 0 40.1%

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

   4. Taylor expanded in z around inf 84.3%

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

   if -2.8000000000000001e-14 < z < 0.13

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf 85.4%

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

      1. *-commutative 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in b around 0 64.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-14} \lor \neg \left(z \leq 0.13\right):\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6800000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 0.00345:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6800000.0)
   (/ a y)
   (if (<= z 0.00345) x (if (<= z 6.5e+238) (/ t b) (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6800000.0) {
		tmp = a / y;
	} else if (z <= 0.00345) {
		tmp = x;
	} else if (z <= 6.5e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6800000.0d0)) then
        tmp = a / y
    else if (z <= 0.00345d0) then
        tmp = x
    else if (z <= 6.5d+238) then
        tmp = t / b
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6800000.0) {
		tmp = a / y;
	} else if (z <= 0.00345) {
		tmp = x;
	} else if (z <= 6.5e+238) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6800000.0:
		tmp = a / y
	elif z <= 0.00345:
		tmp = x
	elif z <= 6.5e+238:
		tmp = t / b
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6800000.0)
		tmp = Float64(a / y);
	elseif (z <= 0.00345)
		tmp = x;
	elseif (z <= 6.5e+238)
		tmp = Float64(t / b);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6800000.0)
		tmp = a / y;
	elseif (z <= 0.00345)
		tmp = x;
	elseif (z <= 6.5e+238)
		tmp = t / b;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6800000.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 0.00345], x, If[LessEqual[z, 6.5e+238], N[(t / b), $MachinePrecision], N[(a / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e6 or 6.5000000000000005e238 < z

   1. Initial program 34.7%

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

   3. Taylor expanded in a around inf 21.2%

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

      1. mul-1-neg 21.2%

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

      2. distribute-lft-neg-out 21.2%

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

      3. *-commutative 21.2%

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

   5. Simplified 21.2%

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

   6. Taylor expanded in z around inf 55.1%

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

      1. associate-*r/ 55.1%

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

      2. neg-mul-1 55.1%

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

   8. Simplified 55.1%

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

   9. Taylor expanded in b around 0 32.2%

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

   if -6.8e6 < z < 0.0034499999999999999

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 48.7%

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

   if 0.0034499999999999999 < z < 6.5000000000000005e238

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. associate-/l* 28.4%

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

      2. +-commutative 28.4%

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

      3. fma-udef 28.4%

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

      4. associate-/r/ 27.1%

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

   5. Simplified 27.1%

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

   6. Taylor expanded in b around inf 32.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6800000:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 0.00345:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+238}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-18} \lor \neg \left(z \leq 3.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e-18) (not (<= z 3.5e+50)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e-18) || !(z <= 3.5e+50)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.95d-18)) .or. (.not. (z <= 3.5d+50))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e-18) || !(z <= 3.5e+50)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e-18) or not (z <= 3.5e+50):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e-18) || !(z <= 3.5e+50))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.95e-18) || ~((z <= 3.5e+50)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e-18], N[Not[LessEqual[z, 3.5e+50]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000002e-18 or 3.50000000000000006e50 < z

   1. Initial program 41.8%

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

   3. Taylor expanded in z around inf 86.0%

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

   if -1.95000000000000002e-18 < z < 3.50000000000000006e50

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-18} \lor \neg \left(z \leq 3.5 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.55e-18)
   (- (/ t (- b y)) (/ a (- b y)))
   (if (<= z 3.5e+50) (/ x (- 1.0 z)) (/ (- t a) (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-18) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 3.5e+50) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.55d-18)) then
        tmp = (t / (b - y)) - (a / (b - y))
    else if (z <= 3.5d+50) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.55e-18) {
		tmp = (t / (b - y)) - (a / (b - y));
	} else if (z <= 3.5e+50) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.55e-18:
		tmp = (t / (b - y)) - (a / (b - y))
	elif z <= 3.5e+50:
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.55e-18)
		tmp = Float64(Float64(t / Float64(b - y)) - Float64(a / Float64(b - y)));
	elseif (z <= 3.5e+50)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.55e-18)
		tmp = (t / (b - y)) - (a / (b - y));
	elseif (z <= 3.5e+50)
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.55e-18], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+50], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.54999999999999991e-18

   1. Initial program 44.3%

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

   3. Taylor expanded in x around 0 44.3%

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

   4. Taylor expanded in z around inf 83.6%

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

   if -2.54999999999999991e-18 < z < 3.50000000000000006e50

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

   if 3.50000000000000006e50 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 88.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;\frac{t}{b - y} - \frac{a}{b - y}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 53.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-78} \lor \neg \left(y \leq 1.8 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e-78) (not (<= y 1.8e+66))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-78) || !(y <= 1.8e+66)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.4d-78)) .or. (.not. (y <= 1.8d+66))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.4e-78) || !(y <= 1.8e+66)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.4e-78) or not (y <= 1.8e+66):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.4e-78) || !(y <= 1.8e+66))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.4e-78) || ~((y <= 1.8e+66)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.4e-78], N[Not[LessEqual[y, 1.8e+66]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e-78 or 1.8e66 < y

   1. Initial program 51.7%

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

   3. Taylor expanded in y around inf 46.9%

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

      1. mul-1-neg 46.9%

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

      2. unsub-neg 46.9%

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

   5. Simplified 46.9%

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

   if -2.4e-78 < y < 1.8e66

   1. Initial program 76.7%

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

   3. Taylor expanded in y around 0 60.5%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-78} \lor \neg \left(y \leq 1.8 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -400000.0) (not (<= z 1.0))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 1.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-400000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = a / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 1.0)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -400000.0) or not (z <= 1.0):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -400000.0) || !(z <= 1.0))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -400000.0) || ~((z <= 1.0)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -400000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4e5 or 1 < z

   1. Initial program 38.3%

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

   3. Taylor expanded in a around inf 22.7%

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

      1. mul-1-neg 22.7%

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

      2. distribute-lft-neg-out 22.7%

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

      3. *-commutative 22.7%

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

   5. Simplified 22.7%

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

   6. Taylor expanded in z around inf 47.5%

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

      1. associate-*r/ 47.5%

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

      2. neg-mul-1 47.5%

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

   8. Simplified 47.5%

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

   9. Taylor expanded in b around 0 27.5%

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

   if -4e5 < z < 1

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 48.3%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.9% 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 62.7%

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

3. Taylor expanded in z around 0 25.4%

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

4. Final simplification 25.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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