Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Percentage Accurate: 99.8% → 99.9%

Time: 8.9s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

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) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
}

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) - (z * log(t))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((x + y) + z) - (z * log(t))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(1 - \log t\right) \cdot z + \left(x + y\right)\right) + \left(a + -0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (* (- 1.0 (log t)) z) (+ x y)) (* (+ a -0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (((1.0 - log(t)) * z) + (x + y)) + ((a + -0.5) * b);
}

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 = (((1.0d0 - log(t)) * z) + (x + y)) + ((a + (-0.5d0)) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (((1.0 - Math.log(t)) * z) + (x + y)) + ((a + -0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return (((1.0 - math.log(t)) * z) + (x + y)) + ((a + -0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(1.0 - log(t)) * z) + Float64(x + y)) + Float64(Float64(a + -0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (((1.0 - log(t)) * z) + (x + y)) + ((a + -0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. remove-double-neg 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

   2. distribute-rgt-neg-out 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

   3. associate--l+ 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

   4. distribute-rgt-neg-in 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

   5. sub-neg 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

   7. remove-double-neg 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

4. Taylor expanded in z around 0 99.9%

   \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

5. Final simplification 99.9%

   \[\leadsto \left(\left(1 - \log t\right) \cdot z + \left(x + y\right)\right) + \left(a + -0.5\right) \cdot b \]

Alternative 2: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t_1 + \left(x + y\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+156}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+84)
     (+ t_1 (+ x y))
     (if (<= t_1 4e+156)
       (+ (* (- 1.0 (log t)) z) (+ x y))
       (+ (+ x y) (+ (* a b) (* -0.5 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = t_1 + (x + y);
	} else if (t_1 <= 4e+156) {
		tmp = ((1.0 - log(t)) * z) + (x + y);
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-5d+84)) then
        tmp = t_1 + (x + y)
    else if (t_1 <= 4d+156) then
        tmp = ((1.0d0 - log(t)) * z) + (x + y)
    else
        tmp = (x + y) + ((a * b) + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+84) {
		tmp = t_1 + (x + y);
	} else if (t_1 <= 4e+156) {
		tmp = ((1.0 - Math.log(t)) * z) + (x + y);
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+84:
		tmp = t_1 + (x + y)
	elif t_1 <= 4e+156:
		tmp = ((1.0 - math.log(t)) * z) + (x + y)
	else:
		tmp = (x + y) + ((a * b) + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+84)
		tmp = Float64(t_1 + Float64(x + y));
	elseif (t_1 <= 4e+156)
		tmp = Float64(Float64(Float64(1.0 - log(t)) * z) + Float64(x + y));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -5e+84)
		tmp = t_1 + (x + y);
	elseif (t_1 <= 4e+156)
		tmp = ((1.0 - log(t)) * z) + (x + y);
	else
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+84], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+156], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5.0000000000000001e84

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 95.6%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   if -5.0000000000000001e84 < (*.f64 (-.f64 a 1/2) b) < 3.9999999999999999e156

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.7%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.9%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in b around 0 90.9%

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

   if 3.9999999999999999e156 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 91.8%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 91.8%

      \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+84}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+156}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \]

Alternative 3: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot z\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+128}:\\ \;\;\;\;\left(z + t_2\right) - t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(z - t_1\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log t) z)) (t_2 (* b (- a 0.5))))
   (if (<= b -2.5e+128)
     (- (+ z t_2) t_1)
     (if (<= b 7.5e+86) (+ (+ (- z t_1) (+ x y)) (* a b)) (+ t_2 (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(t) * z;
	double t_2 = b * (a - 0.5);
	double tmp;
	if (b <= -2.5e+128) {
		tmp = (z + t_2) - t_1;
	} else if (b <= 7.5e+86) {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	} else {
		tmp = t_2 + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(t) * z
    t_2 = b * (a - 0.5d0)
    if (b <= (-2.5d+128)) then
        tmp = (z + t_2) - t_1
    else if (b <= 7.5d+86) then
        tmp = ((z - t_1) + (x + y)) + (a * b)
    else
        tmp = t_2 + (x + 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 = Math.log(t) * z;
	double t_2 = b * (a - 0.5);
	double tmp;
	if (b <= -2.5e+128) {
		tmp = (z + t_2) - t_1;
	} else if (b <= 7.5e+86) {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	} else {
		tmp = t_2 + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(t) * z
	t_2 = b * (a - 0.5)
	tmp = 0
	if b <= -2.5e+128:
		tmp = (z + t_2) - t_1
	elif b <= 7.5e+86:
		tmp = ((z - t_1) + (x + y)) + (a * b)
	else:
		tmp = t_2 + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(t) * z)
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (b <= -2.5e+128)
		tmp = Float64(Float64(z + t_2) - t_1);
	elseif (b <= 7.5e+86)
		tmp = Float64(Float64(Float64(z - t_1) + Float64(x + y)) + Float64(a * b));
	else
		tmp = Float64(t_2 + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(t) * z;
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (b <= -2.5e+128)
		tmp = (z + t_2) - t_1;
	elseif (b <= 7.5e+86)
		tmp = ((z - t_1) + (x + y)) + (a * b);
	else
		tmp = t_2 + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+128], N[(N[(z + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[b, 7.5e+86], N[(N[(N[(z - t$95$1), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e128

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around 0 96.8%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t} \]

   5. Taylor expanded in x around 0 96.8%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + z\right) - z \cdot \log t} \]

   if -2.5e128 < b < 7.4999999999999997e86

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in a around inf 95.0%

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

      1. *-commutative 95.0%

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

   6. Simplified 95.0%

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

   if 7.4999999999999997e86 < b

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 96.5%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+128}:\\ \;\;\;\;\left(z + b \cdot \left(a - 0.5\right)\right) - \log t \cdot z\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\left(\left(z - \log t \cdot z\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot z\\ \mathbf{if}\;x + y \leq 10^{+106}:\\ \;\;\;\;\left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z - t_1\right) + \left(x + y\right)\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log t) z)))
   (if (<= (+ x y) 1e+106)
     (- (+ (* b (- a 0.5)) (+ x z)) t_1)
     (+ (+ (- z t_1) (+ x y)) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(t) * z;
	double tmp;
	if ((x + y) <= 1e+106) {
		tmp = ((b * (a - 0.5)) + (x + z)) - t_1;
	} else {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) * z
    if ((x + y) <= 1d+106) then
        tmp = ((b * (a - 0.5d0)) + (x + z)) - t_1
    else
        tmp = ((z - t_1) + (x + y)) + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(t) * z;
	double tmp;
	if ((x + y) <= 1e+106) {
		tmp = ((b * (a - 0.5)) + (x + z)) - t_1;
	} else {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(t) * z
	tmp = 0
	if (x + y) <= 1e+106:
		tmp = ((b * (a - 0.5)) + (x + z)) - t_1
	else:
		tmp = ((z - t_1) + (x + y)) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(t) * z)
	tmp = 0.0
	if (Float64(x + y) <= 1e+106)
		tmp = Float64(Float64(Float64(b * Float64(a - 0.5)) + Float64(x + z)) - t_1);
	else
		tmp = Float64(Float64(Float64(z - t_1) + Float64(x + y)) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(t) * z;
	tmp = 0.0;
	if ((x + y) <= 1e+106)
		tmp = ((b * (a - 0.5)) + (x + z)) - t_1;
	else
		tmp = ((z - t_1) + (x + y)) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e+106], N[(N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(z - t$95$1), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.00000000000000009e106

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around 0 85.4%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t} \]

   if 1.00000000000000009e106 < (+.f64 x y)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in a around inf 96.7%

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

      1. *-commutative 96.7%

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

   6. Simplified 96.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+106}:\\ \;\;\;\;\left(b \cdot \left(a - 0.5\right) + \left(x + z\right)\right) - \log t \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z - \log t \cdot z\right) + \left(x + y\right)\right) + a \cdot b\\ \end{array} \]

Alternative 5: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+223} \lor \neg \left(z \leq 3 \cdot 10^{+105}\right):\\ \;\;\;\;\left(z + b \cdot \left(a - 0.5\right)\right) - \log t \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.7e+223) (not (<= z 3e+105)))
   (- (+ z (* b (- a 0.5))) (* (log t) z))
   (+ (+ x y) (+ (* a b) (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.7e+223) || !(z <= 3e+105)) {
		tmp = (z + (b * (a - 0.5))) - (log(t) * z);
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.7d+223)) .or. (.not. (z <= 3d+105))) then
        tmp = (z + (b * (a - 0.5d0))) - (log(t) * z)
    else
        tmp = (x + y) + ((a * b) + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.7e+223) || !(z <= 3e+105)) {
		tmp = (z + (b * (a - 0.5))) - (Math.log(t) * z);
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.7e+223) or not (z <= 3e+105):
		tmp = (z + (b * (a - 0.5))) - (math.log(t) * z)
	else:
		tmp = (x + y) + ((a * b) + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.7e+223) || !(z <= 3e+105))
		tmp = Float64(Float64(z + Float64(b * Float64(a - 0.5))) - Float64(log(t) * z));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.7e+223) || ~((z <= 3e+105)))
		tmp = (z + (b * (a - 0.5))) - (log(t) * z);
	else
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.7e+223], N[Not[LessEqual[z, 3e+105]], $MachinePrecision]], N[(N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.70000000000000041e223 or 3.0000000000000001e105 < z

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.5%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around 0 97.6%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t} \]

   5. Taylor expanded in x around 0 95.7%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + z\right) - z \cdot \log t} \]

   if -4.70000000000000041e223 < z < 3.0000000000000001e105

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 93.0%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 93.0%

      \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+223} \lor \neg \left(z \leq 3 \cdot 10^{+105}\right):\\ \;\;\;\;\left(z + b \cdot \left(a - 0.5\right)\right) - \log t \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \]

Alternative 6: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -5 \cdot 10^{+265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+106}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (log t)) z)))
   (if (<= z -5e+265)
     t_1
     (if (<= z 2.3e+106) (+ (+ x y) (+ (* a b) (* -0.5 b))) (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - log(t)) * z;
	double tmp;
	if (z <= -5e+265) {
		tmp = t_1;
	} else if (z <= 2.3e+106) {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + 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 = (1.0d0 - log(t)) * z
    if (z <= (-5d+265)) then
        tmp = t_1
    else if (z <= 2.3d+106) then
        tmp = (x + y) + ((a * b) + ((-0.5d0) * b))
    else
        tmp = y + 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 = (1.0 - Math.log(t)) * z;
	double tmp;
	if (z <= -5e+265) {
		tmp = t_1;
	} else if (z <= 2.3e+106) {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - math.log(t)) * z
	tmp = 0
	if z <= -5e+265:
		tmp = t_1
	elif z <= 2.3e+106:
		tmp = (x + y) + ((a * b) + (-0.5 * b))
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - log(t)) * z)
	tmp = 0.0
	if (z <= -5e+265)
		tmp = t_1;
	elseif (z <= 2.3e+106)
		tmp = Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)));
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - log(t)) * z;
	tmp = 0.0;
	if (z <= -5e+265)
		tmp = t_1;
	elseif (z <= 2.3e+106)
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5e+265], t$95$1, If[LessEqual[z, 2.3e+106], N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000002e265

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.5%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.7%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z} \]

   if -5.0000000000000002e265 < z < 2.3000000000000002e106

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 92.3%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 92.4%

      \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]

   if 2.3000000000000002e106 < z

   1. Initial program 99.3%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.3%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.3%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.3%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.3%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.3%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.3%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.3%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.6%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in b around 0 78.8%

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

   6. Taylor expanded in x around 0 76.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+265}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+106}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(1 - \log t\right) \cdot z\\ \end{array} \]

Alternative 7: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+265}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) - \log t \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.5e+265)
   (* (- 1.0 (log t)) z)
   (if (<= z 1.6e+99)
     (+ (+ x y) (+ (* a b) (* -0.5 b)))
     (- (+ x z) (* (log t) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.5e+265) {
		tmp = (1.0 - log(t)) * z;
	} else if (z <= 1.6e+99) {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	} else {
		tmp = (x + z) - (log(t) * 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 <= (-3.5d+265)) then
        tmp = (1.0d0 - log(t)) * z
    else if (z <= 1.6d+99) then
        tmp = (x + y) + ((a * b) + ((-0.5d0) * b))
    else
        tmp = (x + z) - (log(t) * 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 <= -3.5e+265) {
		tmp = (1.0 - Math.log(t)) * z;
	} else if (z <= 1.6e+99) {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	} else {
		tmp = (x + z) - (Math.log(t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.5e+265:
		tmp = (1.0 - math.log(t)) * z
	elif z <= 1.6e+99:
		tmp = (x + y) + ((a * b) + (-0.5 * b))
	else:
		tmp = (x + z) - (math.log(t) * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.5e+265)
		tmp = Float64(Float64(1.0 - log(t)) * z);
	elseif (z <= 1.6e+99)
		tmp = Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)));
	else
		tmp = Float64(Float64(x + z) - Float64(log(t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.5e+265)
		tmp = (1.0 - log(t)) * z;
	elseif (z <= 1.6e+99)
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	else
		tmp = (x + z) - (log(t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.5e+265], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.6e+99], N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e265

   1. Initial program 99.5%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.5%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.5%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.5%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.7%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in z around inf 99.7%

      \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z} \]

   if -3.5e265 < z < 1.6e99

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 92.3%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 92.3%

      \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]

   if 1.6e99 < z

   1. Initial program 99.4%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.4%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in b around 0 79.1%

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

   5. Taylor expanded in y around 0 73.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+265}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+99}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) - \log t \cdot z\\ \end{array} \]

Alternative 8: 82.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+265} \lor \neg \left(z \leq 2.3 \cdot 10^{+106}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e+265) (not (<= z 2.3e+106)))
   (* (- 1.0 (log t)) z)
   (+ (+ x y) (+ (* a b) (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+265) || !(z <= 2.3e+106)) {
		tmp = (1.0 - log(t)) * z;
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.5d+265)) .or. (.not. (z <= 2.3d+106))) then
        tmp = (1.0d0 - log(t)) * z
    else
        tmp = (x + y) + ((a * b) + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e+265) || !(z <= 2.3e+106)) {
		tmp = (1.0 - Math.log(t)) * z;
	} else {
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e+265) or not (z <= 2.3e+106):
		tmp = (1.0 - math.log(t)) * z
	else:
		tmp = (x + y) + ((a * b) + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e+265) || !(z <= 2.3e+106))
		tmp = Float64(Float64(1.0 - log(t)) * z);
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e+265) || ~((z <= 2.3e+106)))
		tmp = (1.0 - log(t)) * z;
	else
		tmp = (x + y) + ((a * b) + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e+265], N[Not[LessEqual[z, 2.3e+106]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e265 or 2.3000000000000002e106 < z

   1. Initial program 99.4%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.4%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.4%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.4%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.6%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z} \]

   if -3.5e265 < z < 2.3000000000000002e106

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 92.3%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 92.4%

      \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+265} \lor \neg \left(z \leq 2.3 \cdot 10^{+106}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right)\\ \end{array} \]

Alternative 9: 72.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+167} \lor \neg \left(t_1 \leq 2 \cdot 10^{+205}\right):\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+167) (not (<= t_1 2e+205)))
     (+ x t_1)
     (+ (+ x y) (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+167) || !(t_1 <= 2e+205)) {
		tmp = x + t_1;
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+167)) .or. (.not. (t_1 <= 2d+205))) then
        tmp = x + t_1
    else
        tmp = (x + y) + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+167) || !(t_1 <= 2e+205)) {
		tmp = x + t_1;
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+167) or not (t_1 <= 2e+205):
		tmp = x + t_1
	else:
		tmp = (x + y) + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+167) || !(t_1 <= 2e+205))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(x + y) + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+167) || ~((t_1 <= 2e+205)))
		tmp = x + t_1;
	else
		tmp = (x + y) + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+167], N[Not[LessEqual[t$95$1, 2e+205]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1e167 or 2.00000000000000003e205 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around 0 95.7%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t} \]

   5. Taylor expanded in z around 0 89.2%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + x} \]

   if -1e167 < (*.f64 (-.f64 a 1/2) b) < 2.00000000000000003e205

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   2. Taylor expanded in z around 0 72.8%

      \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

   3. Taylor expanded in a around 0 68.6%

      \[\leadsto \left(y + x\right) + \color{blue}{-0.5 \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 68.6%

         \[\leadsto \left(y + x\right) + \color{blue}{b \cdot -0.5} \]

   5. Simplified 68.6%

      \[\leadsto \left(y + x\right) + \color{blue}{b \cdot -0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+167} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+205}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]

Alternative 10: 66.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+130} \lor \neg \left(t_1 \leq 10^{+120}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+130) (not (<= t_1 1e+120))) t_1 (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+130) || !(t_1 <= 1e+120)) {
		tmp = t_1;
	} else {
		tmp = x + 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 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+130)) .or. (.not. (t_1 <= 1d+120))) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+130) || !(t_1 <= 1e+120)) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+130) or not (t_1 <= 1e+120):
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+130) || !(t_1 <= 1e+120))
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+130) || ~((t_1 <= 1e+120)))
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+130], N[Not[LessEqual[t$95$1, 1e+120]], $MachinePrecision]], t$95$1, N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.0000000000000001e130 or 9.9999999999999998e119 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.9%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in b around inf 79.1%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b} \]

   if -1.0000000000000001e130 < (*.f64 (-.f64 a 1/2) b) < 9.9999999999999998e119

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.7%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in b around 0 90.0%

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

   5. Taylor expanded in z around 0 61.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+130} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+120}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 79.0% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (+ x y) (+ (* a b) (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + ((a * b) + (-0.5 * b));
}

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) + ((a * b) + ((-0.5d0) * b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + y) + ((a * b) + (-0.5 * b));
}

Python

def code(x, y, z, t, a, b):
	return (x + y) + ((a * b) + (-0.5 * b))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + y) + Float64(Float64(a * b) + Float64(-0.5 * b)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + y) + ((a * b) + (-0.5 * b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in z around 0 80.2%

   \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

3. Taylor expanded in a around 0 80.2%

   \[\leadsto \left(y + x\right) + \color{blue}{\left(a \cdot b + -0.5 \cdot b\right)} \]

4. Final simplification 80.2%

   \[\leadsto \left(x + y\right) + \left(a \cdot b + -0.5 \cdot b\right) \]

Alternative 12: 62.7% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.8e+129) (+ x (* b (- a 0.5))) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 4.8e+129) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + 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 (y <= 4.8d+129) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = x + 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 (y <= 4.8e+129) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 4.8e+129:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 4.8e+129)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 4.8e+129)
		tmp = x + (b * (a - 0.5));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 4.8e+129], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.7999999999999997e129

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around 0 86.7%

      \[\leadsto \color{blue}{\left(\left(a - 0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t} \]

   5. Taylor expanded in z around 0 64.9%

      \[\leadsto \color{blue}{\left(a - 0.5\right) \cdot b + x} \]

   if 4.7999999999999997e129 < y

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 100.0%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 100.0%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 100.0%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 100.0%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in b around 0 79.9%

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

   5. Taylor expanded in z around 0 74.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 79.0% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a - 0.5\right) + \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (x + 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 = (b * (a - 0.5d0)) + (x + y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (x + y);
}

Python

def code(x, y, z, t, a, b):
	return (b * (a - 0.5)) + (x + y)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(b * Float64(a - 0.5)) + Float64(x + y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a - 0.5)) + (x + y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

2. Taylor expanded in z around 0 80.2%

   \[\leadsto \color{blue}{\left(y + x\right)} + \left(a - 0.5\right) \cdot b \]

3. Final simplification 80.2%

   \[\leadsto b \cdot \left(a - 0.5\right) + \left(x + y\right) \]

Alternative 14: 29.1% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-244}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.45e+83) x (if (<= x 4.4e-244) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.45e+83) {
		tmp = x;
	} else if (x <= 4.4e-244) {
		tmp = a * b;
	} else {
		tmp = 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 (x <= (-1.45d+83)) then
        tmp = x
    else if (x <= 4.4d-244) then
        tmp = a * b
    else
        tmp = 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 (x <= -1.45e+83) {
		tmp = x;
	} else if (x <= 4.4e-244) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.45e+83:
		tmp = x
	elif x <= 4.4e-244:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.45e+83)
		tmp = x;
	elseif (x <= 4.4e-244)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.45e+83)
		tmp = x;
	elseif (x <= 4.4e-244)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.45e+83], x, If[LessEqual[x, 4.4e-244], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e83

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in x around inf 62.0%

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

   if -1.45e83 < x < 4.39999999999999969e-244

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.7%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.7%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.7%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.9%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in a around inf 33.5%

      \[\leadsto \color{blue}{a \cdot b} \]

   if 4.39999999999999969e-244 < x

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around inf 27.6%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-244}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 52.6% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+88}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+127}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.65e+88) (* a b) (if (<= a 5e+127) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.65e+88) {
		tmp = a * b;
	} else if (a <= 5e+127) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-2.65d+88)) then
        tmp = a * b
    else if (a <= 5d+127) then
        tmp = x + y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.65e+88) {
		tmp = a * b;
	} else if (a <= 5e+127) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.65e+88:
		tmp = a * b
	elif a <= 5e+127:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.65e+88)
		tmp = Float64(a * b);
	elseif (a <= 5e+127)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -2.65e+88)
		tmp = a * b;
	elseif (a <= 5e+127)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.65e+88], N[(a * b), $MachinePrecision], If[LessEqual[a, 5e+127], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.64999999999999994e88 or 5.0000000000000004e127 < a

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in z around 0 99.9%

      \[\leadsto \left(\left(x + y\right) + \color{blue}{\left(1 - \log t\right) \cdot z}\right) + \left(a + -0.5\right) \cdot b \]

   5. Taylor expanded in a around inf 65.7%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -2.64999999999999994e88 < a < 5.0000000000000004e127

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in b around 0 71.8%

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

   5. Taylor expanded in z around 0 50.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+88}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+127}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 16: 28.8% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 2.3e+38) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.3e+38) {
		tmp = x;
	} else {
		tmp = 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 (y <= 2.3d+38) then
        tmp = x
    else
        tmp = 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 (y <= 2.3e+38) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.3e+38:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.3e+38)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.3e+38)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.3e+38], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.3000000000000001e38

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.8%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in x around inf 24.7%

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

   if 2.3000000000000001e38 < y

   1. Initial program 99.9%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 99.9%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

      3. associate--l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

      4. distribute-rgt-neg-in 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

      5. sub-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

   4. Taylor expanded in y around inf 46.1%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 21.9% accurate, 115.0× 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 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. Step-by-step derivation

   1. remove-double-neg 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \color{blue}{\left(-\left(-\left(a - 0.5\right) \cdot b\right)\right)} \]

   2. distribute-rgt-neg-out 99.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(-\color{blue}{\left(a - 0.5\right) \cdot \left(-b\right)}\right) \]

   3. associate--l+ 99.8%

      \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(-\left(a - 0.5\right) \cdot \left(-b\right)\right) \]

   4. distribute-rgt-neg-in 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(-\left(-b\right)\right)} \]

   5. sub-neg 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \color{blue}{\left(a + \left(-0.5\right)\right)} \cdot \left(-\left(-b\right)\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + \color{blue}{-0.5}\right) \cdot \left(-\left(-b\right)\right) \]

   7. remove-double-neg 99.8%

      \[\leadsto \left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot \color{blue}{b} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right) + \left(a + -0.5\right) \cdot b} \]

4. Taylor expanded in x around inf 22.7%

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

5. Final simplification 22.7%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \left(\left(x + y\right) + \frac{\left(1 - {\log t}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t))))
  (* (- a 0.5) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - pow(log(t), 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
}

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) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x + y) + (((1.0 - Math.pow(Math.log(t), 2.0)) * z) / (1.0 + Math.log(t)))) + ((a - 0.5) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x + y) + (((1.0 - math.pow(math.log(t), 2.0)) * z) / (1.0 + math.log(t)))) + ((a - 0.5) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x + y) + Float64(Float64(Float64(1.0 - (log(t) ^ 2.0)) * z) / Float64(1.0 + log(t)))) + Float64(Float64(a - 0.5) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x + y) + (((1.0 - (log(t) ^ 2.0)) * z) / (1.0 + log(t)))) + ((a - 0.5) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))