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

Percentage Accurate: 99.8% → 99.8%

Time: 14.0s

Alternatives: 18

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.9%

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

Alternative 2: 92.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+115} \lor \neg \left(t_1 \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + \left(z + b \cdot -0.5\right)\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -1e+115) (not (<= t_1 2e+127)))
     (+ (* b (+ a -0.5)) (+ x y))
     (- (+ x (+ y (+ z (* b -0.5)))) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+115) || !(t_1 <= 2e+127)) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (x + (y + (z + (b * -0.5)))) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((t_1 <= (-1d+115)) .or. (.not. (t_1 <= 2d+127))) then
        tmp = (b * (a + (-0.5d0))) + (x + y)
    else
        tmp = (x + (y + (z + (b * (-0.5d0))))) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+115) || !(t_1 <= 2e+127)) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (x + (y + (z + (b * -0.5)))) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -1e+115) or not (t_1 <= 2e+127):
		tmp = (b * (a + -0.5)) + (x + y)
	else:
		tmp = (x + (y + (z + (b * -0.5)))) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -1e+115) || !(t_1 <= 2e+127))
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	else
		tmp = Float64(Float64(x + Float64(y + Float64(z + Float64(b * -0.5)))) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((t_1 <= -1e+115) || ~((t_1 <= 2e+127)))
		tmp = (b * (a + -0.5)) + (x + y);
	else
		tmp = (x + (y + (z + (b * -0.5)))) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+115], N[Not[LessEqual[t$95$1, 2e+127]], $MachinePrecision]], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y + N[(z + N[(b * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1e115 or 1.99999999999999991e127 < (*.f64 (-.f64 a 1/2) 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. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 96.2%

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

      1. +-commutative 96.2%

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

   6. Simplified 96.2%

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

   if -1e115 < (*.f64 (-.f64 a 1/2) b) < 1.99999999999999991e127

   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. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   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 0 98.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -1 \cdot 10^{+115} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + \left(z + b \cdot -0.5\right)\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 3: 90.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+115} \lor \neg \left(t_1 \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -1e+115) (not (<= t_1 5e+114)))
     (+ (* b (+ a -0.5)) (+ x y))
     (- (+ x (+ y z)) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+115) || !(t_1 <= 5e+114)) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (x + (y + z)) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if ((t_1 <= (-1d+115)) .or. (.not. (t_1 <= 5d+114))) then
        tmp = (b * (a + (-0.5d0))) + (x + y)
    else
        tmp = (x + (y + z)) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -1e+115) || !(t_1 <= 5e+114)) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (x + (y + z)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -1e+115) or not (t_1 <= 5e+114):
		tmp = (b * (a + -0.5)) + (x + y)
	else:
		tmp = (x + (y + z)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -1e+115) || !(t_1 <= 5e+114))
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	else
		tmp = Float64(Float64(x + Float64(y + z)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((t_1 <= -1e+115) || ~((t_1 <= 5e+114)))
		tmp = (b * (a + -0.5)) + (x + y);
	else
		tmp = (x + (y + z)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+115], N[Not[LessEqual[t$95$1, 5e+114]], $MachinePrecision]], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1e115 or 5.0000000000000001e114 < (*.f64 (-.f64 a 1/2) 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. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 94.8%

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

      1. +-commutative 94.8%

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

   6. Simplified 94.8%

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

   if -1e115 < (*.f64 (-.f64 a 1/2) b) < 5.0000000000000001e114

   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. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   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 0 98.6%

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

   5. Taylor expanded in b around 0 93.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -1 \cdot 10^{+115} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+114}\right):\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 4: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a + -0.5\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+125}:\\ \;\;\;\;t_1 + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(y + z \cdot \left(1 - \log t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ a -0.5))))
   (if (<= x -1.45e+125) (+ t_1 (+ x y)) (+ t_1 (+ y (* z (- 1.0 (log t))))))))

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 (x <= -1.45e+125) {
		tmp = t_1 + (x + y);
	} else {
		tmp = t_1 + (y + (z * (1.0 - log(t))));
	}
	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 (x <= (-1.45d+125)) then
        tmp = t_1 + (x + y)
    else
        tmp = t_1 + (y + (z * (1.0d0 - log(t))))
    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 (x <= -1.45e+125) {
		tmp = t_1 + (x + y);
	} else {
		tmp = t_1 + (y + (z * (1.0 - Math.log(t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a + -0.5)
	tmp = 0
	if x <= -1.45e+125:
		tmp = t_1 + (x + y)
	else:
		tmp = t_1 + (y + (z * (1.0 - math.log(t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a + -0.5))
	tmp = 0.0
	if (x <= -1.45e+125)
		tmp = Float64(t_1 + Float64(x + y));
	else
		tmp = Float64(t_1 + Float64(y + Float64(z * Float64(1.0 - log(t)))));
	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 (x <= -1.45e+125)
		tmp = t_1 + (x + y);
	else
		tmp = t_1 + (y + (z * (1.0 - log(t))));
	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[x, -1.45e+125], N[(t$95$1 + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999997e125

   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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 96.8%

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

      1. +-commutative 96.8%

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

   6. Simplified 96.8%

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

   if -1.44999999999999997e125 < 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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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%

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

   5. Taylor expanded in x around 0 87.2%

      \[\leadsto \color{blue}{\left(y + z \cdot \left(1 - \log t\right)\right)} + \left(a + -0.5\right) \cdot b \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+125}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(y + z \cdot \left(1 - \log t\right)\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a + -0.5)) + ((z * (1.0 - log(t))) + (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))) + ((z * (1.0d0 - log(t))) + (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)) + ((z * (1.0 - Math.log(t))) + (x + y));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

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%

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

5. Final simplification 99.9%

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

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((z - (z * log(t))) + (x + y)) + (b * (a + (-0.5d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

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. Final simplification 99.9%

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

Alternative 7: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+239}:\\ \;\;\;\;\left(x + z\right) - t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t_1\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= z -3.7e+239)
     (- (+ x z) t_1)
     (if (<= z 5.5e+60) (+ (* b (+ a -0.5)) (+ x y)) (+ (- z t_1) (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if (z <= -3.7e+239) {
		tmp = (x + z) - t_1;
	} else if (z <= 5.5e+60) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (z - t_1) + (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 = z * log(t)
    if (z <= (-3.7d+239)) then
        tmp = (x + z) - t_1
    else if (z <= 5.5d+60) then
        tmp = (b * (a + (-0.5d0))) + (x + y)
    else
        tmp = (z - t_1) + (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 = z * Math.log(t);
	double tmp;
	if (z <= -3.7e+239) {
		tmp = (x + z) - t_1;
	} else if (z <= 5.5e+60) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = (z - t_1) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if z <= -3.7e+239:
		tmp = (x + z) - t_1
	elif z <= 5.5e+60:
		tmp = (b * (a + -0.5)) + (x + y)
	else:
		tmp = (z - t_1) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (z <= -3.7e+239)
		tmp = Float64(Float64(x + z) - t_1);
	elseif (z <= 5.5e+60)
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	else
		tmp = Float64(Float64(z - t_1) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if (z <= -3.7e+239)
		tmp = (x + z) - t_1;
	elseif (z <= 5.5e+60)
		tmp = (b * (a + -0.5)) + (x + y);
	else
		tmp = (z - t_1) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+239], N[(N[(x + z), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[z, 5.5e+60], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(z - t$95$1), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.69999999999999998e239

   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. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

   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 a around 0 99.4%

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

   5. Taylor expanded in b around 0 99.4%

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

   6. Taylor expanded in y around 0 94.8%

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

      1. +-commutative 94.8%

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

   8. Simplified 94.8%

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

   if -3.69999999999999998e239 < z < 5.5000000000000001e60

   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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 92.6%

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

      1. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if 5.5000000000000001e60 < z

   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. associate--l+ 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   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 0 93.1%

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

   5. Taylor expanded in b around 0 93.1%

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

      1. associate-+r+ 93.1%

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

      2. associate--l+ 93.1%

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

      3. +-commutative 93.1%

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

      4. *-commutative 93.1%

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

   7. Applied egg-rr 93.1%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+239}:\\ \;\;\;\;\left(x + z\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - z \cdot \log t\right) + \left(x + y\right)\\ \end{array} \]

Alternative 8: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+239} \lor \neg \left(z \leq 3.05 \cdot 10^{+113}\right):\\ \;\;\;\;\left(x + z\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+239) (not (<= z 3.05e+113)))
   (- (+ x z) (* z (log t)))
   (+ (* b (+ a -0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e+239) || !(z <= 3.05e+113)) {
		tmp = (x + z) - (z * log(t));
	} else {
		tmp = (b * (a + -0.5)) + (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 ((z <= (-8d+239)) .or. (.not. (z <= 3.05d+113))) then
        tmp = (x + z) - (z * log(t))
    else
        tmp = (b * (a + (-0.5d0))) + (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 ((z <= -8e+239) || !(z <= 3.05e+113)) {
		tmp = (x + z) - (z * Math.log(t));
	} else {
		tmp = (b * (a + -0.5)) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8e+239) or not (z <= 3.05e+113):
		tmp = (x + z) - (z * math.log(t))
	else:
		tmp = (b * (a + -0.5)) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8e+239) || !(z <= 3.05e+113))
		tmp = Float64(Float64(x + z) - Float64(z * log(t)));
	else
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8e+239) || ~((z <= 3.05e+113)))
		tmp = (x + z) - (z * log(t));
	else
		tmp = (b * (a + -0.5)) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8e+239], N[Not[LessEqual[z, 3.05e+113]], $MachinePrecision]], N[(N[(x + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999993e239 or 3.04999999999999998e113 < z

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 95.1%

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

   5. Taylor expanded in b around 0 95.1%

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

   6. Taylor expanded in y around 0 87.6%

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

      1. +-commutative 87.6%

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

   8. Simplified 87.6%

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

   if -7.99999999999999993e239 < z < 3.04999999999999998e113

   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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 91.0%

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

      1. +-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+239} \lor \neg \left(z \leq 3.05 \cdot 10^{+113}\right):\\ \;\;\;\;\left(x + z\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 9: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+239} \lor \neg \left(z \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e+239) (not (<= z 9.8e+113)))
   (* z (- 1.0 (log t)))
   (+ (* b (+ a -0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e+239) || !(z <= 9.8e+113)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (b * (a + -0.5)) + (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 ((z <= (-3d+239)) .or. (.not. (z <= 9.8d+113))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (b * (a + (-0.5d0))) + (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 ((z <= -3e+239) || !(z <= 9.8e+113)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (b * (a + -0.5)) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3e+239) or not (z <= 9.8e+113):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (b * (a + -0.5)) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e+239) || !(z <= 9.8e+113))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3e+239) || ~((z <= 9.8e+113)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (b * (a + -0.5)) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e+239], N[Not[LessEqual[z, 9.8e+113]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e239 or 9.80000000000000043e113 < z

   1. Initial program 99.6%

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

      1. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 95.0%

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

   5. Taylor expanded in b around 0 95.0%

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

   6. Taylor expanded in z around inf 75.9%

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

   if -2.9999999999999999e239 < z < 9.80000000000000043e113

   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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 91.0%

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

      1. +-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+239} \lor \neg \left(z \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \end{array} \]

Alternative 10: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.45e+240)
   (* z (- 1.0 (log t)))
   (if (<= z 9.2e+113) (+ (* b (+ a -0.5)) (+ x y)) (- z (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.45e+240) {
		tmp = z * (1.0 - log(t));
	} else if (z <= 9.2e+113) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = z - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.45d+240)) then
        tmp = z * (1.0d0 - log(t))
    else if (z <= 9.2d+113) then
        tmp = (b * (a + (-0.5d0))) + (x + y)
    else
        tmp = z - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.45e+240) {
		tmp = z * (1.0 - Math.log(t));
	} else if (z <= 9.2e+113) {
		tmp = (b * (a + -0.5)) + (x + y);
	} else {
		tmp = z - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.45e+240:
		tmp = z * (1.0 - math.log(t))
	elif z <= 9.2e+113:
		tmp = (b * (a + -0.5)) + (x + y)
	else:
		tmp = z - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.45e+240)
		tmp = Float64(z * Float64(1.0 - log(t)));
	elseif (z <= 9.2e+113)
		tmp = Float64(Float64(b * Float64(a + -0.5)) + Float64(x + y));
	else
		tmp = Float64(z - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.45e+240)
		tmp = z * (1.0 - log(t));
	elseif (z <= 9.2e+113)
		tmp = (b * (a + -0.5)) + (x + y);
	else
		tmp = z - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.45e+240], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+113], N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45e240

   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. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. metadata-eval 99.3%

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

   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 a around 0 99.4%

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

   5. Taylor expanded in b around 0 99.4%

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

   6. Taylor expanded in z around inf 85.7%

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

   if -2.45e240 < z < 9.19999999999999987e113

   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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 z around 0 91.0%

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

      1. +-commutative 91.0%

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

   6. Simplified 91.0%

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

   if 9.19999999999999987e113 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 78.7%

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

   3. Taylor expanded in b around 0 72.5%

      \[\leadsto \color{blue}{z - z \cdot \log t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(a + -0.5\right) + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - z \cdot \log t\\ \end{array} \]

Alternative 11: 61.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+74} \lor \neg \left(b \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.25e+74) (not (<= b 6.2e+46))) (* (- a 0.5) b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.25e+74) || !(b <= 6.2e+46)) {
		tmp = (a - 0.5) * b;
	} 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 ((b <= (-2.25d+74)) .or. (.not. (b <= 6.2d+46))) then
        tmp = (a - 0.5d0) * b
    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 ((b <= -2.25e+74) || !(b <= 6.2e+46)) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.25e+74) or not (b <= 6.2e+46):
		tmp = (a - 0.5) * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.25e+74) || !(b <= 6.2e+46))
		tmp = Float64(Float64(a - 0.5) * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.25e+74) || ~((b <= 6.2e+46)))
		tmp = (a - 0.5) * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.25e+74], N[Not[LessEqual[b, 6.2e+46]], $MachinePrecision]], N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.25e74 or 6.1999999999999995e46 < 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. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 inf 69.3%

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

   if -2.25e74 < b < 6.1999999999999995e46

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 0 89.1%

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

   5. Taylor expanded in b around 0 86.1%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. +-commutative 59.4%

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

   8. Simplified 59.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+74} \lor \neg \left(b \leq 6.2 \cdot 10^{+46}\right):\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 12: 62.5% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+162}:\\ \;\;\;\;x + b \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.6e+162) (+ 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 <= 1.6e+162) {
		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 <= 1.6d+162) 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 <= 1.6e+162) {
		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 <= 1.6e+162:
		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 <= 1.6e+162)
		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 <= 1.6e+162)
		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, 1.6e+162], 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 < 1.6000000000000001e162

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 64.3%

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

   if 1.6000000000000001e162 < 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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 a around 0 94.6%

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

   5. Taylor expanded in b around 0 91.9%

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

   6. Taylor expanded in z around 0 83.1%

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

      1. +-commutative 83.1%

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

   8. Simplified 83.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{+162}:\\ \;\;\;\;x + b \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 64.0% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a + -0.5\right)\\ \mathbf{if}\;y \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ a -0.5)))) (if (<= y 1.7e+25) (+ x t_1) (+ y t_1))))

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 (y <= 1.7e+25) {
		tmp = x + t_1;
	} 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 = b * (a + (-0.5d0))
    if (y <= 1.7d+25) then
        tmp = x + t_1
    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 = b * (a + -0.5);
	double tmp;
	if (y <= 1.7e+25) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a + -0.5)
	tmp = 0
	if y <= 1.7e+25:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a + -0.5))
	tmp = 0.0
	if (y <= 1.7e+25)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	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 (y <= 1.7e+25)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	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[y, 1.7e+25], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.69999999999999992e25

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 63.9%

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

   if 1.69999999999999992e25 < 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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 83.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;x + b \cdot \left(a + -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a + -0.5\right)\\ \end{array} \]

Alternative 14: 78.3% 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 99.9%

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

   1. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

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 79.7%

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

   1. +-commutative 79.7%

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

6. Simplified 79.7%

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

7. Final simplification 79.7%

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

Alternative 15: 27.9% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 5.1e-46) x (if (<= y 8.5e+161) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 5.1e-46) {
		tmp = x;
	} else if (y <= 8.5e+161) {
		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 (y <= 5.1d-46) then
        tmp = x
    else if (y <= 8.5d+161) 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 (y <= 5.1e-46) {
		tmp = x;
	} else if (y <= 8.5e+161) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 5.1e-46:
		tmp = x
	elif y <= 8.5e+161:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 5.1e-46)
		tmp = x;
	elseif (y <= 8.5e+161)
		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 (y <= 5.1e-46)
		tmp = x;
	elseif (y <= 8.5e+161)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 5.1e-46], x, If[LessEqual[y, 8.5e+161], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 5.0999999999999997e-46

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 0 79.4%

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

   5. Taylor expanded in b around 0 66.7%

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

   6. Taylor expanded in x around inf 30.8%

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

   if 5.0999999999999997e-46 < y < 8.50000000000000007e161

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 46.1%

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

      1. *-commutative 46.1%

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

   6. Simplified 46.1%

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

   if 8.50000000000000007e161 < 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. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 a around 0 94.6%

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

   5. Taylor expanded in b around 0 91.9%

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

   6. Taylor expanded in y around inf 77.0%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.1 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16: 50.1% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+150) (* a b) (if (<= b 2.2e+129) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+150) {
		tmp = a * b;
	} else if (b <= 2.2e+129) {
		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 (b <= (-3.6d+150)) then
        tmp = a * b
    else if (b <= 2.2d+129) 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 (b <= -3.6e+150) {
		tmp = a * b;
	} else if (b <= 2.2e+129) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+150:
		tmp = a * b
	elif b <= 2.2e+129:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+150)
		tmp = Float64(a * b);
	elseif (b <= 2.2e+129)
		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 (b <= -3.6e+150)
		tmp = a * b;
	elseif (b <= 2.2e+129)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+150], N[(a * b), $MachinePrecision], If[LessEqual[b, 2.2e+129], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.59999999999999986e150 or 2.1999999999999999e129 < 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. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   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 a around inf 52.9%

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

      1. *-commutative 52.9%

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

   6. Simplified 52.9%

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

   if -3.59999999999999986e150 < b < 2.1999999999999999e129

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 0 86.3%

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

   5. Taylor expanded in b around 0 81.4%

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

   6. Taylor expanded in z around 0 55.9%

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

      1. +-commutative 55.9%

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

   8. Simplified 55.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+129}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 17: 27.4% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.2e+25) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.2e+25) {
		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 <= 1.2d+25) 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 <= 1.2e+25) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.2e+25:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.2e+25)
		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 <= 1.2e+25)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.2e+25], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.19999999999999998e25

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 0 77.8%

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

   5. Taylor expanded in b around 0 64.4%

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

   6. Taylor expanded in x around inf 28.4%

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

   if 1.19999999999999998e25 < 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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   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 0 75.5%

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

   5. Taylor expanded in b around 0 70.4%

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

   6. Taylor expanded in y around inf 54.4%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 21.6% 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 99.9%

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

   1. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

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 0 77.3%

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

5. Taylor expanded in b around 0 65.7%

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

6. Taylor expanded in x around inf 23.5%

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

7. Final simplification 23.5%

   \[\leadsto x \]

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 2023297 
(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)))