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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

Alternatives: 15

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: 99.9% 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

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((z - (z * log(t))) + (x + y)) + ((a + -0.5) * b);
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[(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. 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. Final simplification 99.9%

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

Alternative 2: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+59} \lor \neg \left(b \leq 1.05 \cdot 10^{+86}\right):\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z - z \cdot \log t\right) + \left(x + y\right)\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+59) (not (<= b 1.05e+86)))
   (+ (+ z (+ x y)) (* b (- a 0.5)))
   (+ (+ (- z (* z (log t))) (+ x y)) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+59) || !(b <= 1.05e+86)) {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	} else {
		tmp = ((z - (z * log(t))) + (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) :: tmp
    if ((b <= (-1.3d+59)) .or. (.not. (b <= 1.05d+86))) then
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    else
        tmp = ((z - (z * log(t))) + (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 tmp;
	if ((b <= -1.3e+59) || !(b <= 1.05e+86)) {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	} else {
		tmp = ((z - (z * Math.log(t))) + (x + y)) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+59) or not (b <= 1.05e+86):
		tmp = (z + (x + y)) + (b * (a - 0.5))
	else:
		tmp = ((z - (z * math.log(t))) + (x + y)) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+59) || !(b <= 1.05e+86))
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(Float64(z - Float64(z * log(t))) + Float64(x + y)) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+59) || ~((b <= 1.05e+86)))
		tmp = (z + (x + y)) + (b * (a - 0.5));
	else
		tmp = ((z - (z * log(t))) + (x + y)) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+59], N[Not[LessEqual[b, 1.05e+86]], $MachinePrecision]], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3e59 or 1.0499999999999999e86 < 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. add-sqr-sqrt 37.7%

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

      2. pow2 37.7%

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

   3. Applied egg-rr 57.8%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 93.6%

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

      1. associate-+r+ 93.6%

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

      2. +-commutative 93.6%

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

      3. +-commutative 93.6%

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

   6. Simplified 93.6%

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

   if -1.3e59 < b < 1.0499999999999999e86

   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 97.5%

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

      1. *-commutative 36.4%

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

   6. Simplified 97.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+59} \lor \neg \left(b \leq 1.05 \cdot 10^{+86}\right):\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z - z \cdot \log t\right) + \left(x + y\right)\right) + a \cdot b\\ \end{array} \]

Alternative 3: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\left(\left(z - t_1\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(\left(y + z\right) - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) -5e-40)
     (+ (+ (- z t_1) (+ x y)) (* a b))
     (+ (* (+ a -0.5) b) (- (+ y z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if ((x + y) <= -5e-40) {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	} else {
		tmp = ((a + -0.5) * b) + ((y + z) - 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 = z * log(t)
    if ((x + y) <= (-5d-40)) then
        tmp = ((z - t_1) + (x + y)) + (a * b)
    else
        tmp = ((a + (-0.5d0)) * b) + ((y + z) - 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 = z * Math.log(t);
	double tmp;
	if ((x + y) <= -5e-40) {
		tmp = ((z - t_1) + (x + y)) + (a * b);
	} else {
		tmp = ((a + -0.5) * b) + ((y + z) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= -5e-40:
		tmp = ((z - t_1) + (x + y)) + (a * b)
	else:
		tmp = ((a + -0.5) * b) + ((y + z) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= -5e-40)
		tmp = Float64(Float64(Float64(z - t_1) + Float64(x + y)) + Float64(a * b));
	else
		tmp = Float64(Float64(Float64(a + -0.5) * b) + Float64(Float64(y + z) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if ((x + y) <= -5e-40)
		tmp = ((z - t_1) + (x + y)) + (a * b);
	else
		tmp = ((a + -0.5) * b) + ((y + z) - t_1);
	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[N[(x + y), $MachinePrecision], -5e-40], N[(N[(N[(z - t$95$1), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(N[(y + z), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.99999999999999965e-40

   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 91.5%

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

      1. *-commutative 49.1%

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

   6. Simplified 91.5%

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

   if -4.99999999999999965e-40 < (+.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 x around 0 87.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\left(\left(z - z \cdot \log t\right) + \left(x + y\right)\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(\left(y + z\right) - z \cdot \log t\right)\\ \end{array} \]

Alternative 4: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+132} \lor \neg \left(z \leq 7.8 \cdot 10^{+25}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.9e+132) (not (<= z 7.8e+25)))
   (+ (* (+ a -0.5) b) (* z (- 1.0 (log t))))
   (+ (+ z (+ x y)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.9e+132) || !(z <= 7.8e+25)) {
		tmp = ((a + -0.5) * b) + (z * (1.0 - log(t)));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	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 <= (-4.9d+132)) .or. (.not. (z <= 7.8d+25))) then
        tmp = ((a + (-0.5d0)) * b) + (z * (1.0d0 - log(t)))
    else
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    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 <= -4.9e+132) || !(z <= 7.8e+25)) {
		tmp = ((a + -0.5) * b) + (z * (1.0 - Math.log(t)));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.9e+132) or not (z <= 7.8e+25):
		tmp = ((a + -0.5) * b) + (z * (1.0 - math.log(t)))
	else:
		tmp = (z + (x + y)) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.9e+132) || !(z <= 7.8e+25))
		tmp = Float64(Float64(Float64(a + -0.5) * b) + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.9e+132) || ~((z <= 7.8e+25)))
		tmp = ((a + -0.5) * b) + (z * (1.0 - log(t)));
	else
		tmp = (z + (x + y)) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.9e+132], N[Not[LessEqual[z, 7.8e+25]], $MachinePrecision]], N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9000000000000002e132 or 7.8000000000000004e25 < z

   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 99.7%

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

   5. Taylor expanded in z around inf 80.9%

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

   if -4.9000000000000002e132 < z < 7.8000000000000004e25

   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. add-sqr-sqrt 35.9%

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

      2. pow2 35.9%

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

   3. Applied egg-rr 54.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 94.2%

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

      1. associate-+r+ 94.2%

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

      2. +-commutative 94.2%

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

      3. +-commutative 94.2%

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

   6. Simplified 94.2%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+132} \lor \neg \left(z \leq 7.8 \cdot 10^{+25}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 5: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+130} \lor \neg \left(z \leq 7.5 \cdot 10^{+83}\right):\\ \;\;\;\;a \cdot b + \left(y + \left(z - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e+130) (not (<= z 7.5e+83)))
   (+ (* a b) (+ y (- z (* z (log t)))))
   (+ (+ z (+ x y)) (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e+130) || !(z <= 7.5e+83)) {
		tmp = (a * b) + (y + (z - (z * log(t))));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	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 <= (-9.5d+130)) .or. (.not. (z <= 7.5d+83))) then
        tmp = (a * b) + (y + (z - (z * log(t))))
    else
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    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 <= -9.5e+130) || !(z <= 7.5e+83)) {
		tmp = (a * b) + (y + (z - (z * Math.log(t))));
	} else {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e+130) or not (z <= 7.5e+83):
		tmp = (a * b) + (y + (z - (z * math.log(t))))
	else:
		tmp = (z + (x + y)) + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e+130) || !(z <= 7.5e+83))
		tmp = Float64(Float64(a * b) + Float64(y + Float64(z - Float64(z * log(t)))));
	else
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e+130) || ~((z <= 7.5e+83)))
		tmp = (a * b) + (y + (z - (z * log(t))));
	else
		tmp = (z + (x + y)) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e+130], N[Not[LessEqual[z, 7.5e+83]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(y + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000009e130 or 7.49999999999999989e83 < z

   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 0 89.6%

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

   5. Taylor expanded in a around inf 82.8%

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

      1. *-commutative 29.3%

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

   7. Simplified 82.8%

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

      1. sub-neg 82.8%

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

      2. associate-+l+ 82.8%

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

      3. sub-neg 82.8%

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

      4. *-commutative 82.8%

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

      5. *-un-lft-identity 82.8%

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

      6. distribute-rgt-out-- 82.8%

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

      7. +-commutative 82.8%

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

      8. distribute-rgt-out-- 82.8%

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

      9. *-un-lft-identity 82.8%

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

      10. *-commutative 82.8%

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

   9. Applied egg-rr 82.8%

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

   if -9.5000000000000009e130 < z < 7.49999999999999989e83

   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. add-sqr-sqrt 35.7%

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

      2. pow2 35.7%

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

   3. Applied egg-rr 54.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 93.3%

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

      1. associate-+r+ 93.3%

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

      2. +-commutative 93.3%

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

      3. +-commutative 93.3%

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

   6. Simplified 93.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+130} \lor \neg \left(z \leq 7.5 \cdot 10^{+83}\right):\\ \;\;\;\;a \cdot b + \left(y + \left(z - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 6: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;a \cdot b + \left(y + \left(z - t_1\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+87}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(\left(y + z\right) - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= z -3.5e+132)
     (+ (* a b) (+ y (- z t_1)))
     (if (<= z 2.1e+87)
       (+ (+ z (+ x y)) (* b (- a 0.5)))
       (+ (* a b) (- (+ y z) t_1))))))

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 <= -3.5e+132) {
		tmp = (a * b) + (y + (z - t_1));
	} else if (z <= 2.1e+87) {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	} else {
		tmp = (a * b) + ((y + z) - 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 = z * log(t)
    if (z <= (-3.5d+132)) then
        tmp = (a * b) + (y + (z - t_1))
    else if (z <= 2.1d+87) then
        tmp = (z + (x + y)) + (b * (a - 0.5d0))
    else
        tmp = (a * b) + ((y + z) - 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 = z * Math.log(t);
	double tmp;
	if (z <= -3.5e+132) {
		tmp = (a * b) + (y + (z - t_1));
	} else if (z <= 2.1e+87) {
		tmp = (z + (x + y)) + (b * (a - 0.5));
	} else {
		tmp = (a * b) + ((y + z) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if z <= -3.5e+132:
		tmp = (a * b) + (y + (z - t_1))
	elif z <= 2.1e+87:
		tmp = (z + (x + y)) + (b * (a - 0.5))
	else:
		tmp = (a * b) + ((y + z) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (z <= -3.5e+132)
		tmp = Float64(Float64(a * b) + Float64(y + Float64(z - t_1)));
	elseif (z <= 2.1e+87)
		tmp = Float64(Float64(z + Float64(x + y)) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(y + z) - t_1));
	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 <= -3.5e+132)
		tmp = (a * b) + (y + (z - t_1));
	elseif (z <= 2.1e+87)
		tmp = (z + (x + y)) + (b * (a - 0.5));
	else
		tmp = (a * b) + ((y + z) - t_1);
	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, -3.5e+132], N[(N[(a * b), $MachinePrecision] + N[(y + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+87], N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(y + z), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e132

   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 x around 0 87.4%

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

   5. Taylor expanded in a around inf 82.5%

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

      1. *-commutative 27.5%

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

   7. Simplified 82.5%

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

      1. sub-neg 82.5%

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

      2. associate-+l+ 82.5%

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

      3. sub-neg 82.5%

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

      4. *-commutative 82.5%

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

      5. *-un-lft-identity 82.5%

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

      6. distribute-rgt-out-- 82.4%

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

      7. +-commutative 82.4%

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

      8. distribute-rgt-out-- 82.5%

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

      9. *-un-lft-identity 82.5%

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

      10. *-commutative 82.5%

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

   9. Applied egg-rr 82.5%

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

   if -3.5000000000000002e132 < z < 2.1e87

   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. add-sqr-sqrt 35.7%

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

      2. pow2 35.7%

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

   3. Applied egg-rr 54.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 93.3%

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

      1. associate-+r+ 93.3%

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

      2. +-commutative 93.3%

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

      3. +-commutative 93.3%

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

   6. Simplified 93.3%

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

   if 2.1e87 < z

   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 0 91.6%

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

   5. Taylor expanded in a around inf 83.0%

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

      1. *-commutative 30.8%

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

   7. Simplified 83.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;a \cdot b + \left(y + \left(z - z \cdot \log t\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+87}:\\ \;\;\;\;\left(z + \left(x + y\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(\left(y + z\right) - z \cdot \log t\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

5. Final simplification 99.9%

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

Alternative 8: 51.4% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot b\\ \mathbf{if}\;y \leq 2.8 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-113}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a b))))
   (if (<= y 2.8e-221)
     t_1
     (if (<= y 2.05e-113)
       (+ x (* -0.5 b))
       (if (<= y 8e-7) t_1 (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * b);
	double tmp;
	if (y <= 2.8e-221) {
		tmp = t_1;
	} else if (y <= 2.05e-113) {
		tmp = x + (-0.5 * b);
	} else if (y <= 8e-7) {
		tmp = t_1;
	} else {
		tmp = 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 = x + (a * b)
    if (y <= 2.8d-221) then
        tmp = t_1
    else if (y <= 2.05d-113) then
        tmp = x + ((-0.5d0) * b)
    else if (y <= 8d-7) then
        tmp = t_1
    else
        tmp = 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 = x + (a * b);
	double tmp;
	if (y <= 2.8e-221) {
		tmp = t_1;
	} else if (y <= 2.05e-113) {
		tmp = x + (-0.5 * b);
	} else if (y <= 8e-7) {
		tmp = t_1;
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * b)
	tmp = 0
	if y <= 2.8e-221:
		tmp = t_1
	elif y <= 2.05e-113:
		tmp = x + (-0.5 * b)
	elif y <= 8e-7:
		tmp = t_1
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * b))
	tmp = 0.0
	if (y <= 2.8e-221)
		tmp = t_1;
	elseif (y <= 2.05e-113)
		tmp = Float64(x + Float64(-0.5 * b));
	elseif (y <= 8e-7)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * b);
	tmp = 0.0;
	if (y <= 2.8e-221)
		tmp = t_1;
	elseif (y <= 2.05e-113)
		tmp = x + (-0.5 * b);
	elseif (y <= 8e-7)
		tmp = t_1;
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.8e-221], t$95$1, If[LessEqual[y, 2.05e-113], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-7], t$95$1, N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.80000000000000019e-221 or 2.05e-113 < y < 7.9999999999999996e-7

   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 58.3%

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

   5. Taylor expanded in a around inf 47.5%

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

      1. *-commutative 47.5%

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

   7. Simplified 47.5%

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

   if 2.80000000000000019e-221 < y < 2.05e-113

   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 77.4%

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

   5. Taylor expanded in a around 0 50.0%

      \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

   if 7.9999999999999996e-7 < 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+ 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 0 89.6%

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

   5. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 30.4%

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

   7. Simplified 81.1%

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

      1. add-sqr-sqrt 33.7%

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

      2. pow2 33.7%

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

   9. Applied egg-rr 33.7%

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

   10. Taylor expanded in y around inf 65.5%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-221}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-113}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]

Alternative 9: 78.0% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 1.2 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot b + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -0.5) (not (<= a 1.2e-22)))
   (+ (* a b) (+ x y))
   (+ (+ x y) (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -0.5) || !(a <= 1.2e-22)) {
		tmp = (a * b) + (x + y);
	} 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) :: tmp
    if ((a <= (-0.5d0)) .or. (.not. (a <= 1.2d-22))) then
        tmp = (a * b) + (x + y)
    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 tmp;
	if ((a <= -0.5) || !(a <= 1.2e-22)) {
		tmp = (a * b) + (x + y);
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -0.5) or not (a <= 1.2e-22):
		tmp = (a * b) + (x + y)
	else:
		tmp = (x + y) + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -0.5) || !(a <= 1.2e-22))
		tmp = Float64(Float64(a * b) + Float64(x + y));
	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)
	tmp = 0.0;
	if ((a <= -0.5) || ~((a <= 1.2e-22)))
		tmp = (a * b) + (x + y);
	else
		tmp = (x + y) + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -0.5], N[Not[LessEqual[a, 1.2e-22]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.5 or 1.20000000000000001e-22 < a

   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 81.6%

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

      1. +-commutative 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in a around inf 81.0%

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

      1. *-commutative 60.1%

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

   9. Simplified 81.0%

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

   if -0.5 < a < 1.20000000000000001e-22

   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 72.2%

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

      1. +-commutative 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in a around 0 72.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 1.2 \cdot 10^{-22}\right):\\ \;\;\;\;a \cdot b + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]

Alternative 10: 79.5% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(z + 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. add-sqr-sqrt 37.7%

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

   2. pow2 37.7%

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

3. Applied egg-rr 52.6%

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

4. Taylor expanded in z around 0 78.0%

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

   1. associate-+r+ 78.0%

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

   2. +-commutative 78.0%

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

   3. +-commutative 78.0%

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

6. Simplified 78.0%

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

7. Final simplification 78.0%

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

Alternative 11: 58.0% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -0.5 or 0.5 < a

   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 62.1%

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

   5. Taylor expanded in a around inf 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if -0.5 < a < 0.5

   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 47.4%

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

   5. Taylor expanded in a around 0 47.4%

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

4. Final simplification 54.5%

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

Alternative 12: 63.4% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+88}:\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.2e+88) (+ x (* (+ a -0.5) b)) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.2e+88) {
		tmp = x + ((a + -0.5) * b);
	} else {
		tmp = 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) :: tmp
    if (y <= 2.2d+88) then
        tmp = x + ((a + (-0.5d0)) * b)
    else
        tmp = 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 tmp;
	if (y <= 2.2e+88) {
		tmp = x + ((a + -0.5) * b);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.2e+88:
		tmp = x + ((a + -0.5) * b)
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.2e+88)
		tmp = Float64(x + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.2e+88)
		tmp = x + ((a + -0.5) * b);
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.2e+88], N[(x + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000009e88

   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 61.0%

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

   if 2.20000000000000009e88 < 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 x around 0 91.5%

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

   5. Taylor expanded in a around inf 87.5%

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

      1. *-commutative 25.3%

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

   7. Simplified 87.5%

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

      1. add-sqr-sqrt 42.2%

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

      2. pow2 42.2%

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

   9. Applied egg-rr 42.2%

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

   10. Taylor expanded in y around inf 74.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+88}:\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]

Alternative 13: 64.3% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;y \leq 1.5 \cdot 10^{+15}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b))) (if (<= y 1.5e+15) (+ x t_1) (+ y t_1))))

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 (y <= 1.5e+15) {
		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 = (a + (-0.5d0)) * b
    if (y <= 1.5d+15) 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 = (a + -0.5) * b;
	double tmp;
	if (y <= 1.5e+15) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if y <= 1.5e+15:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	tmp = 0.0
	if (y <= 1.5e+15)
		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 = (a + -0.5) * b;
	tmp = 0.0;
	if (y <= 1.5e+15)
		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[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, 1.5e+15], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5e15

   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 60.4%

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

   if 1.5e15 < 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+ 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 74.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+15}:\\ \;\;\;\;x + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + \left(a + -0.5\right) \cdot b\\ \end{array} \]

Alternative 14: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(a + -0.5), $MachinePrecision] * b), $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. 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 77.2%

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

   1. +-commutative 77.2%

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

6. Simplified 77.2%

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

7. Final simplification 77.2%

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

Alternative 15: 34.7% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ x + -0.5 \cdot b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(-0.5 * 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. 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 54.8%

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

5. Taylor expanded in a around 0 30.4%

   \[\leadsto x + \color{blue}{-0.5 \cdot b} \]

6. Final simplification 30.4%

   \[\leadsto x + -0.5 \cdot b \]

Developer target: 99.4% 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 2023290 
(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)))