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

Percentage Accurate: 99.8% → 99.8%

Time: 13.7s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. fma-define 99.5%

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

   3. sub-neg 99.5%

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

   4. metadata-eval 99.5%

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

   5. associate--l+ 99.5%

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

   6. associate-+l+ 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a + -0.5, b, x + \left(y + \left(z - z \cdot \log t\right)\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate--l+ 99.5%

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

   3. associate-+r+ 99.5%

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

   4. +-commutative 99.5%

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

   5. *-lft-identity 99.5%

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

   6. metadata-eval 99.5%

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

   7. *-commutative 99.5%

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

   8. distribute-rgt-out-- 99.5%

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

   9. metadata-eval 99.5%

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

   10. fma-define 99.5%

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

   11. sub-neg 99.5%

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

   12. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+90} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+71}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -5e+90) (not (<= t_1 5e+71)))
     (+ x (+ y (* (+ a -0.5) b)))
     (- (+ x (+ y z)) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+90) || !(t_1 <= 5e+71)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (x + (y + z)) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-5d+90)) .or. (.not. (t_1 <= 5d+71))) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = (x + (y + z)) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+90) || !(t_1 <= 5e+71)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (x + (y + z)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -5e+90) or not (t_1 <= 5e+71):
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = (x + (y + z)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -5e+90) || !(t_1 <= 5e+71))
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(Float64(x + Float64(y + z)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -5e+90) || ~((t_1 <= 5e+71)))
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = (x + (y + z)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+90], N[Not[LessEqual[t$95$1, 5e+71]], $MachinePrecision]], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000004e90 or 4.99999999999999972e71 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.1%

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

   3. Taylor expanded in a around 0 99.1%

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

   4. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

      2. distribute-rgt-in 94.8%

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

   6. Simplified 94.8%

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

   if -5.0000000000000004e90 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.99999999999999972e71

   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. Add Preprocessing

   3. Taylor expanded in b around 0 97.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+90} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+71}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{+118} \lor \neg \left(z \leq 1.65 \cdot 10^{+156}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.95e+118) (not (<= z 1.65e+156)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.95e+118) || !(z <= 1.65e+156)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.95d+118)) .or. (.not. (z <= 1.65d+156))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.95e+118) || !(z <= 1.65e+156)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.95e+118) or not (z <= 1.65e+156):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.95e+118) || !(z <= 1.65e+156))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.95e+118) || ~((z <= 1.65e+156)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.95e+118], N[Not[LessEqual[z, 1.65e+156]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9500000000000002e118 or 1.6499999999999999e156 < z

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. associate--l+ 98.4%

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

      3. associate-+r+ 98.4%

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

      4. +-commutative 98.4%

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

      5. *-lft-identity 98.4%

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

      6. metadata-eval 98.4%

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

      7. *-commutative 98.4%

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

      8. distribute-rgt-out-- 98.4%

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

      9. metadata-eval 98.4%

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

      10. fma-define 98.4%

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

      11. sub-neg 98.4%

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

      12. metadata-eval 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 80.0%

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

      1. *-commutative 80.0%

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

   7. Simplified 80.0%

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

   if -3.9500000000000002e118 < z < 1.6499999999999999e156

   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. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in z around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. distribute-rgt-in 95.4%

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

   6. Simplified 95.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.95 \cdot 10^{+118} \lor \neg \left(z \leq 1.65 \cdot 10^{+156}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;y \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + z\right) + \left(a + -0.5\right) \cdot b\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= y 7.5e+16)
     (- (+ x (+ z (* b (- a 0.5)))) t_1)
     (- (+ (+ y z) (* (+ a -0.5) b)) 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 (y <= 7.5e+16) {
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	} else {
		tmp = ((y + z) + ((a + -0.5) * b)) - 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 (y <= 7.5d+16) then
        tmp = (x + (z + (b * (a - 0.5d0)))) - t_1
    else
        tmp = ((y + z) + ((a + (-0.5d0)) * b)) - 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 (y <= 7.5e+16) {
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	} else {
		tmp = ((y + z) + ((a + -0.5) * b)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if y <= 7.5e+16:
		tmp = (x + (z + (b * (a - 0.5)))) - t_1
	else:
		tmp = ((y + z) + ((a + -0.5) * b)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (y <= 7.5e+16)
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(a - 0.5)))) - t_1);
	else
		tmp = Float64(Float64(Float64(y + z) + Float64(Float64(a + -0.5) * b)) - 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 (y <= 7.5e+16)
		tmp = (x + (z + (b * (a - 0.5)))) - t_1;
	else
		tmp = ((y + z) + ((a + -0.5) * b)) - 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[y, 7.5e+16], N[(N[(x + N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(y + z), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5e16

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 78.2%

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

   if 7.5e16 < 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. Add Preprocessing

   3. Taylor expanded in x around 0 91.6%

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

      1. associate-+r+ 91.6%

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

      2. +-commutative 91.6%

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

      3. sub-neg 91.6%

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

      4. metadata-eval 91.6%

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

      5. +-commutative 91.6%

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

   5. Simplified 91.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + z\right) + \left(a + -0.5\right) \cdot b\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.65e+77)
   (- (+ x (+ z (* b (- a 0.5)))) (* z (log t)))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.65e+77) {
		tmp = (x + (z + (b * (a - 0.5)))) - (z * log(t));
	} else {
		tmp = x + (y + ((a + -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 (y <= 1.65d+77) then
        tmp = (x + (z + (b * (a - 0.5d0)))) - (z * log(t))
    else
        tmp = x + (y + ((a + (-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 (y <= 1.65e+77) {
		tmp = (x + (z + (b * (a - 0.5)))) - (z * Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.65e+77:
		tmp = (x + (z + (b * (a - 0.5)))) - (z * math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.65e+77)
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(a - 0.5)))) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.65e+77)
		tmp = (x + (z + (b * (a - 0.5)))) - (z * log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.65e+77], N[(N[(x + N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6499999999999999e77

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 78.5%

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

   if 1.6499999999999999e77 < 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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. distribute-rgt-in 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+77}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+130} \lor \neg \left(z \leq 1.1 \cdot 10^{+156}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e+130) (not (<= z 1.1e+156)))
   (+ x (* z (- 1.0 (log t))))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+130) || !(z <= 1.1e+156)) {
		tmp = x + (z * (1.0 - log(t)));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4d+130)) .or. (.not. (z <= 1.1d+156))) then
        tmp = x + (z * (1.0d0 - log(t)))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+130) || !(z <= 1.1e+156)) {
		tmp = x + (z * (1.0 - Math.log(t)));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e+130) or not (z <= 1.1e+156):
		tmp = x + (z * (1.0 - math.log(t)))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e+130) || !(z <= 1.1e+156))
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4e+130) || ~((z <= 1.1e+156)))
		tmp = x + (z * (1.0 - log(t)));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e+130], N[Not[LessEqual[z, 1.1e+156]], $MachinePrecision]], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000002e130 or 1.10000000000000002e156 < z

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate--l+ 98.3%

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

      3. associate-+r+ 98.3%

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

      4. +-commutative 98.3%

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

      5. *-lft-identity 98.3%

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

      6. metadata-eval 98.3%

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

      7. *-commutative 98.3%

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

      8. distribute-rgt-out-- 98.3%

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

      9. metadata-eval 98.3%

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

      10. fma-define 98.3%

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

      11. sub-neg 98.3%

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

      12. metadata-eval 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.1%

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

   if -4.0000000000000002e130 < z < 1.10000000000000002e156

   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. Add Preprocessing

   3. Taylor expanded in a around 0 100.0%

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

   4. Taylor expanded in z around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. distribute-rgt-in 94.9%

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

   6. Simplified 94.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+130} \lor \neg \left(z \leq 1.1 \cdot 10^{+156}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 9: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+169}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.22e+169) (- 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) {
	double tmp;
	if (z <= -1.22e+169) {
		tmp = z - (z * log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.22d+169)) then
        tmp = z - (z * log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+169) {
		tmp = z - (z * Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.22e+169:
		tmp = z - (z * math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.22e+169)
		tmp = Float64(z - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.22e+169)
		tmp = z - (z * log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.22e+169], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e169

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 87.0%

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

   4. Taylor expanded in b around 0 70.3%

      \[\leadsto \color{blue}{z - z \cdot \log t} \]

   if -1.22e169 < z

   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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. distribute-rgt-in 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+169}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+166) (* z (- 1.0 (log t))) (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+166) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.9d+166)) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+166) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.9e+166:
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+166)
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.9e+166)
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+166], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e166

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate--l+ 96.8%

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

      3. associate-+r+ 96.8%

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

      4. +-commutative 96.8%

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

      5. *-lft-identity 96.8%

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

      6. metadata-eval 96.8%

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

      7. *-commutative 96.8%

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

      8. distribute-rgt-out-- 96.7%

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

      9. metadata-eval 96.7%

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

      10. fma-define 96.7%

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

      11. sub-neg 96.7%

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

      12. metadata-eval 96.7%

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

   3. Simplified 96.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.2%

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

   6. Taylor expanded in z around inf 70.2%

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

   if -2.9000000000000001e166 < z

   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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. distribute-rgt-in 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 6.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+284}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.6e+111)
   (* a b)
   (if (<= b 1.45e+140) (+ x y) (if (<= b 4.5e+284) (* a b) (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+111) {
		tmp = a * b;
	} else if (b <= 1.45e+140) {
		tmp = x + y;
	} else if (b <= 4.5e+284) {
		tmp = a * b;
	} else {
		tmp = -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 (b <= (-6.6d+111)) then
        tmp = a * b
    else if (b <= 1.45d+140) then
        tmp = x + y
    else if (b <= 4.5d+284) then
        tmp = a * b
    else
        tmp = (-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 (b <= -6.6e+111) {
		tmp = a * b;
	} else if (b <= 1.45e+140) {
		tmp = x + y;
	} else if (b <= 4.5e+284) {
		tmp = a * b;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.6e+111:
		tmp = a * b
	elif b <= 1.45e+140:
		tmp = x + y
	elif b <= 4.5e+284:
		tmp = a * b
	else:
		tmp = -0.5 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.6e+111)
		tmp = Float64(a * b);
	elseif (b <= 1.45e+140)
		tmp = Float64(x + y);
	elseif (b <= 4.5e+284)
		tmp = Float64(a * b);
	else
		tmp = Float64(-0.5 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.6e+111)
		tmp = a * b;
	elseif (b <= 1.45e+140)
		tmp = x + y;
	elseif (b <= 4.5e+284)
		tmp = a * b;
	else
		tmp = -0.5 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.6e+111], N[(a * b), $MachinePrecision], If[LessEqual[b, 1.45e+140], N[(x + y), $MachinePrecision], If[LessEqual[b, 4.5e+284], N[(a * b), $MachinePrecision], N[(-0.5 * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.6000000000000002e111 or 1.4499999999999999e140 < b < 4.4999999999999998e284

   1. Initial program 98.5%

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

   3. Taylor expanded in a around inf 65.8%

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

      1. fma-define 65.8%

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

      2. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in a around inf 55.7%

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

   if -6.6000000000000002e111 < b < 1.4499999999999999e140

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x + y\right) + z} \cdot \sqrt[3]{\left(x + y\right) + z}\right) \cdot \sqrt[3]{\left(x + y\right) + z}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 98.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + y\right) + z}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 98.6%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{x + \left(y + z\right)}}\right)}^{3} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 98.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x + \left(y + z\right)}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 73.4%

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

   6. Taylor expanded in b around 0 58.8%

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

      1. +-commutative 58.8%

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

   8. Simplified 58.8%

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

   if 4.4999999999999998e284 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around inf 89.3%

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

   7. Taylor expanded in a around 0 76.6%

      \[\leadsto \color{blue}{-0.5 \cdot b} \]
   8. Step-by-step derivation

      1. *-commutative 76.6%

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

   9. Simplified 76.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+284}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.0% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-7} \lor \neg \left(a \leq 0.5\right):\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -8.2e-7) (not (<= a 0.5)))
   (+ x (+ y (* a b)))
   (+ (+ x y) (* -0.5 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -8.2e-7) || !(a <= 0.5)) {
		tmp = x + (y + (a * b));
	} 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 <= (-8.2d-7)) .or. (.not. (a <= 0.5d0))) then
        tmp = x + (y + (a * b))
    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 <= -8.2e-7) || !(a <= 0.5)) {
		tmp = x + (y + (a * b));
	} else {
		tmp = (x + y) + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -8.2e-7) or not (a <= 0.5):
		tmp = x + (y + (a * b))
	else:
		tmp = (x + y) + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -8.2e-7) || !(a <= 0.5))
		tmp = Float64(x + Float64(y + Float64(a * b)));
	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 <= -8.2e-7) || ~((a <= 0.5)))
		tmp = x + (y + (a * b));
	else
		tmp = (x + y) + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -8.2e-7], N[Not[LessEqual[a, 0.5]], $MachinePrecision]], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.1999999999999998e-7 or 0.5 < a

   1. Initial program 99.1%

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

      1. add-cube-cbrt 98.4%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x + y\right) + z} \cdot \sqrt[3]{\left(x + y\right) + z}\right) \cdot \sqrt[3]{\left(x + y\right) + z}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 98.4%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + y\right) + z}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 98.4%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{x + \left(y + z\right)}}\right)}^{3} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 98.4%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x + \left(y + z\right)}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 84.4%

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

   6. Taylor expanded in a around inf 84.0%

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

      1. *-commutative 84.0%

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

   8. Simplified 84.0%

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

   if -8.1999999999999998e-7 < a < 0.5

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.8%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x + y\right) + z} \cdot \sqrt[3]{\left(x + y\right) + z}\right) \cdot \sqrt[3]{\left(x + y\right) + z}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 98.7%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + y\right) + z}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 98.7%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{x + \left(y + z\right)}}\right)}^{3} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 98.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x + \left(y + z\right)}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 76.1%

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

   6. Taylor expanded in a around 0 75.9%

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

      1. associate-+r+ 75.9%

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

      2. +-commutative 75.9%

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

   8. Simplified 75.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-7} \lor \neg \left(a \leq 0.5\right):\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.3% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+105} \lor \neg \left(b \leq 3 \cdot 10^{+89}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e+105) (not (<= b 3e+89)))
   (* (+ a -0.5) b)
   (+ x (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e+105) || !(b <= 3e+89)) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = 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 <= (-4.4d+105)) .or. (.not. (b <= 3d+89))) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = 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 <= -4.4e+105) || !(b <= 3e+89)) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e+105) or not (b <= 3e+89):
		tmp = (a + -0.5) * b
	else:
		tmp = x + (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e+105) || !(b <= 3e+89))
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = Float64(x + Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e+105) || ~((b <= 3e+89)))
		tmp = (a + -0.5) * b;
	else
		tmp = x + (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e+105], N[Not[LessEqual[b, 3e+89]], $MachinePrecision]], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.40000000000000014e105 or 3.00000000000000013e89 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in b around inf 98.7%

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

      1. associate--l+ 98.8%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around inf 79.6%

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

   if -4.40000000000000014e105 < b < 3.00000000000000013e89

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x + y\right) + z} \cdot \sqrt[3]{\left(x + y\right) + z}\right) \cdot \sqrt[3]{\left(x + y\right) + z}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 98.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + y\right) + z}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 98.6%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{x + \left(y + z\right)}}\right)}^{3} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 98.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x + \left(y + z\right)}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 72.6%

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

   6. Taylor expanded in a around inf 70.9%

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

      1. *-commutative 70.9%

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

   8. Simplified 70.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+105} \lor \neg \left(b \leq 3 \cdot 10^{+89}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.8% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.06 \cdot 10^{+55} \lor \neg \left(b \leq 1.6 \cdot 10^{+79}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.06e+55) (not (<= b 1.6e+79))) (* (+ a -0.5) b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.06e+55) || !(b <= 1.6e+79)) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.06d+55)) .or. (.not. (b <= 1.6d+79))) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.06e+55) || !(b <= 1.6e+79)) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.06e+55) or not (b <= 1.6e+79):
		tmp = (a + -0.5) * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.06e+55) || !(b <= 1.6e+79))
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.06e+55) || ~((b <= 1.6e+79)))
		tmp = (a + -0.5) * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.06e+55], N[Not[LessEqual[b, 1.6e+79]], $MachinePrecision]], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.06e55 or 1.60000000000000001e79 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in b around inf 98.8%

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

      1. associate--l+ 98.9%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around inf 78.4%

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

   if -2.06e55 < b < 1.60000000000000001e79

   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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.6%

         \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\left(x + y\right) + z} \cdot \sqrt[3]{\left(x + y\right) + z}\right) \cdot \sqrt[3]{\left(x + y\right) + z}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      2. pow3 98.6%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\left(x + y\right) + z}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

      3. associate-+l+ 98.6%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{x + \left(y + z\right)}}\right)}^{3} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   4. Applied egg-rr 98.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{x + \left(y + z\right)}\right)}^{3}} - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]

   5. Taylor expanded in z around 0 71.2%

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

   6. Taylor expanded in b around 0 61.8%

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

      1. +-commutative 61.8%

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

   8. Simplified 61.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.06 \cdot 10^{+55} \lor \neg \left(b \leq 1.6 \cdot 10^{+79}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+143}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.5e-67) x (if (<= y 2.85e+143) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.5e-67) {
		tmp = x;
	} else if (y <= 2.85e+143) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.5d-67) then
        tmp = x
    else if (y <= 2.85d+143) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.5e-67) {
		tmp = x;
	} else if (y <= 2.85e+143) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.5e-67:
		tmp = x
	elif y <= 2.85e+143:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.5e-67)
		tmp = x;
	elseif (y <= 2.85e+143)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.5e-67)
		tmp = x;
	elseif (y <= 2.85e+143)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.5e-67], x, If[LessEqual[y, 2.85e+143], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 1.50000000000000016e-67

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. *-lft-identity 99.3%

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

      6. metadata-eval 99.3%

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

      7. *-commutative 99.3%

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

      8. distribute-rgt-out-- 99.3%

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

      9. metadata-eval 99.3%

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

      10. fma-define 99.3%

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

      11. sub-neg 99.3%

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

      12. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 43.9%

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

   6. Taylor expanded in z around 0 22.4%

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

   if 1.50000000000000016e-67 < y < 2.85000000000000011e143

   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. Add Preprocessing

   3. Taylor expanded in a around inf 59.7%

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

      1. fma-define 59.7%

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

      2. associate-/l* 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in a around inf 29.9%

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

   if 2.85000000000000011e143 < 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. Add Preprocessing

   3. Taylor expanded in a around inf 58.6%

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

      1. fma-define 58.6%

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

      2. associate-/l* 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in y around inf 60.7%

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

Alternative 16: 78.5% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in a around 0 99.5%

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

4. Taylor expanded in z around 0 79.9%

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

   1. +-commutative 79.9%

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

   2. distribute-rgt-in 79.9%

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

6. Simplified 79.9%

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

7. Final simplification 79.9%

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

Alternative 17: 28.8% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 6e+29) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6e+29) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6d+29) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6e+29) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6e+29:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6e+29)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6e+29)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6e+29], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.9999999999999998e29

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. associate-+r+ 99.4%

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

      4. +-commutative 99.4%

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

      5. *-lft-identity 99.4%

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

      6. metadata-eval 99.4%

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

      7. *-commutative 99.4%

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

      8. distribute-rgt-out-- 99.4%

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

      9. metadata-eval 99.4%

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

      10. fma-define 99.4%

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

      11. sub-neg 99.4%

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

      12. metadata-eval 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 42.9%

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

   6. Taylor expanded in z around 0 20.8%

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

   if 5.9999999999999998e29 < 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. Add Preprocessing

   3. Taylor expanded in a around inf 60.4%

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

      1. fma-define 60.4%

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

      2. associate-/l* 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in y around inf 48.1%

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

Alternative 18: 22.6% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate--l+ 99.5%

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

   3. associate-+r+ 99.5%

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

   4. +-commutative 99.5%

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

   5. *-lft-identity 99.5%

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

   6. metadata-eval 99.5%

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

   7. *-commutative 99.5%

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

   8. distribute-rgt-out-- 99.5%

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

   9. metadata-eval 99.5%

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

   10. fma-define 99.5%

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

   11. sub-neg 99.5%

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

   12. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \mathsf{fma}\left(a + -0.5, b, x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 37.5%

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

6. Taylor expanded in z around 0 18.3%

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

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x + y) + (((1.0d0 - (log(t) ** 2.0d0)) * z) / (1.0d0 + log(t)))) + ((a - 0.5d0) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024177 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

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