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

Percentage Accurate: 99.9% → 99.9%

Time: 17.7s

Alternatives: 20

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, 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 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

   3. sub-neg 99.9%

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

   4. metadata-eval 99.9%

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

   5. associate--l+ 99.9%

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

   6. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y + z\right)\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_2 \leq -4.7 \cdot 10^{+78} \lor \neg \left(t_2 \leq 10^{+76}\right):\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y z))) (t_2 (* b (- a 0.5))))
   (if (or (<= t_2 -4.7e+78) (not (<= t_2 1e+76)))
     (+ t_2 t_1)
     (- t_1 (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + z);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((t_2 <= -4.7e+78) || !(t_2 <= 1e+76)) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_1 - (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) :: t_2
    real(8) :: tmp
    t_1 = x + (y + z)
    t_2 = b * (a - 0.5d0)
    if ((t_2 <= (-4.7d+78)) .or. (.not. (t_2 <= 1d+76))) then
        tmp = t_2 + t_1
    else
        tmp = t_1 - (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 = x + (y + z);
	double t_2 = b * (a - 0.5);
	double tmp;
	if ((t_2 <= -4.7e+78) || !(t_2 <= 1e+76)) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_1 - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y + z)
	t_2 = b * (a - 0.5)
	tmp = 0
	if (t_2 <= -4.7e+78) or not (t_2 <= 1e+76):
		tmp = t_2 + t_1
	else:
		tmp = t_1 - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + z))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_2 <= -4.7e+78) || !(t_2 <= 1e+76))
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_1 - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y + z);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_2 <= -4.7e+78) || ~((t_2 <= 1e+76)))
		tmp = t_2 + t_1;
	else
		tmp = t_1 - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -4.7e+78], N[Not[LessEqual[t$95$2, 1e+76]], $MachinePrecision]], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$1 - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -4.70000000000000006e78 or 1e76 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. +-commutative 91.0%

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

   6. Simplified 91.0%

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

   if -4.70000000000000006e78 < (*.f64 (-.f64 a 1/2) b) < 1e76

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 97.0%

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

      1. associate-+r+ 97.0%

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

      2. +-commutative 97.0%

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

      3. *-commutative 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in b around 0 94.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4.7 \cdot 10^{+78} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+76}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y + z\right)\right) - z \cdot \log t\\ \end{array} \]

Alternative 3: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -7.7 \cdot 10^{+241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+225}:\\ \;\;\;\;\left(x + y\right) + t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+182} \lor \neg \left(z \leq 10^{+169}\right):\\ \;\;\;\;t_2 + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (* z (- 1.0 (log t)))))
   (if (<= z -7.7e+241)
     t_2
     (if (<= z -2.4e+225)
       (+ (+ x y) t_1)
       (if (or (<= z -1.6e+182) (not (<= z 1e+169)))
         (+ t_2 (* -0.5 b))
         (+ t_1 (+ x (+ y z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = z * (1.0 - log(t));
	double tmp;
	if (z <= -7.7e+241) {
		tmp = t_2;
	} else if (z <= -2.4e+225) {
		tmp = (x + y) + t_1;
	} else if ((z <= -1.6e+182) || !(z <= 1e+169)) {
		tmp = t_2 + (-0.5 * b);
	} else {
		tmp = t_1 + (x + (y + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = z * (1.0d0 - log(t))
    if (z <= (-7.7d+241)) then
        tmp = t_2
    else if (z <= (-2.4d+225)) then
        tmp = (x + y) + t_1
    else if ((z <= (-1.6d+182)) .or. (.not. (z <= 1d+169))) then
        tmp = t_2 + ((-0.5d0) * b)
    else
        tmp = t_1 + (x + (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -7.7e+241) {
		tmp = t_2;
	} else if (z <= -2.4e+225) {
		tmp = (x + y) + t_1;
	} else if ((z <= -1.6e+182) || !(z <= 1e+169)) {
		tmp = t_2 + (-0.5 * b);
	} else {
		tmp = t_1 + (x + (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -7.7e+241:
		tmp = t_2
	elif z <= -2.4e+225:
		tmp = (x + y) + t_1
	elif (z <= -1.6e+182) or not (z <= 1e+169):
		tmp = t_2 + (-0.5 * b)
	else:
		tmp = t_1 + (x + (y + z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -7.7e+241)
		tmp = t_2;
	elseif (z <= -2.4e+225)
		tmp = Float64(Float64(x + y) + t_1);
	elseif ((z <= -1.6e+182) || !(z <= 1e+169))
		tmp = Float64(t_2 + Float64(-0.5 * b));
	else
		tmp = Float64(t_1 + Float64(x + Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -7.7e+241)
		tmp = t_2;
	elseif (z <= -2.4e+225)
		tmp = (x + y) + t_1;
	elseif ((z <= -1.6e+182) || ~((z <= 1e+169)))
		tmp = t_2 + (-0.5 * b);
	else
		tmp = t_1 + (x + (y + z));
	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]}, Block[{t$95$2 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.7e+241], t$95$2, If[LessEqual[z, -2.4e+225], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[z, -1.6e+182], N[Not[LessEqual[z, 1e+169]], $MachinePrecision]], N[(t$95$2 + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.69999999999999998e241

   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. Taylor expanded in z around inf 84.9%

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

   3. Taylor expanded in z around inf 70.8%

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

   if -7.69999999999999998e241 < z < -2.4000000000000001e225

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -2.4000000000000001e225 < z < -1.5999999999999999e182 or 9.99999999999999934e168 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 89.8%

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

   3. Taylor expanded in a around 0 79.8%

      \[\leadsto z \cdot \left(1 - \log t\right) + \color{blue}{-0.5 \cdot b} \]
   4. Step-by-step derivation

      1. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -1.5999999999999999e182 < z < 9.99999999999999934e168

   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-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. +-commutative 92.7%

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

   6. Simplified 92.7%

      \[\leadsto \color{blue}{\left(\left(z + y\right) + x\right)} + \left(a - 0.5\right) \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+241}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+225}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+182} \lor \neg \left(z \leq 10^{+169}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(y + z\right)\right)\\ \end{array} \]

Alternative 4: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;y \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;\left(x + \left(z + t_1\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= y 2.4e+51)
     (- (+ x (+ z t_1)) (* z (log t)))
     (+ t_1 (+ x (+ y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (y <= 2.4e+51) {
		tmp = (x + (z + t_1)) - (z * log(t));
	} else {
		tmp = t_1 + (x + (y + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (y <= 2.4d+51) then
        tmp = (x + (z + t_1)) - (z * log(t))
    else
        tmp = t_1 + (x + (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (y <= 2.4e+51) {
		tmp = (x + (z + t_1)) - (z * Math.log(t));
	} else {
		tmp = t_1 + (x + (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if y <= 2.4e+51:
		tmp = (x + (z + t_1)) - (z * math.log(t))
	else:
		tmp = t_1 + (x + (y + z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (y <= 2.4e+51)
		tmp = Float64(Float64(x + Float64(z + t_1)) - Float64(z * log(t)));
	else
		tmp = Float64(t_1 + Float64(x + Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (y <= 2.4e+51)
		tmp = (x + (z + t_1)) - (z * log(t));
	else
		tmp = t_1 + (x + (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.4e+51], N[(N[(x + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 2.3999999999999999e51

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.0%

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

   if 2.3999999999999999e51 < 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. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. +-commutative 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(y + z\right)\right)\\ \end{array} \]

Alternative 5: 99.9% 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 99.9%

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

2. Final simplification 99.9%

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

Alternative 6: 84.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+241} \lor \neg \left(z \leq 2.75 \cdot 10^{+169}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.2e+241) (not (<= z 2.75e+169)))
   (* z (- 1.0 (log t)))
   (+ (* b (- a 0.5)) (+ x (+ y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e+241) || !(z <= 2.75e+169)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (y + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.2d+241)) .or. (.not. (z <= 2.75d+169))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (b * (a - 0.5d0)) + (x + (y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e+241) || !(z <= 2.75e+169)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (b * (a - 0.5)) + (x + (y + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.2e+241) or not (z <= 2.75e+169):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (b * (a - 0.5)) + (x + (y + z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.2e+241) || !(z <= 2.75e+169))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(x + Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.2e+241) || ~((z <= 2.75e+169)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (b * (a - 0.5)) + (x + (y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.2e+241], N[Not[LessEqual[z, 2.75e+169]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999998e241 or 2.74999999999999986e169 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 85.9%

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

   3. Taylor expanded in z around inf 72.6%

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

   if -9.1999999999999998e241 < z < 2.74999999999999986e169

   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-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 90.7%

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

      1. +-commutative 90.7%

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

      2. +-commutative 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+241} \lor \neg \left(z \leq 2.75 \cdot 10^{+169}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(x + \left(y + z\right)\right)\\ \end{array} \]

Alternative 7: 48.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-287}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-125}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+122)
   (+ x y)
   (if (<= (+ x y) -1e-287)
     (* a b)
     (if (<= (+ x y) 4e-125)
       (* -0.5 b)
       (if (<= (+ x y) 4e+127) (* a b) (+ x y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= -1e-287) {
		tmp = a * b;
	} else if ((x + y) <= 4e-125) {
		tmp = -0.5 * b;
	} else if ((x + y) <= 4e+127) {
		tmp = a * 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 ((x + y) <= (-1d+122)) then
        tmp = x + y
    else if ((x + y) <= (-1d-287)) then
        tmp = a * b
    else if ((x + y) <= 4d-125) then
        tmp = (-0.5d0) * b
    else if ((x + y) <= 4d+127) then
        tmp = a * 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 ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= -1e-287) {
		tmp = a * b;
	} else if ((x + y) <= 4e-125) {
		tmp = -0.5 * b;
	} else if ((x + y) <= 4e+127) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+122:
		tmp = x + y
	elif (x + y) <= -1e-287:
		tmp = a * b
	elif (x + y) <= 4e-125:
		tmp = -0.5 * b
	elif (x + y) <= 4e+127:
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+122)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= -1e-287)
		tmp = Float64(a * b);
	elseif (Float64(x + y) <= 4e-125)
		tmp = Float64(-0.5 * b);
	elseif (Float64(x + y) <= 4e+127)
		tmp = Float64(a * 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 ((x + y) <= -1e+122)
		tmp = x + y;
	elseif ((x + y) <= -1e-287)
		tmp = a * b;
	elseif ((x + y) <= 4e-125)
		tmp = -0.5 * b;
	elseif ((x + y) <= 4e+127)
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+122], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -1e-287], N[(a * b), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e-125], N[(-0.5 * b), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e+127], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000001e122 or 3.99999999999999982e127 < (+.f64 x 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. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. +-commutative 92.4%

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

      2. +-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in z around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. sub-neg 92.1%

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

      3. metadata-eval 92.1%

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

      4. *-commutative 92.1%

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

      5. associate-+l+ 92.1%

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

      6. *-commutative 92.1%

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

      7. fma-def 92.2%

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

   9. Simplified 92.2%

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

   10. Taylor expanded in b around 0 71.5%

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

   if -1.00000000000000001e122 < (+.f64 x y) < -1.00000000000000002e-287 or 4.00000000000000005e-125 < (+.f64 x y) < 3.99999999999999982e127

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 43.1%

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

      1. *-commutative 43.1%

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

   4. Simplified 43.1%

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

   if -1.00000000000000002e-287 < (+.f64 x y) < 4.00000000000000005e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 83.1%

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

      1. associate-+r+ 83.1%

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

      2. +-commutative 83.1%

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

      3. *-commutative 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in b around inf 83.1%

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

      1. *-commutative 83.1%

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

   7. Simplified 83.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq -1 \cdot 10^{-287}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-125}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 69.8% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+98} \lor \neg \left(t_1 \leq 3 \cdot 10^{+85}\right):\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+98) (not (<= t_1 3e+85))) (+ x t_1) (+ z (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+98) || !(t_1 <= 3e+85)) {
		tmp = x + t_1;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+98)) .or. (.not. (t_1 <= 3d+85))) then
        tmp = x + t_1
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+98) || !(t_1 <= 3e+85)) {
		tmp = x + t_1;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+98) or not (t_1 <= 3e+85):
		tmp = x + t_1
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+98) || !(t_1 <= 3e+85))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+98) || ~((t_1 <= 3e+85)))
		tmp = x + t_1;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+98], N[Not[LessEqual[t$95$1, 3e+85]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -9.99999999999999998e97 or 3e85 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 79.1%

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

   if -9.99999999999999998e97 < (*.f64 (-.f64 a 1/2) b) < 3e85

   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-cube-cbrt 99.5%

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

      2. pow3 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in z around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. +-commutative 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in b around 0 69.5%

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

      1. associate-+r+ 69.5%

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

      2. +-commutative 69.5%

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

      3. +-commutative 69.5%

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

      4. +-commutative 69.5%

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

   9. Simplified 69.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+98} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 3 \cdot 10^{+85}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]

Alternative 9: 71.8% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+98} \lor \neg \left(t_1 \leq 2 \cdot 10^{+125}\right):\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -1e+98) (not (<= t_1 2e+125)))
     (+ x t_1)
     (+ x (+ y (* -0.5 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+98) || !(t_1 <= 2e+125)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((t_1 <= (-1d+98)) .or. (.not. (t_1 <= 2d+125))) then
        tmp = x + t_1
    else
        tmp = x + (y + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+98) || !(t_1 <= 2e+125)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+98) or not (t_1 <= 2e+125):
		tmp = x + t_1
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+98) || !(t_1 <= 2e+125))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+98) || ~((t_1 <= 2e+125)))
		tmp = x + t_1;
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+98], N[Not[LessEqual[t$95$1, 2e+125]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -9.99999999999999998e97 or 1.9999999999999998e125 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 81.4%

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

   if -9.99999999999999998e97 < (*.f64 (-.f64 a 1/2) b) < 1.9999999999999998e125

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 95.1%

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

      1. associate-+r+ 95.1%

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

      2. +-commutative 95.1%

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

      3. *-commutative 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in z around 0 70.1%

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

      1. *-commutative 70.1%

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

   7. Simplified 70.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+98} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+125}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]

Alternative 10: 57.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+122)
   (+ x y)
   (if (<= (+ x y) 4e+127) (* b (- a 0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-1d+122)) then
        tmp = x + y
    else if ((x + y) <= 4d+127) then
        tmp = b * (a - 0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+122:
		tmp = x + y
	elif (x + y) <= 4e+127:
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+122)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= 4e+127)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e+122)
		tmp = x + y;
	elseif ((x + y) <= 4e+127)
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+122], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e+127], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000001e122 or 3.99999999999999982e127 < (+.f64 x 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. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 92.4%

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

      1. +-commutative 92.4%

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

      2. +-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in z around 0 92.1%

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

      1. +-commutative 92.1%

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

      2. sub-neg 92.1%

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

      3. metadata-eval 92.1%

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

      4. *-commutative 92.1%

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

      5. associate-+l+ 92.1%

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

      6. *-commutative 92.1%

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

      7. fma-def 92.2%

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

   9. Simplified 92.2%

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

   10. Taylor expanded in b around 0 71.5%

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

   if -1.00000000000000001e122 < (+.f64 x y) < 3.99999999999999982e127

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 57.8%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 50.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+122)
   (+ x y)
   (if (<= (+ x y) 4e+127) (* b (- a 0.5)) (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = 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 ((x + y) <= (-1d+122)) then
        tmp = x + y
    else if ((x + y) <= 4d+127) then
        tmp = b * (a - 0.5d0)
    else
        tmp = 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 ((x + y) <= -1e+122) {
		tmp = x + y;
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+122:
		tmp = x + y
	elif (x + y) <= 4e+127:
		tmp = b * (a - 0.5)
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+122)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= 4e+127)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e+122)
		tmp = x + y;
	elseif ((x + y) <= 4e+127)
		tmp = b * (a - 0.5);
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+122], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e+127], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000001e122

   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-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. +-commutative 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. sub-neg 93.7%

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

      3. metadata-eval 93.7%

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

      4. *-commutative 93.7%

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

      5. associate-+l+ 93.7%

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

      6. *-commutative 93.7%

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

      7. fma-def 93.7%

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

   9. Simplified 93.7%

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

   10. Taylor expanded in b around 0 78.3%

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

   if -1.00000000000000001e122 < (+.f64 x y) < 3.99999999999999982e127

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 57.8%

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

   if 3.99999999999999982e127 < (+.f64 x 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. Taylor expanded in y around inf 59.7%

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

   3. Taylor expanded in a around 0 35.9%

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

      1. *-commutative 35.9%

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

   5. Simplified 35.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]

Alternative 12: 50.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -1e+122)
   (+ z (+ x y))
   (if (<= (+ x y) 4e+127) (* b (- a 0.5)) (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -1e+122) {
		tmp = z + (x + y);
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = 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 ((x + y) <= (-1d+122)) then
        tmp = z + (x + y)
    else if ((x + y) <= 4d+127) then
        tmp = b * (a - 0.5d0)
    else
        tmp = 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 ((x + y) <= -1e+122) {
		tmp = z + (x + y);
	} else if ((x + y) <= 4e+127) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -1e+122:
		tmp = z + (x + y)
	elif (x + y) <= 4e+127:
		tmp = b * (a - 0.5)
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -1e+122)
		tmp = Float64(z + Float64(x + y));
	elseif (Float64(x + y) <= 4e+127)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -1e+122)
		tmp = z + (x + y);
	elseif ((x + y) <= 4e+127)
		tmp = b * (a - 0.5);
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+122], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e+127], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.00000000000000001e122

   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-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. +-commutative 94.1%

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

   6. Simplified 94.1%

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

   7. Taylor expanded in b around 0 78.7%

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

      1. associate-+r+ 78.7%

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

      2. +-commutative 78.7%

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

      3. +-commutative 78.7%

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

      4. +-commutative 78.7%

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

   9. Simplified 78.7%

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

   if -1.00000000000000001e122 < (+.f64 x y) < 3.99999999999999982e127

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 57.8%

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

   if 3.99999999999999982e127 < (+.f64 x 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. Taylor expanded in y around inf 59.7%

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

   3. Taylor expanded in a around 0 35.9%

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

      1. *-commutative 35.9%

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

   5. Simplified 35.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+122}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]

Alternative 13: 58.5% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-65}:\\ \;\;\;\;\left(x + z\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 2e-65) (+ (+ x z) (* (+ a -0.5) b)) (+ y (* b (- a 0.5)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 2e-65) {
		tmp = (x + z) + ((a + -0.5) * b);
	} else {
		tmp = 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 ((x + y) <= 2d-65) then
        tmp = (x + z) + ((a + (-0.5d0)) * b)
    else
        tmp = 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 ((x + y) <= 2e-65) {
		tmp = (x + z) + ((a + -0.5) * b);
	} else {
		tmp = y + (b * (a - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 2e-65:
		tmp = (x + z) + ((a + -0.5) * b)
	else:
		tmp = y + (b * (a - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 2e-65)
		tmp = Float64(Float64(x + z) + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(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 ((x + y) <= 2e-65)
		tmp = (x + z) + ((a + -0.5) * b);
	else
		tmp = y + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e-65], N[(N[(x + z), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.99999999999999985e-65

   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-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 82.5%

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

      1. +-commutative 82.5%

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

      2. +-commutative 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in y around 0 67.2%

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

      1. associate-+r+ 67.2%

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

      2. sub-neg 67.2%

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

      3. metadata-eval 67.2%

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

   9. Simplified 67.2%

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

   if 1.99999999999999985e-65 < (+.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. Taylor expanded in y around inf 61.4%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-65}:\\ \;\;\;\;\left(x + z\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 14: 57.8% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{-30}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -4e-30) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -4e-30) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-4d-30)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -4e-30) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -4e-30:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -4e-30)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -4e-30)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -4e-30], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4e-30

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 66.6%

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

   if -4e-30 < (+.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. Taylor expanded in y around inf 62.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-30}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 15: 79.2% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y + z), $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-cube-cbrt 99.7%

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

   2. pow3 99.7%

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

3. Applied egg-rr 99.7%

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

4. Taylor expanded in z around 0 82.9%

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

   1. +-commutative 82.9%

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

   2. +-commutative 82.9%

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

6. Simplified 82.9%

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

7. Final simplification 82.9%

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

Alternative 16: 78.4% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + y), $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. Taylor expanded in z around 0 81.9%

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

   1. +-commutative 81.9%

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

4. Simplified 81.9%

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

5. Final simplification 81.9%

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

Alternative 17: 28.7% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.7e-287)
   x
   (if (<= y 8.5e-239) (* -0.5 b) (if (<= y 1.45e+54) x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.7e-287) {
		tmp = x;
	} else if (y <= 8.5e-239) {
		tmp = -0.5 * b;
	} else if (y <= 1.45e+54) {
		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 <= (-3.7d-287)) then
        tmp = x
    else if (y <= 8.5d-239) then
        tmp = (-0.5d0) * b
    else if (y <= 1.45d+54) 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 <= -3.7e-287) {
		tmp = x;
	} else if (y <= 8.5e-239) {
		tmp = -0.5 * b;
	} else if (y <= 1.45e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.7e-287:
		tmp = x
	elif y <= 8.5e-239:
		tmp = -0.5 * b
	elif y <= 1.45e+54:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.7e-287)
		tmp = x;
	elseif (y <= 8.5e-239)
		tmp = Float64(-0.5 * b);
	elseif (y <= 1.45e+54)
		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 <= -3.7e-287)
		tmp = x;
	elseif (y <= 8.5e-239)
		tmp = -0.5 * b;
	elseif (y <= 1.45e+54)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.7e-287], x, If[LessEqual[y, 8.5e-239], N[(-0.5 * b), $MachinePrecision], If[LessEqual[y, 1.45e+54], x, y]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.70000000000000027e-287 or 8.49999999999999958e-239 < y < 1.4499999999999999e54

   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-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. +-commutative 80.2%

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

   6. Simplified 80.2%

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

   7. Taylor expanded in x around inf 27.1%

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

   if -3.70000000000000027e-287 < y < 8.49999999999999958e-239

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 62.5%

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

      1. associate-+r+ 62.5%

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

      2. +-commutative 62.5%

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

      3. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in b around inf 19.9%

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

      1. *-commutative 19.9%

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

   7. Simplified 19.9%

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

   if 1.4499999999999999e54 < 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. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. +-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in y around inf 45.0%

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

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 30.1% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.55e+122) x (if (<= x 4.2e-103) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+122) {
		tmp = x;
	} else if (x <= 4.2e-103) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.55d+122)) then
        tmp = x
    else if (x <= 4.2d-103) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.55e+122) {
		tmp = x;
	} else if (x <= 4.2e-103) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.55e+122:
		tmp = x
	elif x <= 4.2e-103:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.55e+122)
		tmp = x;
	elseif (x <= 4.2e-103)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.55e+122)
		tmp = x;
	elseif (x <= 4.2e-103)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.55e+122], x, If[LessEqual[x, 4.2e-103], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -1.54999999999999999e122

   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-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around 0 95.1%

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

      1. +-commutative 95.1%

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

      2. +-commutative 95.1%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in x around inf 69.3%

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

   if -1.54999999999999999e122 < x < 4.20000000000000009e-103

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

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

   4. Simplified 31.8%

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

   if 4.20000000000000009e-103 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. +-commutative 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in y around inf 14.1%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-103}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 19: 29.4% accurate, 37.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 7.5e+54) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 7.5e+54) {
		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 <= 7.5d+54) 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 <= 7.5e+54) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 7.5e+54:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 7.5e+54)
		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 <= 7.5e+54)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 7.5e+54], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 7.50000000000000042e54

   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-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. +-commutative 81.0%

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

      2. +-commutative 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in x around inf 28.0%

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

   if 7.50000000000000042e54 < 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. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. +-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in y around inf 45.0%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 20: 22.9% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.7%

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

   2. pow3 99.7%

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

3. Applied egg-rr 99.7%

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

4. Taylor expanded in z around 0 82.9%

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

   1. +-commutative 82.9%

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

   2. +-commutative 82.9%

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

6. Simplified 82.9%

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

7. Taylor expanded in x around inf 25.7%

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

8. Final simplification 25.7%

   \[\leadsto x \]

Developer target: 99.6% 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 2023280 
(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)))