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

Percentage Accurate: 99.8% → 99.9%

Time: 13.2s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate--l+ 99.8%

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

   3. associate-+r+ 99.8%

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

   4. +-commutative 99.8%

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

   5. *-lft-identity 99.8%

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

   6. metadata-eval 99.8%

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

   7. *-commutative 99.8%

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

   8. distribute-rgt-out-- 99.9%

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

   9. metadata-eval 99.9%

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

   10. fma-define 99.9%

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

   11. sub-neg 99.9%

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

   12. metadata-eval 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(1 + \left(\frac{y}{x} + b \cdot \frac{a + -0.5}{x}\right)\right)\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{+138}:\\ \;\;\;\;\left(\left(z + x\right) + -0.5 \cdot b\right) - t\_1\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) -5e+196)
     (* x (+ 1.0 (+ (/ y x) (* b (/ (+ a -0.5) x)))))
     (if (<= (+ x y) -2e+138)
       (- (+ (+ z x) (* -0.5 b)) t_1)
       (if (<= (+ x y) -5e+34)
         (+ x (+ y (* (+ a -0.5) b)))
         (- (+ y (+ z (* b (- a 0.5)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if ((x + y) <= -5e+196) {
		tmp = x * (1.0 + ((y / x) + (b * ((a + -0.5) / x))));
	} else if ((x + y) <= -2e+138) {
		tmp = ((z + x) + (-0.5 * b)) - t_1;
	} else if ((x + y) <= -5e+34) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (y + (z + (b * (a - 0.5)))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if ((x + y) <= (-5d+196)) then
        tmp = x * (1.0d0 + ((y / x) + (b * ((a + (-0.5d0)) / x))))
    else if ((x + y) <= (-2d+138)) then
        tmp = ((z + x) + ((-0.5d0) * b)) - t_1
    else if ((x + y) <= (-5d+34)) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = (y + (z + (b * (a - 0.5d0)))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double tmp;
	if ((x + y) <= -5e+196) {
		tmp = x * (1.0 + ((y / x) + (b * ((a + -0.5) / x))));
	} else if ((x + y) <= -2e+138) {
		tmp = ((z + x) + (-0.5 * b)) - t_1;
	} else if ((x + y) <= -5e+34) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (y + (z + (b * (a - 0.5)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= -5e+196:
		tmp = x * (1.0 + ((y / x) + (b * ((a + -0.5) / x))))
	elif (x + y) <= -2e+138:
		tmp = ((z + x) + (-0.5 * b)) - t_1
	elif (x + y) <= -5e+34:
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = (y + (z + (b * (a - 0.5)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= -5e+196)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y / x) + Float64(b * Float64(Float64(a + -0.5) / x)))));
	elseif (Float64(x + y) <= -2e+138)
		tmp = Float64(Float64(Float64(z + x) + Float64(-0.5 * b)) - t_1);
	elseif (Float64(x + y) <= -5e+34)
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(Float64(y + Float64(z + Float64(b * Float64(a - 0.5)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if ((x + y) <= -5e+196)
		tmp = x * (1.0 + ((y / x) + (b * ((a + -0.5) / x))));
	elseif ((x + y) <= -2e+138)
		tmp = ((z + x) + (-0.5 * b)) - t_1;
	elseif ((x + y) <= -5e+34)
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = (y + (z + (b * (a - 0.5)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e+196], N[(x * N[(1.0 + N[(N[(y / x), $MachinePrecision] + N[(b * N[(N[(a + -0.5), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -2e+138], N[(N[(N[(z + x), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], -5e+34], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x y) < -4.9999999999999998e196

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 90.5%

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

      1. distribute-rgt-out 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in x around inf 68.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{y}{x} + \frac{b \cdot \left(a - 0.5\right)}{x}\right)\right)} \]
   8. Step-by-step derivation

      1. associate-/l* 68.2%

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

      2. sub-neg 68.2%

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

      3. metadata-eval 68.2%

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

   9. Simplified 68.2%

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

   if -4.9999999999999998e196 < (+.f64 x y) < -2.0000000000000001e138

   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. Add Preprocessing

   3. Taylor expanded in y around 0 83.0%

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

      1. associate-+r+ 83.0%

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

      2. +-commutative 83.0%

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

      3. sub-neg 83.0%

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

      4. metadata-eval 83.0%

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

      5. +-commutative 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in a around 0 83.0%

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

      1. *-commutative 83.0%

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

   8. Simplified 83.0%

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

   if -2.0000000000000001e138 < (+.f64 x y) < -4.9999999999999998e34

   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. Add Preprocessing

   3. Taylor expanded in a around 0 99.7%

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

   4. Taylor expanded in z around 0 81.3%

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

      1. distribute-rgt-out 81.3%

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

   6. Simplified 81.3%

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

   if -4.9999999999999998e34 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(1 + \left(\frac{y}{x} + b \cdot \frac{a + -0.5}{x}\right)\right)\\ \mathbf{elif}\;x + y \leq -2 \cdot 10^{+138}:\\ \;\;\;\;\left(\left(z + x\right) + -0.5 \cdot b\right) - z \cdot \log t\\ \mathbf{elif}\;x + y \leq -5 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-115}:\\ \;\;\;\;\left(\left(z + x\right) + \left(a + -0.5\right) \cdot b\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(z + b \cdot \left(a - 0.5\right)\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) -5e-115)
     (- (+ (+ z x) (* (+ a -0.5) b)) t_1)
     (- (+ y (+ z (* b (- a 0.5)))) t_1))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if ((x + y) <= (-5d-115)) then
        tmp = ((z + x) + ((a + (-0.5d0)) * b)) - t_1
    else
        tmp = (y + (z + (b * (a - 0.5d0)))) - t_1
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= -5e-115:
		tmp = ((z + x) + ((a + -0.5) * b)) - t_1
	else:
		tmp = (y + (z + (b * (a - 0.5)))) - t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-115], N[(N[(N[(z + x), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(y + N[(z + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000003e-115

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. associate-+r+ 82.1%

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

      2. +-commutative 82.1%

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

      3. sub-neg 82.1%

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

      4. metadata-eval 82.1%

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

      5. +-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -5.0000000000000003e-115 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.4%

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

4. Final simplification 83.2%

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

Alternative 4: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-85} \lor \neg \left(b \leq 8.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.2e-85) (not (<= b 8.4e-5)))
   (+ x (+ y (* (+ a -0.5) b)))
   (+ (* z (- 1.0 (log t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e-85) || !(b <= 8.4e-5)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (z * (1.0 - log(t))) + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.2d-85)) .or. (.not. (b <= 8.4d-5))) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = (z * (1.0d0 - log(t))) + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.2e-85) || !(b <= 8.4e-5)) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.2e-85) or not (b <= 8.4e-5):
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = (z * (1.0 - math.log(t))) + (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.2e-85) || !(b <= 8.4e-5))
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.2e-85) || ~((b <= 8.4e-5)))
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = (z * (1.0 - log(t))) + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.2e-85], N[Not[LessEqual[b, 8.4e-5]], $MachinePrecision]], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e-85 or 8.39999999999999954e-5 < 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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 89.2%

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

      1. distribute-rgt-out 89.2%

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

   6. Simplified 89.2%

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

   if -1.2e-85 < b < 8.39999999999999954e-5

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0 89.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-85} \lor \neg \left(b \leq 8.4 \cdot 10^{-5}\right):\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+189} \lor \neg \left(z \leq 3.9 \cdot 10^{+202}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e+189) (not (<= z 3.9e+202)))
   (+ (* z (- 1.0 (log t))) x)
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e+189) || !(z <= 3.9e+202)) {
		tmp = (z * (1.0 - log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.6d+189)) .or. (.not. (z <= 3.9d+202))) then
        tmp = (z * (1.0d0 - log(t))) + x
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e+189) || !(z <= 3.9e+202)) {
		tmp = (z * (1.0 - Math.log(t))) + x;
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e+189) or not (z <= 3.9e+202):
		tmp = (z * (1.0 - math.log(t))) + x
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e+189) || !(z <= 3.9e+202))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.6e+189) || ~((z <= 3.9e+202)))
		tmp = (z * (1.0 - log(t))) + x;
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e+189], N[Not[LessEqual[z, 3.9e+202]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e189 or 3.89999999999999983e202 < z

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. *-lft-identity 99.5%

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

      6. metadata-eval 99.5%

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

      7. *-commutative 99.5%

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

      8. distribute-rgt-out-- 99.7%

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

      9. metadata-eval 99.7%

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

      10. fma-define 99.7%

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

      11. sub-neg 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 79.9%

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

   if -1.6e189 < z < 3.89999999999999983e202

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 87.9%

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

      1. distribute-rgt-out 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+189} \lor \neg \left(z \leq 3.9 \cdot 10^{+202}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -6.3 \cdot 10^{+184}:\\ \;\;\;\;t\_1 + a \cdot b\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+202}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -6.3e+184)
     (+ t_1 (* a b))
     (if (<= z 4.8e+202) (+ x (+ y (* (+ a -0.5) b))) (+ t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -6.3e+184) {
		tmp = t_1 + (a * b);
	} else if (z <= 4.8e+202) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-6.3d+184)) then
        tmp = t_1 + (a * b)
    else if (z <= 4.8d+202) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -6.3e+184) {
		tmp = t_1 + (a * b);
	} else if (z <= 4.8e+202) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -6.3e+184:
		tmp = t_1 + (a * b)
	elif z <= 4.8e+202:
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -6.3e+184)
		tmp = Float64(t_1 + Float64(a * b));
	elseif (z <= 4.8e+202)
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -6.3e+184)
		tmp = t_1 + (a * b);
	elseif (z <= 4.8e+202)
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.3e+184], N[(t$95$1 + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+202], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.3e184

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. *-lft-identity 99.7%

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

      6. metadata-eval 99.7%

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

      7. *-commutative 99.7%

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

      8. distribute-rgt-out-- 99.8%

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

      9. metadata-eval 99.8%

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

      10. fma-define 99.8%

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

      11. sub-neg 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   if -6.3e184 < z < 4.8000000000000004e202

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 87.9%

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

      1. distribute-rgt-out 87.9%

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

   6. Simplified 87.9%

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

   if 4.8000000000000004e202 < z

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. associate-+r+ 99.3%

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

      4. +-commutative 99.3%

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

      5. *-lft-identity 99.3%

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

      6. metadata-eval 99.3%

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

      7. *-commutative 99.3%

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

      8. distribute-rgt-out-- 99.5%

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

      9. metadata-eval 99.5%

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

      10. fma-define 99.5%

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

      11. sub-neg 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 80.3%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+202}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+211} \lor \neg \left(z \leq 10^{+203}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e+211) (not (<= z 1e+203)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e+211) || !(z <= 1e+203)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.4d+211)) .or. (.not. (z <= 1d+203))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e+211) || !(z <= 1e+203)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4e+211) or not (z <= 1e+203):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e+211) || !(z <= 1e+203))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.4e+211) || ~((z <= 1e+203)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e+211], N[Not[LessEqual[z, 1e+203]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000018e211 or 9.9999999999999999e202 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 99.4%

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

   4. Taylor expanded in z around inf 76.8%

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

   if -2.40000000000000018e211 < z < 9.9999999999999999e202

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 86.6%

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

      1. distribute-rgt-out 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+211} \lor \neg \left(z \leq 10^{+203}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 9: 50.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+178} \lor \neg \left(a \leq -8 \cdot 10^{+88}\right) \land \left(a \leq -5.2 \cdot 10^{+22} \lor \neg \left(a \leq 3.4 \cdot 10^{+109}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.5e+178)
         (and (not (<= a -8e+88)) (or (<= a -5.2e+22) (not (<= a 3.4e+109)))))
   (* a b)
   (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.5e+178) || (!(a <= -8e+88) && ((a <= -5.2e+22) || !(a <= 3.4e+109)))) {
		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 ((a <= (-6.5d+178)) .or. (.not. (a <= (-8d+88))) .and. (a <= (-5.2d+22)) .or. (.not. (a <= 3.4d+109))) 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 ((a <= -6.5e+178) || (!(a <= -8e+88) && ((a <= -5.2e+22) || !(a <= 3.4e+109)))) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.5e+178) or (not (a <= -8e+88) and ((a <= -5.2e+22) or not (a <= 3.4e+109))):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.5e+178) || (!(a <= -8e+88) && ((a <= -5.2e+22) || !(a <= 3.4e+109))))
		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 ((a <= -6.5e+178) || (~((a <= -8e+88)) && ((a <= -5.2e+22) || ~((a <= 3.4e+109)))))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.5e+178], And[N[Not[LessEqual[a, -8e+88]], $MachinePrecision], Or[LessEqual[a, -5.2e+22], N[Not[LessEqual[a, 3.4e+109]], $MachinePrecision]]]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000005e178 or -7.99999999999999968e88 < a < -5.2e22 or 3.40000000000000006e109 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in a around inf 59.3%

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

      1. *-commutative 59.3%

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

   6. Simplified 59.3%

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

   if -6.5000000000000005e178 < a < -7.99999999999999968e88 or -5.2e22 < a < 3.40000000000000006e109

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 74.6%

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

      1. distribute-rgt-out 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in b around 0 51.1%

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

      1. +-commutative 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+178} \lor \neg \left(a \leq -8 \cdot 10^{+88}\right) \land \left(a \leq -5.2 \cdot 10^{+22} \lor \neg \left(a \leq 3.4 \cdot 10^{+109}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-218}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.15e+107)
   x
   (if (<= x 1.15e-218)
     (* a b)
     (if (<= x 1.4e-104) y (if (<= x 3.3e-57) (* -0.5 b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.15e+107) {
		tmp = x;
	} else if (x <= 1.15e-218) {
		tmp = a * b;
	} else if (x <= 1.4e-104) {
		tmp = y;
	} else if (x <= 3.3e-57) {
		tmp = -0.5 * 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 <= (-1.15d+107)) then
        tmp = x
    else if (x <= 1.15d-218) then
        tmp = a * b
    else if (x <= 1.4d-104) then
        tmp = y
    else if (x <= 3.3d-57) then
        tmp = (-0.5d0) * 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 <= -1.15e+107) {
		tmp = x;
	} else if (x <= 1.15e-218) {
		tmp = a * b;
	} else if (x <= 1.4e-104) {
		tmp = y;
	} else if (x <= 3.3e-57) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.15e+107:
		tmp = x
	elif x <= 1.15e-218:
		tmp = a * b
	elif x <= 1.4e-104:
		tmp = y
	elif x <= 3.3e-57:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.15e+107)
		tmp = x;
	elseif (x <= 1.15e-218)
		tmp = Float64(a * b);
	elseif (x <= 1.4e-104)
		tmp = y;
	elseif (x <= 3.3e-57)
		tmp = Float64(-0.5 * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.15e+107)
		tmp = x;
	elseif (x <= 1.15e-218)
		tmp = a * b;
	elseif (x <= 1.4e-104)
		tmp = y;
	elseif (x <= 3.3e-57)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.15e+107], x, If[LessEqual[x, 1.15e-218], N[(a * b), $MachinePrecision], If[LessEqual[x, 1.4e-104], y, If[LessEqual[x, 3.3e-57], N[(-0.5 * b), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.15e107

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in x around inf 60.0%

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

   if -1.15e107 < x < 1.14999999999999997e-218

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in a around inf 32.4%

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

      1. *-commutative 32.4%

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

   6. Simplified 32.4%

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

   if 1.14999999999999997e-218 < x < 1.4e-104 or 3.2999999999999998e-57 < 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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in y around inf 24.9%

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

   if 1.4e-104 < x < 3.2999999999999998e-57

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. associate-+r+ 86.7%

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

      2. +-commutative 86.7%

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

      3. sub-neg 86.7%

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

      4. metadata-eval 86.7%

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

      5. +-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in a around 0 48.0%

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

      1. *-commutative 48.0%

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

   8. Simplified 48.0%

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

   9. Taylor expanded in b around inf 34.8%

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

       1. *-commutative 34.8%

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

   11. Simplified 34.8%

       \[\leadsto \color{blue}{b \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-218}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+205}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.2e+87)
   (+ x (* b (- a 0.5)))
   (if (<= y 9.6e+205) (+ x (+ y (* -0.5 b))) (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e+87) {
		tmp = x + (b * (a - 0.5));
	} else if (y <= 9.6e+205) {
		tmp = x + (y + (-0.5 * b));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 6.2d+87) then
        tmp = x + (b * (a - 0.5d0))
    else if (y <= 9.6d+205) then
        tmp = x + (y + ((-0.5d0) * b))
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e+87) {
		tmp = x + (b * (a - 0.5));
	} else if (y <= 9.6e+205) {
		tmp = x + (y + (-0.5 * b));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.2e+87:
		tmp = x + (b * (a - 0.5))
	elif y <= 9.6e+205:
		tmp = x + (y + (-0.5 * b))
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.2e+87)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	elseif (y <= 9.6e+205)
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.2e+87)
		tmp = x + (b * (a - 0.5));
	elseif (y <= 9.6e+205)
		tmp = x + (y + (-0.5 * b));
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.2e+87], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+205], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.1999999999999999e87

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.1%

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

      1. associate-+r+ 87.2%

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

      2. +-commutative 87.2%

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

      3. sub-neg 87.2%

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

      4. metadata-eval 87.2%

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

      5. +-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in z around 0 60.3%

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

   if 6.1999999999999999e87 < y < 9.59999999999999945e205

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. distribute-rgt-out 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in a around 0 73.5%

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

      1. +-commutative 73.5%

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

      2. *-commutative 73.5%

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

   9. Simplified 73.5%

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

   if 9.59999999999999945e205 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 62.9%

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

      1. associate--l+ 62.9%

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

      2. associate-/l* 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around inf 56.2%

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

   7. Taylor expanded in b around 0 73.4%

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

      1. *-commutative 73.4%

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

   9. Simplified 73.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+87}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+205}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.2% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+136} \lor \neg \left(b \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.15e+136) (not (<= b 2e-19))) (* b (- a 0.5)) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.15e+136) || !(b <= 2e-19)) {
		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 ((b <= (-1.15d+136)) .or. (.not. (b <= 2d-19))) 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 ((b <= -1.15e+136) || !(b <= 2e-19)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.15e+136) or not (b <= 2e-19):
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.15e+136) || !(b <= 2e-19))
		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 ((b <= -1.15e+136) || ~((b <= 2e-19)))
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.15e+136], N[Not[LessEqual[b, 2e-19]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e136 or 2e-19 < 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. Add Preprocessing

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in b around inf 69.9%

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

   if -1.15e136 < b < 2e-19

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. distribute-rgt-out 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in b around 0 51.3%

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

      1. +-commutative 51.3%

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

   9. Simplified 51.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+136} \lor \neg \left(b \leq 2 \cdot 10^{-19}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.4% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{-12}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.55e-12)
   (+ x (* a b))
   (if (<= x -4.3e-200) (* b (- a 0.5)) (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.55e-12) {
		tmp = x + (a * b);
	} else if (x <= -4.3e-200) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.55d-12)) then
        tmp = x + (a * b)
    else if (x <= (-4.3d-200)) then
        tmp = b * (a - 0.5d0)
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.55e-12) {
		tmp = x + (a * b);
	} else if (x <= -4.3e-200) {
		tmp = b * (a - 0.5);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.55e-12:
		tmp = x + (a * b)
	elif x <= -4.3e-200:
		tmp = b * (a - 0.5)
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.55e-12)
		tmp = Float64(x + Float64(a * b));
	elseif (x <= -4.3e-200)
		tmp = Float64(b * Float64(a - 0.5));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.55e-12)
		tmp = x + (a * b);
	elseif (x <= -4.3e-200)
		tmp = b * (a - 0.5);
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.55e-12], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e-200], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.55e-12

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in z around 0 80.8%

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

      1. distribute-rgt-out 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in a around inf 63.3%

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

      1. *-commutative 63.3%

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

   9. Simplified 63.3%

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

   if -3.55e-12 < x < -4.29999999999999975e-200

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in b around inf 43.2%

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

   if -4.29999999999999975e-200 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. associate-/l* 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around inf 42.9%

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

   7. Taylor expanded in b around 0 49.1%

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

      1. *-commutative 49.1%

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

   9. Simplified 49.1%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.55 \cdot 10^{-12}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 2.65e-92)
   (+ x (* a b))
   (if (<= y 1.2e+88) (* b (- a 0.5)) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.65e-92) {
		tmp = x + (a * b);
	} else if (y <= 1.2e+88) {
		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 (y <= 2.65d-92) then
        tmp = x + (a * b)
    else if (y <= 1.2d+88) 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 (y <= 2.65e-92) {
		tmp = x + (a * b);
	} else if (y <= 1.2e+88) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.65e-92:
		tmp = x + (a * b)
	elif y <= 1.2e+88:
		tmp = b * (a - 0.5)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.65e-92)
		tmp = Float64(x + Float64(a * b));
	elseif (y <= 1.2e+88)
		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 (y <= 2.65e-92)
		tmp = x + (a * b);
	elseif (y <= 1.2e+88)
		tmp = b * (a - 0.5);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.65e-92], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+88], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.65000000000000015e-92

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in z around 0 71.5%

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

      1. distribute-rgt-out 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in a around inf 48.6%

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

      1. *-commutative 48.6%

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

   9. Simplified 48.6%

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

   if 2.65000000000000015e-92 < y < 1.2e88

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in b around inf 53.4%

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

   if 1.2e88 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 99.9%

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

   4. Taylor expanded in z around 0 83.1%

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

      1. distribute-rgt-out 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in b around 0 62.1%

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

      1. +-commutative 62.1%

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

   9. Simplified 62.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.6% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-200}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e-12) x (if (<= x -3.8e-200) (* -0.5 b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e-12) {
		tmp = x;
	} else if (x <= -3.8e-200) {
		tmp = -0.5 * 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 <= (-2.2d-12)) then
        tmp = x
    else if (x <= (-3.8d-200)) then
        tmp = (-0.5d0) * 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 <= -2.2e-12) {
		tmp = x;
	} else if (x <= -3.8e-200) {
		tmp = -0.5 * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e-12:
		tmp = x
	elif x <= -3.8e-200:
		tmp = -0.5 * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e-12)
		tmp = x;
	elseif (x <= -3.8e-200)
		tmp = Float64(-0.5 * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.2e-12)
		tmp = x;
	elseif (x <= -3.8e-200)
		tmp = -0.5 * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e-12], x, If[LessEqual[x, -3.8e-200], N[(-0.5 * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -2.19999999999999992e-12

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in x around inf 44.4%

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

   if -2.19999999999999992e-12 < x < -3.8e-200

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. associate-+r+ 83.1%

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

      2. +-commutative 83.1%

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

      3. sub-neg 83.1%

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

      4. metadata-eval 83.1%

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

      5. +-commutative 83.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in a around 0 53.0%

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

      1. *-commutative 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in b around inf 16.2%

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

       1. *-commutative 16.2%

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

   11. Simplified 16.2%

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

   if -3.8e-200 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in y around inf 22.1%

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

4. Final simplification 27.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-200}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+95}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.65e+95) (+ x (* b (- a 0.5))) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.65e+95) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.65d+95) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.65e+95) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.65e+95:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.65e+95)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.65e+95)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.65e+95], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6499999999999999e95

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. associate-+r+ 86.9%

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

      2. +-commutative 86.9%

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

      3. sub-neg 86.9%

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

      4. metadata-eval 86.9%

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

      5. +-commutative 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 60.4%

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

   if 1.6499999999999999e95 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 62.6%

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

      1. associate--l+ 62.6%

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

      2. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around inf 41.7%

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

   7. Taylor expanded in b around 0 55.4%

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

      1. *-commutative 55.4%

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

   9. Simplified 55.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+95}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 78.8% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around 0 99.8%

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

4. Taylor expanded in z around 0 74.7%

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

   1. distribute-rgt-out 74.7%

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

6. Simplified 74.7%

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

7. Final simplification 74.7%

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

Alternative 18: 28.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -2.8e+46) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.8e+46) {
		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 (x <= (-2.8d+46)) 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 (x <= -2.8e+46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.8e+46:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.8e+46)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.8e+46)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.8e+46], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000018e46

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in x around inf 50.7%

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

   if -2.80000000000000018e46 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 99.8%

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

   4. Taylor expanded in y around inf 21.4%

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

Alternative 19: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around 0 99.8%

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

4. Taylor expanded in x around inf 22.1%

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

Developer target: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (+ (+ (+ 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)))