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

Percentage Accurate: 99.9% → 99.9%

Time: 10.9s

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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

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

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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   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: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \cdot 10^{+42}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{elif}\;a - 0.5 \leq -0.4:\\ \;\;\;\;\left(x + \left(y + \left(z + -0.5 \cdot b\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- a 0.5) -1e+42)
   (+ x (+ y (* a b)))
   (if (<= (- a 0.5) -0.4)
     (- (+ x (+ y (+ z (* -0.5 b)))) (* z (log t)))
     (+ x (+ y (* (+ a -0.5) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a - 0.5) <= -1e+42) {
		tmp = x + (y + (a * b));
	} else if ((a - 0.5) <= -0.4) {
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a - 0.5d0) <= (-1d+42)) then
        tmp = x + (y + (a * b))
    else if ((a - 0.5d0) <= (-0.4d0)) then
        tmp = (x + (y + (z + ((-0.5d0) * b)))) - (z * log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a - 0.5) <= -1e+42) {
		tmp = x + (y + (a * b));
	} else if ((a - 0.5) <= -0.4) {
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a - 0.5) <= -1e+42:
		tmp = x + (y + (a * b))
	elif (a - 0.5) <= -0.4:
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(a - 0.5) <= -1e+42)
		tmp = Float64(x + Float64(y + Float64(a * b)));
	elseif (Float64(a - 0.5) <= -0.4)
		tmp = Float64(Float64(x + Float64(y + Float64(z + Float64(-0.5 * b)))) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a - 0.5) <= -1e+42)
		tmp = x + (y + (a * b));
	elseif ((a - 0.5) <= -0.4)
		tmp = (x + (y + (z + (-0.5 * b)))) - (z * log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(a - 0.5), $MachinePrecision], -1e+42], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4], N[(N[(x + N[(y + N[(z + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -1.00000000000000004e42

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 89.1%

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

   7. Taylor expanded in a around inf 89.1%

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

      1. *-commutative 89.1%

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

   9. Simplified 89.1%

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

   if -1.00000000000000004e42 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 98.6%

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

   if -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

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

      1. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. distribute-rgt-in 84.3%

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

   8. Simplified 84.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -1 \cdot 10^{+42}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \mathbf{elif}\;a - 0.5 \leq -0.4:\\ \;\;\;\;\left(x + \left(y + \left(z + -0.5 \cdot b\right)\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+183} \lor \neg \left(z \leq 8 \cdot 10^{+73}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.45e+183) (not (<= z 8e+73)))
   (+ (* (+ a -0.5) b) (- z (* z (log t))))
   (+ x (+ y (+ (* a b) (* -0.5 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e+183) || !(z <= 8e+73)) {
		tmp = ((a + -0.5) * b) + (z - (z * log(t)));
	} else {
		tmp = x + (y + ((a * b) + (-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 <= (-1.45d+183)) .or. (.not. (z <= 8d+73))) then
        tmp = ((a + (-0.5d0)) * b) + (z - (z * log(t)))
    else
        tmp = x + (y + ((a * b) + ((-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 <= -1.45e+183) || !(z <= 8e+73)) {
		tmp = ((a + -0.5) * b) + (z - (z * Math.log(t)));
	} else {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.45e+183) or not (z <= 8e+73):
		tmp = ((a + -0.5) * b) + (z - (z * math.log(t)))
	else:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.45e+183) || !(z <= 8e+73))
		tmp = Float64(Float64(Float64(a + -0.5) * b) + Float64(z - Float64(z * log(t))));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.45e+183) || ~((z <= 8e+73)))
		tmp = ((a + -0.5) * b) + (z - (z * log(t)));
	else
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.45e+183], N[Not[LessEqual[z, 8e+73]], $MachinePrecision]], N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e183 or 7.99999999999999986e73 < z

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l- 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l+ 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 85.1%

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

   if -1.45e183 < z < 7.99999999999999986e73

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 94.5%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+183} \lor \neg \left(z \leq 8 \cdot 10^{+73}\right):\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(z - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+183} \lor \neg \left(z \leq 8 \cdot 10^{+73}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e+183) (not (<= z 8e+73)))
   (+ (* z (- 1.0 (log t))) (* a b))
   (+ x (+ y (+ (* a b) (* -0.5 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e+183) || !(z <= 8e+73)) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a * b) + (-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 <= (-1.1d+183)) .or. (.not. (z <= 8d+73))) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else
        tmp = x + (y + ((a * b) + ((-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 <= -1.1e+183) || !(z <= 8e+73)) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.1e+183) or not (z <= 8e+73):
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	else:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e+183) || !(z <= 8e+73))
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.1e+183) || ~((z <= 8e+73)))
		tmp = (z * (1.0 - log(t))) + (a * b);
	else
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e+183], N[Not[LessEqual[z, 8e+73]], $MachinePrecision]], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999995e183 or 7.99999999999999986e73 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      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 a around inf 78.0%

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

      1. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   if -1.09999999999999995e183 < z < 7.99999999999999986e73

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 94.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+183} \lor \neg \left(z \leq 8 \cdot 10^{+73}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+120}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + y\right)\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+182)
   (+ (* z (- 1.0 (log t))) (* a b))
   (if (<= z 8.8e+120)
     (+ x (+ y (+ (* a b) (* -0.5 b))))
     (- (+ x (+ z y)) (* z (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+182) {
		tmp = (z * (1.0 - log(t))) + (a * b);
	} else if (z <= 8.8e+120) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (x + (z + y)) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.5d+182)) then
        tmp = (z * (1.0d0 - log(t))) + (a * b)
    else if (z <= 8.8d+120) then
        tmp = x + (y + ((a * b) + ((-0.5d0) * b)))
    else
        tmp = (x + (z + y)) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+182) {
		tmp = (z * (1.0 - Math.log(t))) + (a * b);
	} else if (z <= 8.8e+120) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (x + (z + y)) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+182:
		tmp = (z * (1.0 - math.log(t))) + (a * b)
	elif z <= 8.8e+120:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	else:
		tmp = (x + (z + y)) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+182)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(a * b));
	elseif (z <= 8.8e+120)
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	else
		tmp = Float64(Float64(x + Float64(z + y)) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+182)
		tmp = (z * (1.0 - log(t))) + (a * b);
	elseif (z <= 8.8e+120)
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	else
		tmp = (x + (z + y)) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+182], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+120], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e182

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-define 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around inf 75.1%

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

      1. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   if -8.5e182 < z < 8.8000000000000005e120

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 93.3%

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

   if 8.8000000000000005e120 < z

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l- 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 84.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+182}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + a \cdot b\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+120}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(z + y\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;y \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;\left(t\_1 + \left(z + x\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= y 9.5e+55) (- (+ t_1 (+ z x)) (* z (log t))) (+ x (+ y t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (y <= 9.5e+55) {
		tmp = (t_1 + (z + x)) - (z * log(t));
	} else {
		tmp = x + (y + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + (-0.5d0)) * b
    if (y <= 9.5d+55) then
        tmp = (t_1 + (z + x)) - (z * log(t))
    else
        tmp = x + (y + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (y <= 9.5e+55) {
		tmp = (t_1 + (z + x)) - (z * Math.log(t));
	} else {
		tmp = x + (y + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if y <= 9.5e+55:
		tmp = (t_1 + (z + x)) - (z * math.log(t))
	else:
		tmp = x + (y + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	tmp = 0.0
	if (y <= 9.5e+55)
		tmp = Float64(Float64(t_1 + Float64(z + x)) - Float64(z * log(t)));
	else
		tmp = Float64(x + Float64(y + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + -0.5) * b;
	tmp = 0.0;
	if (y <= 9.5e+55)
		tmp = (t_1 + (z + x)) - (z * log(t));
	else
		tmp = x + (y + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[y, 9.5e+55], N[(N[(t$95$1 + N[(z + x), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 9.49999999999999989e55

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. associate-+r+ 84.4%

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

      2. +-commutative 84.4%

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

      3. sub-neg 84.4%

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

      4. metadata-eval 84.4%

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

      5. +-commutative 84.4%

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

   7. Simplified 84.4%

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

   if 9.49999999999999989e55 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 94.8%

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

      1. +-commutative 94.8%

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

      2. distribute-rgt-in 94.8%

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

   8. Simplified 94.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;\left(\left(a + -0.5\right) \cdot b + \left(z + x\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l- 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. sub-neg 99.9%

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

   7. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 8: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{+121}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 8.2e+121)
   (+ x (+ y (+ (* a b) (* -0.5 b))))
   (- (+ z x) (* z (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8.2e+121) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (z + x) - (z * log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 8.2d+121) then
        tmp = x + (y + ((a * b) + ((-0.5d0) * b)))
    else
        tmp = (z + x) - (z * log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8.2e+121) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (z + x) - (z * Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 8.2e+121:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	else:
		tmp = (z + x) - (z * math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 8.2e+121)
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	else
		tmp = Float64(Float64(z + x) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 8.2e+121)
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	else
		tmp = (z + x) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 8.2e+121], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.2e121

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 89.2%

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

   if 8.2e121 < z

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l- 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in b around 0 84.5%

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

   6. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

   8. Simplified 71.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.2 \cdot 10^{+121}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 7.8e+121)
   (+ x (+ y (+ (* a b) (* -0.5 b))))
   (+ (* z (- 1.0 (log t))) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 7.8e+121) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (z * (1.0 - log(t))) + 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) :: tmp
    if (z <= 7.8d+121) then
        tmp = x + (y + ((a * b) + ((-0.5d0) * b)))
    else
        tmp = (z * (1.0d0 - log(t))) + 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 tmp;
	if (z <= 7.8e+121) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 7.8e+121:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	else:
		tmp = (z * (1.0 - math.log(t))) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 7.8e+121)
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 7.8e+121)
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	else
		tmp = (z * (1.0 - log(t))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 7.8e+121], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.79999999999999967e121

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 89.2%

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

   if 7.79999999999999967e121 < z

   1. Initial program 99.7%

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

      1. +-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-- 99.7%

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

      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 71.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+167}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.35e+167)
   (+ x (+ y (+ (* a b) (* -0.5 b))))
   (* z (- 1.0 (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.35e+167) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 1.35d+167) then
        tmp = x + (y + ((a * b) + ((-0.5d0) * b)))
    else
        tmp = z * (1.0d0 - log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.35e+167) {
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 1.35e+167:
		tmp = x + (y + ((a * b) + (-0.5 * b)))
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.35e+167)
		tmp = Float64(x + Float64(y + Float64(Float64(a * b) + Float64(-0.5 * b))));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 1.35e+167)
		tmp = x + (y + ((a * b) + (-0.5 * b)));
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.35e+167], N[(x + N[(y + N[(N[(a * b), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35000000000000003e167

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 88.0%

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

   if 1.35000000000000003e167 < z

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. +-commutative 99.6%

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

      5. *-lft-identity 99.6%

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

      6. metadata-eval 99.6%

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

      7. *-commutative 99.6%

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

      8. distribute-rgt-out-- 99.6%

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

      9. metadata-eval 99.6%

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

      10. fma-define 99.6%

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

      11. sub-neg 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 81.0%

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

   6. Taylor expanded in z around inf 81.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{+167}:\\ \;\;\;\;x + \left(y + \left(a \cdot b + -0.5 \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-146} \lor \neg \left(b \leq 1.75 \cdot 10^{-29}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6e-146) (not (<= b 1.75e-29))) (+ x (* b (- a 0.5))) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e-146) || !(b <= 1.75e-29)) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6d-146)) .or. (.not. (b <= 1.75d-29))) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e-146) || !(b <= 1.75e-29)) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6e-146) or not (b <= 1.75e-29):
		tmp = x + (b * (a - 0.5))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6e-146) || !(b <= 1.75e-29))
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6e-146) || ~((b <= 1.75e-29)))
		tmp = x + (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, -6e-146], N[Not[LessEqual[b, 1.75e-29]], $MachinePrecision]], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.00000000000000038e-146 or 1.7499999999999999e-29 < b

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.6%

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

      1. associate-+r+ 85.6%

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

      2. +-commutative 85.6%

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

      3. sub-neg 85.6%

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

      4. metadata-eval 85.6%

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

      5. +-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around 0 73.4%

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

   if -6.00000000000000038e-146 < b < 1.7499999999999999e-29

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 74.0%

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

   7. Taylor expanded in b around 0 67.2%

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

      1. +-commutative 67.2%

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

   9. Simplified 67.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{-146} \lor \neg \left(b \leq 1.75 \cdot 10^{-29}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+42} \lor \neg \left(b \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+42) (not (<= b 3.2e+111))) (* 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 <= -1.35e+42) || !(b <= 3.2e+111)) {
		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 <= (-1.35d+42)) .or. (.not. (b <= 3.2d+111))) 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 <= -1.35e+42) || !(b <= 3.2e+111)) {
		tmp = b * (a - 0.5);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.35e+42) or not (b <= 3.2e+111):
		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 <= -1.35e+42) || !(b <= 3.2e+111))
		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 <= -1.35e+42) || ~((b <= 3.2e+111)))
		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, -1.35e+42], N[Not[LessEqual[b, 3.2e+111]], $MachinePrecision]], N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e42 or 3.2000000000000001e111 < b

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 100.0%

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

   6. Taylor expanded in z around 0 94.0%

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

   7. Taylor expanded in b around inf 81.5%

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

   if -1.35e42 < b < 3.2000000000000001e111

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.8%

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

   6. Taylor expanded in z around 0 75.7%

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

   7. Taylor expanded in b around 0 59.4%

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

      1. +-commutative 59.4%

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

   9. Simplified 59.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+42} \lor \neg \left(b \leq 3.2 \cdot 10^{+111}\right):\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.8% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+85} \lor \neg \left(a \leq 1.4 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.7e+85) (not (<= a 1.4e+95))) (* a b) (+ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.7e+85) || !(a <= 1.4e+95)) {
		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 <= (-1.7d+85)) .or. (.not. (a <= 1.4d+95))) 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 <= -1.7e+85) || !(a <= 1.4e+95)) {
		tmp = a * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.7e+85) or not (a <= 1.4e+95):
		tmp = a * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.7e+85) || !(a <= 1.4e+95))
		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 <= -1.7e+85) || ~((a <= 1.4e+95)))
		tmp = a * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.7e+85], N[Not[LessEqual[a, 1.4e+95]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7000000000000002e85 or 1.3999999999999999e95 < a

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 85.0%

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

   7. Taylor expanded in a around inf 63.5%

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

      1. *-commutative 63.5%

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

   9. Simplified 63.5%

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

   if -1.7000000000000002e85 < a < 1.3999999999999999e95

   1. Initial program 99.9%

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

      1. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 80.7%

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

   7. Taylor expanded in b around 0 55.7%

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

      1. +-commutative 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+85} \lor \neg \left(a \leq 1.4 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.4% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.3e-280) x (if (<= y 6.5e+127) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.3e-280) {
		tmp = x;
	} else if (y <= 6.5e+127) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.3d-280)) then
        tmp = x
    else if (y <= 6.5d+127) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.3e-280) {
		tmp = x;
	} else if (y <= 6.5e+127) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.3e-280:
		tmp = x
	elif y <= 6.5e+127:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.3e-280)
		tmp = x;
	elseif (y <= 6.5e+127)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.3e-280)
		tmp = x;
	elseif (y <= 6.5e+127)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.3e-280], x, If[LessEqual[y, 6.5e+127], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2999999999999999e-280

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      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. Taylor expanded in x around inf 34.6%

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

   6. Taylor expanded in z around 0 19.1%

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

   if -4.2999999999999999e-280 < y < 6.5e127

   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. associate-+l- 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l- 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 75.8%

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

   7. Taylor expanded in a around inf 31.6%

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

      1. *-commutative 31.6%

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

   9. Simplified 31.6%

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

   if 6.5e127 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in y around inf 56.5%

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

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+100}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 3.1e+100) (+ x (* b (- a 0.5))) (+ x (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.1e+100) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 3.1d+100) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = x + (y + (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.1e+100) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = x + (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.1e+100:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = x + (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.1e+100)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(x + Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.1e+100)
		tmp = x + (b * (a - 0.5));
	else
		tmp = x + (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.1e+100], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.10000000000000007e100

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 84.8%

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

      1. associate-+r+ 84.8%

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

      2. +-commutative 84.8%

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

      3. sub-neg 84.8%

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

      4. metadata-eval 84.8%

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

      5. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in z around 0 64.8%

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

   if 3.10000000000000007e100 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in z around 0 95.6%

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

   7. Taylor expanded in a around inf 91.0%

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

      1. *-commutative 91.0%

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

   9. Simplified 91.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{+100}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.9% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l- 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. sub-neg 99.9%

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

   7. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in a around 0 99.9%

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

6. Taylor expanded in z around 0 82.4%

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

7. Final simplification 82.4%

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

Alternative 17: 78.9% 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 99.9%

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

   1. associate-+l- 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l- 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. sub-neg 99.9%

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

   7. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in a around 0 99.9%

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

6. Taylor expanded in z around 0 82.4%

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

   1. +-commutative 82.4%

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

   2. distribute-rgt-in 82.4%

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

8. Simplified 82.4%

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

9. Final simplification 82.4%

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

Alternative 18: 27.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 1.55e-5) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e-5) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.55d-5) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e-5) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.55e-5:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.55e-5)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.55e-5)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.55e-5], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.55000000000000007e-5

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. *-lft-identity 99.9%

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

      6. metadata-eval 99.9%

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

      7. *-commutative 99.9%

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

      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. Taylor expanded in x around inf 41.2%

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

   6. Taylor expanded in z around 0 22.4%

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

   if 1.55000000000000007e-5 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 99.9%

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

   6. Taylor expanded in y around inf 40.5%

      \[\leadsto \color{blue}{y} \]
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 99.9%

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

   1. +-commutative 99.9%

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

   2. associate--l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. *-lft-identity 99.9%

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

   6. metadata-eval 99.9%

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

   7. *-commutative 99.9%

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

   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. Taylor expanded in x around inf 39.2%

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

6. Taylor expanded in z around 0 22.3%

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

Developer Target 1: 99.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

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

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