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

Percentage Accurate: 99.9% → 99.9%

Time: 15.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = y + ((x + ((a + (-0.5d0)) * b)) - (z * (log(t) + (-1.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

      \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

   2. associate-+l+ N/A

      \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

   3. +-commutative N/A

      \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   4. associate-+l+ N/A

      \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   5. associate-+l+ N/A

      \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   11. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

   13. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

   14. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

   15. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

3. Simplified 99.9%

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

Alternative 2: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a + \left(-0.5 + \frac{y}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+25)
     (+ x (+ y (* (+ a -0.5) b)))
     (if (<= t_1 2e+58)
       (+ (* z (- 1.0 (log t))) (+ y x))
       (+ x (* b (+ a (+ -0.5 (/ y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = x + (y + ((a + -0.5) * b));
	} else if (t_1 <= 2e+58) {
		tmp = (z * (1.0 - log(t))) + (y + x);
	} else {
		tmp = x + (b * (a + (-0.5 + (y / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-2d+25)) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else if (t_1 <= 2d+58) then
        tmp = (z * (1.0d0 - log(t))) + (y + x)
    else
        tmp = x + (b * (a + ((-0.5d0) + (y / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+25) {
		tmp = x + (y + ((a + -0.5) * b));
	} else if (t_1 <= 2e+58) {
		tmp = (z * (1.0 - Math.log(t))) + (y + x);
	} else {
		tmp = x + (b * (a + (-0.5 + (y / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -2e+25:
		tmp = x + (y + ((a + -0.5) * b))
	elif t_1 <= 2e+58:
		tmp = (z * (1.0 - math.log(t))) + (y + x)
	else:
		tmp = x + (b * (a + (-0.5 + (y / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+25)
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	elseif (t_1 <= 2e+58)
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + Float64(y + x));
	else
		tmp = Float64(x + Float64(b * Float64(a + Float64(-0.5 + Float64(y / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -2e+25)
		tmp = x + (y + ((a + -0.5) * b));
	elseif (t_1 <= 2e+58)
		tmp = (z * (1.0 - log(t))) + (y + x);
	else
		tmp = x + (b * (a + (-0.5 + (y / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+25], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+58], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(a + N[(-0.5 + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.00000000000000018e25

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

      7. +-lowering-+.f64 92.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

   7. Simplified 92.5%

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

   if -2.00000000000000018e25 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999989e58

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(\log t - 1\right)\right)\right)}\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\mathsf{neg}\left(\color{blue}{z \cdot \left(\log t - 1\right)}\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\log t - 1\right)\right)\right)}\right)\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(0 - \color{blue}{\left(\log t - 1\right)}\right)\right)\right) \]

      6. associate-+l- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(\left(0 - \log t\right) + \color{blue}{1}\right)\right)\right) \]

      7. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(\left(\mathsf{neg}\left(\log t\right)\right) + 1\right)\right)\right) \]

      8. log-rec N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(\log \left(\frac{1}{t}\right) + 1\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(1 + \color{blue}{\log \left(\frac{1}{t}\right)}\right)\right)\right) \]

      10. log-rec N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(z \cdot \left(1 + -1 \cdot \color{blue}{\log t}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(1 + -1 \cdot \log t\right)}\right)\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(1 - \color{blue}{\log t}\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right) \]

      16. log-lowering-log.f64 94.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right) \]

   7. Simplified 94.0%

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

   if 1.99999999999999989e58 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

      7. +-lowering-+.f64 96.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

   7. Simplified 96.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(\left(a + \frac{y}{b}\right) - \frac{1}{2}\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(\left(\frac{y}{b} + a\right) - \frac{1}{2}\right)\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(\frac{y}{b} + \color{blue}{\left(a - \frac{1}{2}\right)}\right)\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(\left(a - \frac{1}{2}\right) + \color{blue}{\frac{y}{b}}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(\left(a - \frac{1}{2}\right) + \frac{y}{b}\right)}\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\frac{y}{b} + \color{blue}{\left(a - \frac{1}{2}\right)}\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\frac{y}{b} + a\right) - \color{blue}{\frac{1}{2}}\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(a + \frac{y}{b}\right) - \frac{1}{2}\right)\right)\right) \]

      8. associate--l+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(a + \color{blue}{\left(\frac{y}{b} - \frac{1}{2}\right)}\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{y}{b} - \frac{1}{2}\right)}\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{y}{b} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{y}{b} + \frac{-1}{2}\right)\right)\right)\right) \]

      12. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\left(\frac{y}{b}\right), \color{blue}{\frac{-1}{2}}\right)\right)\right)\right) \]

      13. /-lowering-/.f64 95.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, b\right), \frac{-1}{2}\right)\right)\right)\right) \]

   10. Simplified 95.0%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a + \left(-0.5 + \frac{y}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+200}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- 1.0 (log t))))))
   (if (<= z -1.65e+207)
     t_1
     (if (<= z 1.7e+200) (+ x (+ y (* (+ a -0.5) b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (1.0 - log(t)));
	double tmp;
	if (z <= -1.65e+207) {
		tmp = t_1;
	} else if (z <= 1.7e+200) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = 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 = y + (z * (1.0d0 - log(t)))
    if (z <= (-1.65d+207)) then
        tmp = t_1
    else if (z <= 1.7d+200) then
        tmp = x + (y + ((a + (-0.5d0)) * b))
    else
        tmp = 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 = y + (z * (1.0 - Math.log(t)));
	double tmp;
	if (z <= -1.65e+207) {
		tmp = t_1;
	} else if (z <= 1.7e+200) {
		tmp = x + (y + ((a + -0.5) * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (1.0 - math.log(t)))
	tmp = 0
	if z <= -1.65e+207:
		tmp = t_1
	elif z <= 1.7e+200:
		tmp = x + (y + ((a + -0.5) * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(1.0 - log(t))))
	tmp = 0.0
	if (z <= -1.65e+207)
		tmp = t_1;
	elseif (z <= 1.7e+200)
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (1.0 - log(t)));
	tmp = 0.0;
	if (z <= -1.65e+207)
		tmp = t_1;
	elseif (z <= 1.7e+200)
		tmp = x + (y + ((a + -0.5) * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+207], t$95$1, If[LessEqual[z, 1.7e+200], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e207 or 1.69999999999999985e200 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(1 - \log t\right)\right)}\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(z \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(\log t\right)\right)}\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(z \cdot \left(1 + -1 \cdot \color{blue}{\log t}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(1 + -1 \cdot \log t\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \left(1 - \color{blue}{\log t}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right)\right) \]

      7. log-lowering-log.f64 71.2%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right)\right) \]

   7. Simplified 71.2%

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

   if -1.65e207 < z < 1.69999999999999985e200

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

      7. +-lowering-+.f64 89.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

   7. Simplified 89.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+207}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+200}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e+208) (* z (- 1.0 (log t))) (+ x (+ y (* (+ a -0.5) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+208) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.8d+208)) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + ((a + (-0.5d0)) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+208) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + ((a + -0.5) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.8e+208:
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + ((a + -0.5) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e+208)
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(a + -0.5) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.8e+208)
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + ((a + -0.5) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e+208], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999973e208

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(1 + -1 \cdot \log t\right)}\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(1 + \left(\mathsf{neg}\left(\log t\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(1 - \color{blue}{\log t}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \color{blue}{\log t}\right)\right) \]

      7. log-lowering-log.f64 62.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(1, \mathsf{log.f64}\left(t\right)\right)\right) \]

   7. Simplified 62.6%

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

   if -4.79999999999999973e208 < z

   1. Initial program 99.9%

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

      1. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

      7. +-lowering-+.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

   7. Simplified 85.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \left(a + -0.5\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;b \leq -850000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= b -850000000000.0) t_1 (if (<= b 2.25e+49) (+ y x) 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 (b <= -850000000000.0) {
		tmp = t_1;
	} else if (b <= 2.25e+49) {
		tmp = y + x;
	} else {
		tmp = 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 (b <= (-850000000000.0d0)) then
        tmp = t_1
    else if (b <= 2.25d+49) then
        tmp = y + x
    else
        tmp = 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 (b <= -850000000000.0) {
		tmp = t_1;
	} else if (b <= 2.25e+49) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if b <= -850000000000.0:
		tmp = t_1
	elif b <= 2.25e+49:
		tmp = y + x
	else:
		tmp = 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 (b <= -850000000000.0)
		tmp = t_1;
	elseif (b <= 2.25e+49)
		tmp = Float64(y + x);
	else
		tmp = 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 (b <= -850000000000.0)
		tmp = t_1;
	elseif (b <= 2.25e+49)
		tmp = y + x;
	else
		tmp = 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[b, -850000000000.0], t$95$1, If[LessEqual[b, 2.25e+49], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.5e11 or 2.24999999999999991e49 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(a - \frac{1}{2}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right) \]

      4. +-lowering-+.f64 78.3%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\frac{-1}{2}}\right)\right) \]

   7. Simplified 78.3%

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

   if -8.5e11 < b < 2.24999999999999991e49

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]
   6. Step-by-step derivation

   7. Simplified 62.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -850000000000:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+49}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -29000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -29000000000000.0) (* a b) (if (<= b 1.7e+102) (+ y x) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -29000000000000.0) {
		tmp = a * b;
	} else if (b <= 1.7e+102) {
		tmp = y + x;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-29000000000000.0d0)) then
        tmp = a * b
    else if (b <= 1.7d+102) then
        tmp = y + x
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -29000000000000.0) {
		tmp = a * b;
	} else if (b <= 1.7e+102) {
		tmp = y + x;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -29000000000000.0:
		tmp = a * b
	elif b <= 1.7e+102:
		tmp = y + x
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -29000000000000.0)
		tmp = Float64(a * b);
	elseif (b <= 1.7e+102)
		tmp = Float64(y + x);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -29000000000000.0)
		tmp = a * b;
	elseif (b <= 1.7e+102)
		tmp = y + x;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -29000000000000.0], N[(a * b), $MachinePrecision], If[LessEqual[b, 1.7e+102], N[(y + x), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.9e13 or 1.7e102 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 53.1%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{a}\right) \]

   7. Simplified 53.1%

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

   if -2.9e13 < b < 1.7e102

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{x}\right) \]
   6. Step-by-step derivation

   7. Simplified 61.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -29000000000000:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+102}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 28.8% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.4e+37) x (if (<= x 1.75e-245) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+37) {
		tmp = x;
	} else if (x <= 1.75e-245) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.4d+37)) then
        tmp = x
    else if (x <= 1.75d-245) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.4e+37) {
		tmp = x;
	} else if (x <= 1.75e-245) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.4e+37:
		tmp = x
	elif x <= 1.75e-245:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.4e+37)
		tmp = x;
	elseif (x <= 1.75e-245)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.4e+37)
		tmp = x;
	elseif (x <= 1.75e-245)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.4e+37], x, If[LessEqual[x, 1.75e-245], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -8.4000000000000004e37

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 45.5%

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

   if -8.4000000000000004e37 < x < 1.75000000000000008e-245

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 31.2%

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{a}\right) \]

   7. Simplified 31.2%

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

   if 1.75000000000000008e-245 < x

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 25.9%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-28}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.55e-28) (+ 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 <= 1.55e-28) {
		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 <= 1.55d-28) 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 <= 1.55e-28) {
		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 <= 1.55e-28:
		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 <= 1.55e-28)
		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 <= 1.55e-28)
		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, 1.55e-28], 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 < 1.54999999999999996e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 62.1%

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

   if 1.54999999999999996e-28 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

      7. +-lowering-+.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

   7. Simplified 93.4%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, y\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot a\right), y\right)\right) \]

      2. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, a\right), y\right)\right) \]

   10. Simplified 90.8%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-28}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 3.5e+53) (+ x (* b (- a 0.5))) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.5e+53) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 3.5d+53) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.5e+53) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.5e+53:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.5e+53)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.5e+53)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.5e+53], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.50000000000000019e53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(a, \frac{1}{2}\right), b\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 63.2%

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

   if 3.50000000000000019e53 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(a \cdot b\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(b \cdot \color{blue}{a}\right)\right) \]

      2. *-lowering-*.f64 77.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]

   7. Simplified 77.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.4% 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. sub-neg N/A

      \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

   2. associate-+l+ N/A

      \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

   3. +-commutative N/A

      \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   4. associate-+l+ N/A

      \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   5. associate-+l+ N/A

      \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   11. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

   13. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

   14. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

   15. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
6. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y + b \cdot \left(a - \frac{1}{2}\right)\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \left(a - \frac{1}{2}\right) + \color{blue}{y}\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\left(b \cdot \left(a - \frac{1}{2}\right)\right), \color{blue}{y}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a - \frac{1}{2}\right)\right), y\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right)\right), y\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{-1}{2}\right)\right), y\right)\right) \]

   7. +-lowering-+.f64 81.8%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \frac{-1}{2}\right)\right), y\right)\right) \]

7. Simplified 81.8%

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

8. Final simplification 81.8%

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

Alternative 11: 28.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 2.7e+53) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.7e+53) {
		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 <= 2.7d+53) 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 <= 2.7e+53) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.7e+53:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.7e+53)
		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 <= 2.7e+53)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.7e+53], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.70000000000000019e53

   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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 23.6%

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

   if 2.70000000000000019e53 < 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. sub-neg N/A

         \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

      2. associate-+l+ N/A

         \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

      3. +-commutative N/A

         \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      4. associate-+l+ N/A

         \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

      5. associate-+l+ N/A

         \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      10. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

      11. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

      13. associate-+r+ N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

      15. associate-+l- N/A

          \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   6. Step-by-step derivation

   7. Simplified 51.7%

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

Alternative 12: 22.4% 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. sub-neg N/A

      \[\leadsto \left(\left(\left(x + y\right) + z\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{\left(a - \frac{1}{2}\right)} \cdot b \]

   2. associate-+l+ N/A

      \[\leadsto \left(\left(x + y\right) + z\right) + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)} \]

   3. +-commutative N/A

      \[\leadsto \left(\left(y + x\right) + z\right) + \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   4. associate-+l+ N/A

      \[\leadsto \left(y + \left(x + z\right)\right) + \left(\color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)} + \left(a - \frac{1}{2}\right) \cdot b\right) \]

   5. associate-+l+ N/A

      \[\leadsto y + \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)} \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(\left(x + z\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \left(a - \frac{1}{2}\right) \cdot b\right)\right)}\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(x + z\right) + \left(\left(a - \frac{1}{2}\right) \cdot b + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(x + z\right) + \left(a - \frac{1}{2}\right) \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(z \cdot \log t\right)\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + \left(x + z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   10. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + z\right) + \left(\mathsf{neg}\left(\color{blue}{z \cdot \log t}\right)\right)\right)\right) \]

   11. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \color{blue}{\left(z + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right)}\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\left(\mathsf{neg}\left(z \cdot \log t\right)\right) + \color{blue}{z}\right)\right)\right) \]

   13. associate-+r+ N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) + \left(\mathsf{neg}\left(z \cdot \log t\right)\right)\right) + \color{blue}{z}\right)\right) \]

   14. unsub-neg N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - z \cdot \log t\right) + z\right)\right) \]

   15. associate-+l- N/A

       \[\leadsto \mathsf{+.f64}\left(y, \left(\left(\left(a - \frac{1}{2}\right) \cdot b + x\right) - \color{blue}{\left(z \cdot \log t - z\right)}\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around inf

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

7. Simplified 21.5%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024192 
(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)))