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

Percentage Accurate: 99.8% → 99.9%

Time: 12.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* 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) {
	return (z * (1.0 - log(t))) + ((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 = (z * (1.0d0 - log(t))) + ((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 (z * (1.0 - Math.log(t))) + ((x + y) + ((a + -0.5) * b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

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

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

   6. *-commutative N/A

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

   7. cancel-sign-sub-inv N/A

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

   8. distribute-rgt1-in N/A

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

   9. *-commutative N/A

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

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

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

   11. +-commutative N/A

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

   12. unsub-neg N/A

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

   13. --lowering--.f64 N/A

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

   14. log-lowering-log.f64 N/A

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

   15. +-commutative N/A

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

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

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

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

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

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

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

   19. sub-neg N/A

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

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

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

   21. metadata-eval 99.5%

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

3. Simplified 99.5%

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

Alternative 2: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+101}:\\ \;\;\;\;t\_1 + \left(y - z \cdot \log t\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+21}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -4e+101)
     (+ t_1 (- y (* z (log t))))
     (if (<= t_1 1e+21) (+ x (+ (* z (- 1.0 (log t))) y)) (+ (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+101) {
		tmp = t_1 + (y - (z * log(t)));
	} else if (t_1 <= 1e+21) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-4d+101)) then
        tmp = t_1 + (y - (z * log(t)))
    else if (t_1 <= 1d+21) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = (x + y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+101) {
		tmp = t_1 + (y - (z * Math.log(t)));
	} else if (t_1 <= 1e+21) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = (x + y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -4e+101:
		tmp = t_1 + (y - (z * math.log(t)))
	elif t_1 <= 1e+21:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = (x + y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -4e+101)
		tmp = Float64(t_1 + Float64(y - Float64(z * log(t))));
	elseif (t_1 <= 1e+21)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = Float64(Float64(x + y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -4e+101)
		tmp = t_1 + (y - (z * log(t)));
	elseif (t_1 <= 1e+21)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = (x + y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+101], N[(t$95$1 + N[(y - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+21], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -3.9999999999999999e101

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 86.2%

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

   if -3.9999999999999999e101 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1e21

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 96.7%

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

   7. Simplified 96.7%

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

   if 1e21 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(y - z \cdot \log t\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 10^{+21}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(x + y\right) + t\_1\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+21}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ (+ x y) t_1)))
   (if (<= t_1 -4e+101)
     t_2
     (if (<= t_1 1e+21) (+ x (+ (* z (- 1.0 (log t))) y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -4e+101) {
		tmp = t_2;
	} else if (t_1 <= 1e+21) {
		tmp = x + ((z * (1.0 - log(t))) + y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = (x + y) + t_1
    if (t_1 <= (-4d+101)) then
        tmp = t_2
    else if (t_1 <= 1d+21) then
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = (x + y) + t_1;
	double tmp;
	if (t_1 <= -4e+101) {
		tmp = t_2;
	} else if (t_1 <= 1e+21) {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = (x + y) + t_1
	tmp = 0
	if t_1 <= -4e+101:
		tmp = t_2
	elif t_1 <= 1e+21:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(Float64(x + y) + t_1)
	tmp = 0.0
	if (t_1 <= -4e+101)
		tmp = t_2;
	elseif (t_1 <= 1e+21)
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	t_2 = (x + y) + t_1;
	tmp = 0.0;
	if (t_1 <= -4e+101)
		tmp = t_2;
	elseif (t_1 <= 1e+21)
		tmp = x + ((z * (1.0 - log(t))) + y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+101], t$95$2, If[LessEqual[t$95$1, 1e+21], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -3.9999999999999999e101 or 1e21 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 91.6%

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

   5. Simplified 91.6%

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

   if -3.9999999999999999e101 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1e21

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 96.7%

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

   7. Simplified 96.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+101}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 10^{+21}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+81}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (* b (- a 0.5)))))
   (if (<= b -3.9e+86)
     t_1
     (if (<= b 1.9e+81) (+ (- (+ z (+ x y)) (* z (log t))) (* a b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + y) + (b * (a - 0.5));
	double tmp;
	if (b <= -3.9e+86) {
		tmp = t_1;
	} else if (b <= 1.9e+81) {
		tmp = ((z + (x + y)) - (z * log(t))) + (a * 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 = (x + y) + (b * (a - 0.5d0))
    if (b <= (-3.9d+86)) then
        tmp = t_1
    else if (b <= 1.9d+81) then
        tmp = ((z + (x + y)) - (z * log(t))) + (a * 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 = (x + y) + (b * (a - 0.5));
	double tmp;
	if (b <= -3.9e+86) {
		tmp = t_1;
	} else if (b <= 1.9e+81) {
		tmp = ((z + (x + y)) - (z * Math.log(t))) + (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + y) + (b * (a - 0.5))
	tmp = 0
	if b <= -3.9e+86:
		tmp = t_1
	elif b <= 1.9e+81:
		tmp = ((z + (x + y)) - (z * math.log(t))) + (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)))
	tmp = 0.0
	if (b <= -3.9e+86)
		tmp = t_1;
	elseif (b <= 1.9e+81)
		tmp = Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + y) + (b * (a - 0.5));
	tmp = 0.0;
	if (b <= -3.9e+86)
		tmp = t_1;
	elseif (b <= 1.9e+81)
		tmp = ((z + (x + y)) - (z * log(t))) + (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.9e+86], t$95$1, If[LessEqual[b, 1.9e+81], N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.9000000000000002e86 or 1.9e81 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 96.5%

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

   5. Simplified 96.5%

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

   if -3.9000000000000002e86 < b < 1.9e81

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), z\right), \mathsf{*.f64}\left(z, \mathsf{log.f64}\left(t\right)\right)\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+86}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+81}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right) + y\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+107}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- 1.0 (log t))) y)))
   (if (<= z -5.5e+172)
     t_1
     (if (<= z 4.2e+107) (+ (+ x y) (* b (- a 0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - log(t))) + y;
	double tmp;
	if (z <= -5.5e+172) {
		tmp = t_1;
	} else if (z <= 4.2e+107) {
		tmp = (x + y) + (b * (a - 0.5));
	} 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 = (z * (1.0d0 - log(t))) + y
    if (z <= (-5.5d+172)) then
        tmp = t_1
    else if (z <= 4.2d+107) then
        tmp = (x + y) + (b * (a - 0.5d0))
    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 = (z * (1.0 - Math.log(t))) + y;
	double tmp;
	if (z <= -5.5e+172) {
		tmp = t_1;
	} else if (z <= 4.2e+107) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (1.0 - math.log(t))) + y
	tmp = 0
	if z <= -5.5e+172:
		tmp = t_1
	elif z <= 4.2e+107:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(1.0 - log(t))) + y)
	tmp = 0.0
	if (z <= -5.5e+172)
		tmp = t_1;
	elseif (z <= 4.2e+107)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (1.0 - log(t))) + y;
	tmp = 0.0;
	if (z <= -5.5e+172)
		tmp = t_1;
	elseif (z <= 4.2e+107)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -5.5e+172], t$95$1, If[LessEqual[z, 4.2e+107], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999999e172 or 4.1999999999999999e107 < z

   1. Initial program 98.2%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 76.1%

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

   7. Simplified 76.1%

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

   8. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. log-lowering-log.f64 60.7%

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

   10. Simplified 60.7%

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

   if -5.4999999999999999e172 < z < 4.1999999999999999e107

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+172}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+107}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right) + x\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+204}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- 1.0 (log t))) x)))
   (if (<= z -4.9e+174)
     t_1
     (if (<= z 3.7e+204) (+ (+ x y) (* b (- a 0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - log(t))) + x;
	double tmp;
	if (z <= -4.9e+174) {
		tmp = t_1;
	} else if (z <= 3.7e+204) {
		tmp = (x + y) + (b * (a - 0.5));
	} 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 = (z * (1.0d0 - log(t))) + x
    if (z <= (-4.9d+174)) then
        tmp = t_1
    else if (z <= 3.7d+204) then
        tmp = (x + y) + (b * (a - 0.5d0))
    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 = (z * (1.0 - Math.log(t))) + x;
	double tmp;
	if (z <= -4.9e+174) {
		tmp = t_1;
	} else if (z <= 3.7e+204) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (1.0 - math.log(t))) + x
	tmp = 0
	if z <= -4.9e+174:
		tmp = t_1
	elif z <= 3.7e+204:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(1.0 - log(t))) + x)
	tmp = 0.0
	if (z <= -4.9e+174)
		tmp = t_1;
	elseif (z <= 3.7e+204)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (1.0 - log(t))) + x;
	tmp = 0.0;
	if (z <= -4.9e+174)
		tmp = t_1;
	elseif (z <= 3.7e+204)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -4.9e+174], t$95$1, If[LessEqual[z, 3.7e+204], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8999999999999997e174 or 3.7e204 < z

   1. Initial program 97.5%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. log-lowering-log.f64 65.4%

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

   10. Simplified 65.4%

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

   if -4.8999999999999997e174 < z < 3.7e204

   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 z around 0

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

      1. +-lowering-+.f64 91.8%

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

   5. Simplified 91.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+204}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+204}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.8e+204) (+ (+ x y) (* b (- a 0.5))) (* z (- 1.0 (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.8e+204) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 3.8d+204) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = z * (1.0d0 - log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.8e+204) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3.8e+204:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.8e+204)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 3.8e+204)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.8e+204], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.7999999999999998e204

   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 z around 0

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

      1. +-lowering-+.f64 86.4%

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

   5. Simplified 86.4%

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

   if 3.7999999999999998e204 < z

   1. Initial program 95.4%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 95.4%

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

   3. Simplified 95.4%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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. *-lowering-*.f64 N/A

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

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

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

      3. log-lowering-log.f64 60.2%

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

   7. Simplified 60.2%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{+204}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.3% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 10^{-144}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e-49)
   (+ x (* a b))
   (if (<= (+ x y) 1e-144) (* (+ a -0.5) b) (+ y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e-49) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e-144) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-5d-49)) then
        tmp = x + (a * b)
    else if ((x + y) <= 1d-144) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e-49) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e-144) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -5e-49:
		tmp = x + (a * b)
	elif (x + y) <= 1e-144:
		tmp = (a + -0.5) * b
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e-49)
		tmp = Float64(x + Float64(a * b));
	elseif (Float64(x + y) <= 1e-144)
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -5e-49)
		tmp = x + (a * b);
	elseif ((x + y) <= 1e-144)
		tmp = (a + -0.5) * b;
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-49], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e-144], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -4.9999999999999999e-49

   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 61.0%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 50.0%

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

   8. Simplified 50.0%

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

   if -4.9999999999999999e-49 < (+.f64 x y) < 9.9999999999999995e-145

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 51.3%

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

   7. Simplified 51.3%

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

   if 9.9999999999999995e-145 < (+.f64 x y)

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. associate-+l+ N/A

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

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

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

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

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

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

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 46.0%

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

   10. Simplified 46.0%

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

   11. Taylor expanded in b around 0

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

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 53.2%

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

   13. Simplified 53.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 10^{-144}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= b -1.05e+21) t_1 (if (<= b 2.5e-9) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (b <= -1.05e+21) {
		tmp = t_1;
	} else if (b <= 2.5e-9) {
		tmp = x + y;
	} 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 <= (-1.05d+21)) then
        tmp = t_1
    else if (b <= 2.5d-9) then
        tmp = x + y
    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 <= -1.05e+21) {
		tmp = t_1;
	} else if (b <= 2.5e-9) {
		tmp = x + y;
	} 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 <= -1.05e+21:
		tmp = t_1
	elif b <= 2.5e-9:
		tmp = x + y
	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 <= -1.05e+21)
		tmp = t_1;
	elseif (b <= 2.5e-9)
		tmp = Float64(x + y);
	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 <= -1.05e+21)
		tmp = t_1;
	elseif (b <= 2.5e-9)
		tmp = x + y;
	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, -1.05e+21], t$95$1, If[LessEqual[b, 2.5e-9], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.05e21 or 2.5000000000000001e-9 < b

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 72.0%

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

   7. Simplified 72.0%

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

   if -1.05e21 < b < 2.5000000000000001e-9

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 70.2%

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

   10. Simplified 70.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+21}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.5% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -5e-49) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-49) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-5d-49)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e-49) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -5e-49:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -5e-49)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -5e-49)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e-49], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999999e-49

   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 61.0%

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

   if -4.9999999999999999e-49 < (+.f64 x y)

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 59.0%

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

4. Final simplification 59.7%

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

Alternative 11: 53.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-144}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e-144) (+ 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 ((x + y) <= 1e-144) {
		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 ((x + y) <= 1d-144) 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 ((x + y) <= 1e-144) {
		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 (x + y) <= 1e-144:
		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 (Float64(x + y) <= 1e-144)
		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 ((x + y) <= 1e-144)
		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[N[(x + y), $MachinePrecision], 1e-144], 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 (+.f64 x y) < 9.9999999999999995e-145

   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 58.6%

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

   if 9.9999999999999995e-145 < (+.f64 x y)

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in b around -inf

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

      1. mul-1-neg N/A

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

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

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

      3. distribute-lft-out N/A

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

      4. mul-1-neg N/A

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

      5. remove-double-neg N/A

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. associate-+l+ N/A

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

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

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

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

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

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

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 46.0%

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

   10. Simplified 46.0%

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

   11. Taylor expanded in b around 0

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

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 53.2%

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

   13. Simplified 53.2%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-144}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+114}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.8e+114) (* a b) (if (<= b 1.95e-10) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.8e+114) {
		tmp = a * b;
	} else if (b <= 1.95e-10) {
		tmp = x + y;
	} 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 <= (-6.8d+114)) then
        tmp = a * b
    else if (b <= 1.95d-10) then
        tmp = x + y
    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 <= -6.8e+114) {
		tmp = a * b;
	} else if (b <= 1.95e-10) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.8e+114:
		tmp = a * b
	elif b <= 1.95e-10:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.8e+114)
		tmp = Float64(a * b);
	elseif (b <= 1.95e-10)
		tmp = Float64(x + y);
	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 <= -6.8e+114)
		tmp = a * b;
	elseif (b <= 1.95e-10)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.8e+114], N[(a * b), $MachinePrecision], If[LessEqual[b, 1.95e-10], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.8000000000000001e114 or 1.95e-10 < b

   1. Initial program 99.0%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.0%

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 55.7%

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

   7. Simplified 55.7%

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

   if -6.8000000000000001e114 < b < 1.95e-10

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 64.8%

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

   10. Simplified 64.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+114}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-10}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.7e+77) x (if (<= y 8e+47) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+77) {
		tmp = x;
	} else if (y <= 8e+47) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.7d+77)) then
        tmp = x
    else if (y <= 8d+47) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.7e+77) {
		tmp = x;
	} else if (y <= 8e+47) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.7e+77:
		tmp = x
	elif y <= 8e+47:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.7e+77)
		tmp = x;
	elseif (y <= 8e+47)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.7e+77)
		tmp = x;
	elseif (y <= 8e+47)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.7e+77], x, If[LessEqual[y, 8e+47], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999998e77

   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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 18.8%

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

   if -1.69999999999999998e77 < y < 8.0000000000000004e47

   1. Initial program 99.2%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 34.5%

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

   7. Simplified 34.5%

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

   if 8.0000000000000004e47 < y

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 46.0%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.1% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in z around 0

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

   1. +-lowering-+.f64 82.1%

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

5. Simplified 82.1%

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

6. Final simplification 82.1%

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

Alternative 15: 28.3% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y 3.8e+46) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.8e+46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 3.8d+46) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 3.8e+46) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 3.8e+46:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 3.8e+46)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 3.8e+46)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 3.8e+46], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.7999999999999999e46

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 22.7%

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

   if 3.7999999999999999e46 < y

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

      7. cancel-sign-sub-inv N/A

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

      13. --lowering--.f64 N/A

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

      14. log-lowering-log.f64 N/A

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 46.0%

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

Alternative 16: 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 99.5%

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. associate-+r+ N/A

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

   4. +-commutative N/A

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

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

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

   6. *-commutative N/A

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

   7. cancel-sign-sub-inv N/A

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

   8. distribute-rgt1-in N/A

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

   9. *-commutative N/A

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

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

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

   11. +-commutative N/A

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

   12. unsub-neg N/A

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

   13. --lowering--.f64 N/A

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

   14. log-lowering-log.f64 N/A

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

   15. +-commutative N/A

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

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

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

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

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

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

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

   19. sub-neg N/A

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

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

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

   21. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around inf

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

7. Simplified 22.4%

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

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(N[(N[(1.0 - N[Power[N[Log[t], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] / N[(1.0 + N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024152 
(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)))