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

Percentage Accurate: 99.8% → 99.8%

Time: 12.0s

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: 99.8% 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 99.9%

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

   1. +-commutative 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. Add Preprocessing

Alternative 2: 90.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(x + y\right) + t\_1\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2e+57)
     t_2
     (if (<= t_1 2e+34) (+ 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 <= -2e+57) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		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 <= (-2d+57)) then
        tmp = t_2
    else if (t_1 <= 2d+34) 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 <= -2e+57) {
		tmp = t_2;
	} else if (t_1 <= 2e+34) {
		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 <= -2e+57:
		tmp = t_2
	elif t_1 <= 2e+34:
		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 <= -2e+57)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		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 <= -2e+57)
		tmp = t_2;
	elseif (t_1 <= 2e+34)
		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, -2e+57], t$95$2, If[LessEqual[t$95$1, 2e+34], 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) < -2.0000000000000001e57 or 1.99999999999999989e34 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 90.8%

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

   5. Simplified 90.8%

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

   if -2.0000000000000001e57 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999989e34

   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 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+57}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(z + y\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+155}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (+ z y) (* z (log t))) (* a b))))
   (if (<= z -5.5e+98)
     t_1
     (if (<= z 3.1e+155) (+ (+ 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 + y) - (z * log(t))) + (a * b);
	double tmp;
	if (z <= -5.5e+98) {
		tmp = t_1;
	} else if (z <= 3.1e+155) {
		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 + y) - (z * log(t))) + (a * b)
    if (z <= (-5.5d+98)) then
        tmp = t_1
    else if (z <= 3.1d+155) 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 + y) - (z * Math.log(t))) + (a * b);
	double tmp;
	if (z <= -5.5e+98) {
		tmp = t_1;
	} else if (z <= 3.1e+155) {
		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 + y) - (z * math.log(t))) + (a * b)
	tmp = 0
	if z <= -5.5e+98:
		tmp = t_1
	elif z <= 3.1e+155:
		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(Float64(z + y) - Float64(z * log(t))) + Float64(a * b))
	tmp = 0.0
	if (z <= -5.5e+98)
		tmp = t_1;
	elseif (z <= 3.1e+155)
		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 + y) - (z * log(t))) + (a * b);
	tmp = 0.0;
	if (z <= -5.5e+98)
		tmp = t_1;
	elseif (z <= 3.1e+155)
		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[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+98], t$95$1, If[LessEqual[z, 3.1e+155], 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 < -5.49999999999999946e98 or 3.09999999999999989e155 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 84.8%

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

   8. Simplified 84.8%

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

   if -5.49999999999999946e98 < z < 3.09999999999999989e155

   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 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;\left(\left(z + y\right) - z \cdot \log t\right) + a \cdot b\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+155}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + y\right) - z \cdot \log t\right) + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{+106}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= (+ x y) -5e+106)
     (+ (+ x y) t_1)
     (+ t_1 (- (+ z y) (* z (log t)))))))

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+106) {
		tmp = (x + y) + t_1;
	} else {
		tmp = t_1 + ((z + y) - (z * log(t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= (-5d+106)) then
        tmp = (x + y) + t_1
    else
        tmp = t_1 + ((z + y) - (z * log(t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= -5e+106) {
		tmp = (x + y) + t_1;
	} else {
		tmp = t_1 + ((z + y) - (z * Math.log(t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -5e+106:
		tmp = (x + y) + t_1
	else:
		tmp = t_1 + ((z + y) - (z * math.log(t)))
	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+106)
		tmp = Float64(Float64(x + y) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(z + y) - Float64(z * log(t))));
	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+106)
		tmp = (x + y) + t_1;
	else
		tmp = t_1 + ((z + y) - (z * log(t)));
	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+106], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999998e106

   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 92.0%

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

   5. Simplified 92.0%

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

   if -4.9999999999999998e106 < (+.f64 x y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+106}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(\left(z + y\right) - z \cdot \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+100}:\\ \;\;\;\;t\_1 + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= z -2.3e+100)
     (+ t_1 (- z (* z (log t))))
     (if (<= z 1.16e+157) (+ (+ x y) t_1) (+ x (+ (* z (- 1.0 (log t))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= -2.3e+100) {
		tmp = t_1 + (z - (z * log(t)));
	} else if (z <= 1.16e+157) {
		tmp = (x + y) + t_1;
	} else {
		tmp = x + ((z * (1.0 - log(t))) + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (z <= (-2.3d+100)) then
        tmp = t_1 + (z - (z * log(t)))
    else if (z <= 1.16d+157) then
        tmp = (x + y) + t_1
    else
        tmp = x + ((z * (1.0d0 - log(t))) + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (z <= -2.3e+100) {
		tmp = t_1 + (z - (z * Math.log(t)));
	} else if (z <= 1.16e+157) {
		tmp = (x + y) + t_1;
	} else {
		tmp = x + ((z * (1.0 - Math.log(t))) + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if z <= -2.3e+100:
		tmp = t_1 + (z - (z * math.log(t)))
	elif z <= 1.16e+157:
		tmp = (x + y) + t_1
	else:
		tmp = x + ((z * (1.0 - math.log(t))) + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= -2.3e+100)
		tmp = Float64(t_1 + Float64(z - Float64(z * log(t))));
	elseif (z <= 1.16e+157)
		tmp = Float64(Float64(x + y) + t_1);
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - log(t))) + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= -2.3e+100)
		tmp = t_1 + (z - (z * log(t)));
	elseif (z <= 1.16e+157)
		tmp = (x + y) + t_1;
	else
		tmp = x + ((z * (1.0 - log(t))) + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+100], N[(t$95$1 + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+157], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e100

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 81.2%

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

   if -2.2999999999999999e100 < z < 1.16000000000000004e157

   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 96.7%

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

   5. Simplified 96.7%

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

   if 1.16000000000000004e157 < z

   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 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 79.5%

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

   7. Simplified 79.5%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right) + y\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- 1.0 (log t))) y)))
   (if (<= z -4.5e+216)
     t_1
     (if (<= z 1.4e+157) (+ (+ 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 <= -4.5e+216) {
		tmp = t_1;
	} else if (z <= 1.4e+157) {
		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 <= (-4.5d+216)) then
        tmp = t_1
    else if (z <= 1.4d+157) 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 <= -4.5e+216) {
		tmp = t_1;
	} else if (z <= 1.4e+157) {
		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 <= -4.5e+216:
		tmp = t_1
	elif z <= 1.4e+157:
		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 <= -4.5e+216)
		tmp = t_1;
	elseif (z <= 1.4e+157)
		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 <= -4.5e+216)
		tmp = t_1;
	elseif (z <= 1.4e+157)
		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, -4.5e+216], t$95$1, If[LessEqual[z, 1.4e+157], 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 < -4.50000000000000025e216 or 1.4000000000000001e157 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in b around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

         \[\leadsto \left(z - \log t \cdot z\right) + y \]

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

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

      5. log-rec N/A

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

      6. *-commutative N/A

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

      7. sum3-undefine N/A

         \[\leadsto \mathsf{sum3}\left(z, \color{blue}{\left(z \cdot \log \left(\frac{1}{t}\right)\right)}, y\right) \]

      8. *-rgt-identity N/A

         \[\leadsto \mathsf{sum3}\left(\left(z \cdot 1\right), \left(\color{blue}{z} \cdot \log \left(\frac{1}{t}\right)\right), y\right) \]

      9. sum3-define N/A

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

      10. distribute-lft-in N/A

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

      11. log-rec N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

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

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

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

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

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

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

      17. log-lowering-log.f64 71.3%

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

   8. Simplified 71.3%

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

   if -4.50000000000000025e216 < z < 1.4000000000000001e157

   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 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+157}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+229}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -2.7e+222)
     t_1
     (if (<= z 3.8e+229) (+ (+ 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));
	double tmp;
	if (z <= -2.7e+222) {
		tmp = t_1;
	} else if (z <= 3.8e+229) {
		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))
    if (z <= (-2.7d+222)) then
        tmp = t_1
    else if (z <= 3.8d+229) 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));
	double tmp;
	if (z <= -2.7e+222) {
		tmp = t_1;
	} else if (z <= 3.8e+229) {
		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))
	tmp = 0
	if z <= -2.7e+222:
		tmp = t_1
	elif z <= 3.8e+229:
		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(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -2.7e+222)
		tmp = t_1;
	elseif (z <= 3.8e+229)
		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));
	tmp = 0.0;
	if (z <= -2.7e+222)
		tmp = t_1;
	elseif (z <= 3.8e+229)
		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[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+222], t$95$1, If[LessEqual[z, 3.8e+229], 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 < -2.70000000000000013e222 or 3.80000000000000018e229 < z

   1. Initial program 99.5%

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

      1. +-commutative 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 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 71.9%

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

   7. Simplified 71.9%

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

   if -2.70000000000000013e222 < z < 3.80000000000000018e229

   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 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+222}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+229}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 41.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+155) x (if (<= x 4.8e-152) (* (+ a -0.5) b) (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+155) {
		tmp = x;
	} else if (x <= 4.8e-152) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9d+155)) then
        tmp = x
    else if (x <= 4.8d-152) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = y + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+155) {
		tmp = x;
	} else if (x <= 4.8e-152) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9e+155:
		tmp = x
	elif x <= 4.8e-152:
		tmp = (a + -0.5) * b
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9e+155)
		tmp = x;
	elseif (x <= 4.8e-152)
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9e+155)
		tmp = x;
	elseif (x <= 4.8e-152)
		tmp = (a + -0.5) * b;
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9e+155], x, If[LessEqual[x, 4.8e-152], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999947e155

   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 63.7%

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

   if -8.99999999999999947e155 < x < 4.8e-152

   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 42.5%

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

   7. Simplified 42.5%

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

   if 4.8e-152 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 65.6%

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

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{y + \frac{-1}{2} \cdot b} \]
   7. Step-by-step derivation

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 37.4%

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

   8. Simplified 37.4%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 13500000:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.5e+155) x (if (<= x 13500000.0) (* (+ a -0.5) b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+155) {
		tmp = x;
	} else if (x <= 13500000.0) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.5d+155)) then
        tmp = x
    else if (x <= 13500000.0d0) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.5e+155) {
		tmp = x;
	} else if (x <= 13500000.0) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.5e+155:
		tmp = x
	elif x <= 13500000.0:
		tmp = (a + -0.5) * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.5e+155)
		tmp = x;
	elseif (x <= 13500000.0)
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.5e+155)
		tmp = x;
	elseif (x <= 13500000.0)
		tmp = (a + -0.5) * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.5e+155], x, If[LessEqual[x, 13500000.0], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000006e155

   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 63.7%

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

   if -9.5000000000000006e155 < x < 1.35e7

   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 46.1%

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

   7. Simplified 46.1%

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

   if 1.35e7 < x

   1. Initial program 99.9%

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

      1. +-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 18.3%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 13500000:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-151}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.6e+155) x (if (<= x 1.55e-151) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.6e+155) {
		tmp = x;
	} else if (x <= 1.55e-151) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.6d+155)) then
        tmp = x
    else if (x <= 1.55d-151) then
        tmp = a * b
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.6e+155) {
		tmp = x;
	} else if (x <= 1.55e-151) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.6e+155:
		tmp = x
	elif x <= 1.55e-151:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.6e+155)
		tmp = x;
	elseif (x <= 1.55e-151)
		tmp = Float64(a * b);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.6e+155)
		tmp = x;
	elseif (x <= 1.55e-151)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.6e+155], x, If[LessEqual[x, 1.55e-151], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -4.59999999999999996e155

   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 63.7%

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

   if -4.59999999999999996e155 < x < 1.54999999999999992e-151

   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 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 32.6%

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

   7. Simplified 32.6%

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

   if 1.54999999999999992e-151 < x

   1. Initial program 99.9%

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

      1. +-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 20.9%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-151}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= x -2.15e+101) (+ 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 <= -2.15e+101) {
		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 <= (-2.15d+101)) 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 <= -2.15e+101) {
		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 <= -2.15e+101:
		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 (x <= -2.15e+101)
		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 <= -2.15e+101)
		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[x, -2.15e+101], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e101

   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 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 74.7%

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

   if -2.15e101 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 68.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+101}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+72}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.12e+72) (+ x (* b (- a 0.5))) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.12e+72) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.12d+72) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.12e+72) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.12e+72:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.12e+72)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.12e+72)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.12e+72], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.12000000000000001e72

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.0%

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

   if 1.12000000000000001e72 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in 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 82.1%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 76.8%

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

   8. Simplified 76.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+72}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.6% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.12e+156) x (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.12e+156) {
		tmp = x;
	} 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 <= (-1.12d+156)) then
        tmp = x
    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 <= -1.12e+156) {
		tmp = x;
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.12e+156:
		tmp = x
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.12e+156)
		tmp = x;
	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 <= -1.12e+156)
		tmp = x;
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.12e+156], x, N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.12000000000000007e156

   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 63.7%

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

   if -1.12000000000000007e156 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in 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 67.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 54.9%

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

   8. Simplified 54.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \]
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 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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 81.0%

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

5. Simplified 81.0%

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

6. Final simplification 81.0%

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

Alternative 15: 28.8% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -1e+113) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+113) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1d+113)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1e+113) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1e+113:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1e+113)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1e+113)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1e+113], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1e113

   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 59.6%

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

   if -1e113 < x

   1. Initial program 99.8%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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 24.9%

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

Alternative 16: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 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 x around inf

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

7. Simplified 19.0%

   \[\leadsto \color{blue}{x} \]
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 2024161 
(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)))