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

Percentage Accurate: 99.9% → 99.9%

Time: 12.4s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(x + y\right) + t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+106}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -5e+45)
     t_2
     (if (<= t_1 5e+106) (+ 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 <= -5e+45) {
		tmp = t_2;
	} else if (t_1 <= 5e+106) {
		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 <= (-5d+45)) then
        tmp = t_2
    else if (t_1 <= 5d+106) 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 <= -5e+45) {
		tmp = t_2;
	} else if (t_1 <= 5e+106) {
		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 <= -5e+45:
		tmp = t_2
	elif t_1 <= 5e+106:
		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 <= -5e+45)
		tmp = t_2;
	elseif (t_1 <= 5e+106)
		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 <= -5e+45)
		tmp = t_2;
	elseif (t_1 <= 5e+106)
		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, -5e+45], t$95$2, If[LessEqual[t$95$1, 5e+106], 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) < -5e45 or 4.9999999999999998e106 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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 92.1%

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

   5. Simplified 92.1%

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

   if -5e45 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.9999999999999998e106

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 90.5%

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

   7. Simplified 90.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+45}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+106}:\\ \;\;\;\;x + \left(z \cdot \left(1 - \log t\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;\left(z - t\_1\right) + t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;\left(x + y\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - t\_1\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))))
   (if (<= z -5.6e+94)
     (+ (- z t_1) t_2)
     (if (<= z 2.9e-28) (+ (+ x y) t_2) (+ (- (+ z (+ x y)) t_1) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= -5.6e+94) {
		tmp = (z - t_1) + t_2;
	} else if (z <= 2.9e-28) {
		tmp = (x + y) + t_2;
	} else {
		tmp = ((z + (x + y)) - t_1) + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    if (z <= (-5.6d+94)) then
        tmp = (z - t_1) + t_2
    else if (z <= 2.9d-28) then
        tmp = (x + y) + t_2
    else
        tmp = ((z + (x + y)) - t_1) + (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 t_1 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= -5.6e+94) {
		tmp = (z - t_1) + t_2;
	} else if (z <= 2.9e-28) {
		tmp = (x + y) + t_2;
	} else {
		tmp = ((z + (x + y)) - t_1) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	tmp = 0
	if z <= -5.6e+94:
		tmp = (z - t_1) + t_2
	elif z <= 2.9e-28:
		tmp = (x + y) + t_2
	else:
		tmp = ((z + (x + y)) - t_1) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= -5.6e+94)
		tmp = Float64(Float64(z - t_1) + t_2);
	elseif (z <= 2.9e-28)
		tmp = Float64(Float64(x + y) + t_2);
	else
		tmp = Float64(Float64(Float64(z + Float64(x + y)) - t_1) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= -5.6e+94)
		tmp = (z - t_1) + t_2;
	elseif (z <= 2.9e-28)
		tmp = (x + y) + t_2;
	else
		tmp = ((z + (x + y)) - t_1) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+94], N[(N[(z - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, 2.9e-28], N[(N[(x + y), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999997e94

   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 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 89.8%

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

   if -5.59999999999999997e94 < z < 2.90000000000000013e-28

   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 98.0%

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

   5. Simplified 98.0%

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

   if 2.90000000000000013e-28 < 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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 90.3%

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

   5. Simplified 90.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;\left(z - z \cdot \log t\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-28}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ t_2 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\left(z - t\_1\right) + t\_2\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+117}:\\ \;\;\;\;\left(x + y\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + a \cdot b\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))) (t_2 (* b (- a 0.5))))
   (if (<= z -7e+109)
     (+ (- z t_1) t_2)
     (if (<= z 1.18e+117) (+ (+ x y) t_2) (- (+ z (+ x (* a b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= -7e+109) {
		tmp = (z - t_1) + t_2;
	} else if (z <= 1.18e+117) {
		tmp = (x + y) + t_2;
	} else {
		tmp = (z + (x + (a * b))) - 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) :: t_2
    real(8) :: tmp
    t_1 = z * log(t)
    t_2 = b * (a - 0.5d0)
    if (z <= (-7d+109)) then
        tmp = (z - t_1) + t_2
    else if (z <= 1.18d+117) then
        tmp = (x + y) + t_2
    else
        tmp = (z + (x + (a * b))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * Math.log(t);
	double t_2 = b * (a - 0.5);
	double tmp;
	if (z <= -7e+109) {
		tmp = (z - t_1) + t_2;
	} else if (z <= 1.18e+117) {
		tmp = (x + y) + t_2;
	} else {
		tmp = (z + (x + (a * b))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	t_2 = b * (a - 0.5)
	tmp = 0
	if z <= -7e+109:
		tmp = (z - t_1) + t_2
	elif z <= 1.18e+117:
		tmp = (x + y) + t_2
	else:
		tmp = (z + (x + (a * b))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	t_2 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (z <= -7e+109)
		tmp = Float64(Float64(z - t_1) + t_2);
	elseif (z <= 1.18e+117)
		tmp = Float64(Float64(x + y) + t_2);
	else
		tmp = Float64(Float64(z + Float64(x + Float64(a * b))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	t_2 = b * (a - 0.5);
	tmp = 0.0;
	if (z <= -7e+109)
		tmp = (z - t_1) + t_2;
	elseif (z <= 1.18e+117)
		tmp = (x + y) + t_2;
	else
		tmp = (z + (x + (a * b))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+109], N[(N[(z - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[z, 1.18e+117], N[(N[(x + y), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(z + N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999966e109

   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 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 89.8%

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

   if -6.99999999999999966e109 < z < 1.18e117

   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 92.5%

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

   5. Simplified 92.5%

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

   if 1.18e117 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. Add Preprocessing
   3. 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. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-+r- N/A

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

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

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

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

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

      14. +-commutative N/A

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

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

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

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

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

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

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

      18. log-lowering-log.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 87.9%

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

   10. Simplified 87.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+109}:\\ \;\;\;\;\left(z - z \cdot \log t\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+117}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(x + a \cdot b\right)\right) - z \cdot \log t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \log t\\ \mathbf{if}\;x + y \leq 10^{-23}:\\ \;\;\;\;\left(z + \left(x + \left(a + -0.5\right) \cdot b\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - t\_1\right) + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (log t))))
   (if (<= (+ x y) 1e-23)
     (- (+ z (+ x (* (+ a -0.5) b))) t_1)
     (+ (- (+ z (+ x y)) t_1) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * log(t);
	double tmp;
	if ((x + y) <= 1e-23) {
		tmp = (z + (x + ((a + -0.5) * b))) - t_1;
	} else {
		tmp = ((z + (x + y)) - t_1) + (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) :: t_1
    real(8) :: tmp
    t_1 = z * log(t)
    if ((x + y) <= 1d-23) then
        tmp = (z + (x + ((a + (-0.5d0)) * b))) - t_1
    else
        tmp = ((z + (x + y)) - t_1) + (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 t_1 = z * Math.log(t);
	double tmp;
	if ((x + y) <= 1e-23) {
		tmp = (z + (x + ((a + -0.5) * b))) - t_1;
	} else {
		tmp = ((z + (x + y)) - t_1) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * math.log(t)
	tmp = 0
	if (x + y) <= 1e-23:
		tmp = (z + (x + ((a + -0.5) * b))) - t_1
	else:
		tmp = ((z + (x + y)) - t_1) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * log(t))
	tmp = 0.0
	if (Float64(x + y) <= 1e-23)
		tmp = Float64(Float64(z + Float64(x + Float64(Float64(a + -0.5) * b))) - t_1);
	else
		tmp = Float64(Float64(Float64(z + Float64(x + y)) - t_1) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * log(t);
	tmp = 0.0;
	if ((x + y) <= 1e-23)
		tmp = (z + (x + ((a + -0.5) * b))) - t_1;
	else
		tmp = ((z + (x + y)) - t_1) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e-23], N[(N[(z + N[(x + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999996e-24

   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. 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. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-+r- N/A

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

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

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

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

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

      14. +-commutative N/A

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

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

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

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

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

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

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

      18. log-lowering-log.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 84.8%

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

   7. Simplified 84.8%

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

   if 9.9999999999999996e-24 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-23}:\\ \;\;\;\;\left(z + \left(x + \left(a + -0.5\right) \cdot b\right)\right) - z \cdot \log t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+159}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e+159)
   (- (+ z x) (* z (log t)))
   (if (<= z 2.45e+179)
     (+ (+ x y) (* b (- a 0.5)))
     (+ (* z (- 1.0 (log t))) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+159) {
		tmp = (z + x) - (z * log(t));
	} else if (z <= 2.45e+179) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (z * (1.0 - log(t))) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d+159)) then
        tmp = (z + x) - (z * log(t))
    else if (z <= 2.45d+179) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = (z * (1.0d0 - log(t))) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+159) {
		tmp = (z + x) - (z * Math.log(t));
	} else if (z <= 2.45e+179) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = (z * (1.0 - Math.log(t))) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e+159:
		tmp = (z + x) - (z * math.log(t))
	elif z <= 2.45e+179:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = (z * (1.0 - math.log(t))) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e+159)
		tmp = Float64(Float64(z + x) - Float64(z * log(t)));
	elseif (z <= 2.45e+179)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e+159)
		tmp = (z + x) - (z * log(t));
	elseif (z <= 2.45e+179)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = (z * (1.0 - log(t))) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e+159], N[(N[(z + x), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+179], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999995e159

   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. 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. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-+r- N/A

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

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

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

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

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

      14. +-commutative N/A

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

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

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

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

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

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

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

      18. log-lowering-log.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in x around inf

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

   10. Simplified 62.3%

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

   if -2.29999999999999995e159 < z < 2.4499999999999999e179

   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 90.4%

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

   5. Simplified 90.4%

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

   if 2.4499999999999999e179 < z

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. log-lowering-log.f64 82.7%

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

   10. Simplified 82.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+159}:\\ \;\;\;\;\left(z + x\right) - z \cdot \log t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+179}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right) + x\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+178}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- 1.0 (log t))) x)))
   (if (<= z -1.95e+158)
     t_1
     (if (<= z 2.75e+178) (+ (+ x y) (* b (- a 0.5))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - log(t))) + x;
	double tmp;
	if (z <= -1.95e+158) {
		tmp = t_1;
	} else if (z <= 2.75e+178) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (1.0d0 - log(t))) + x
    if (z <= (-1.95d+158)) then
        tmp = t_1
    else if (z <= 2.75d+178) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - Math.log(t))) + x;
	double tmp;
	if (z <= -1.95e+158) {
		tmp = t_1;
	} else if (z <= 2.75e+178) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (1.0 - math.log(t))) + x
	tmp = 0
	if z <= -1.95e+158:
		tmp = t_1
	elif z <= 2.75e+178:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(1.0 - log(t))) + x)
	tmp = 0.0
	if (z <= -1.95e+158)
		tmp = t_1;
	elseif (z <= 2.75e+178)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (1.0 - log(t))) + x;
	tmp = 0.0;
	if (z <= -1.95e+158)
		tmp = t_1;
	elseif (z <= 2.75e+178)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.95e+158], t$95$1, If[LessEqual[z, 2.75e+178], 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 < -1.95e158 or 2.7500000000000001e178 < 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 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in y around 0

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

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

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

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

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

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

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

      4. log-lowering-log.f64 71.5%

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

   10. Simplified 71.5%

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

   if -1.95e158 < z < 2.7500000000000001e178

   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 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+178}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+227}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+182}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e+227)
   (- z (* z (log t)))
   (if (<= z 1.85e+182) (+ (+ x y) (* b (- a 0.5))) (* z (- 1.0 (log t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+227) {
		tmp = z - (z * log(t));
	} else if (z <= 1.85e+182) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.2d+227)) then
        tmp = z - (z * log(t))
    else if (z <= 1.85d+182) then
        tmp = (x + y) + (b * (a - 0.5d0))
    else
        tmp = z * (1.0d0 - log(t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+227) {
		tmp = z - (z * Math.log(t));
	} else if (z <= 1.85e+182) {
		tmp = (x + y) + (b * (a - 0.5));
	} else {
		tmp = z * (1.0 - Math.log(t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e+227:
		tmp = z - (z * math.log(t))
	elif z <= 1.85e+182:
		tmp = (x + y) + (b * (a - 0.5))
	else:
		tmp = z * (1.0 - math.log(t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e+227)
		tmp = Float64(z - Float64(z * log(t)));
	elseif (z <= 1.85e+182)
		tmp = Float64(Float64(x + y) + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e+227)
		tmp = z - (z * log(t));
	elseif (z <= 1.85e+182)
		tmp = (x + y) + (b * (a - 0.5));
	else
		tmp = z * (1.0 - log(t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e+227], N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+182], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999988e227

   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. 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. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. associate-+r- N/A

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

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

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

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

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. sub-neg N/A

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

      12. metadata-eval N/A

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

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

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

      14. +-commutative N/A

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

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

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

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

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

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

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

      18. log-lowering-log.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 77.9%

      \[\leadsto \color{blue}{z} - z \cdot \log t \]

   if -3.19999999999999988e227 < z < 1.84999999999999988e182

   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 87.6%

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

   5. Simplified 87.6%

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

   if 1.84999999999999988e182 < z

   1. Initial program 99.7%

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

      1. +-commutative 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 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 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+227}:\\ \;\;\;\;z - z \cdot \log t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+182}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+181}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.25e+232)
     t_1
     (if (<= z 2.45e+181) (+ (+ 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 <= -1.25e+232) {
		tmp = t_1;
	} else if (z <= 2.45e+181) {
		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 <= (-1.25d+232)) then
        tmp = t_1
    else if (z <= 2.45d+181) 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 <= -1.25e+232) {
		tmp = t_1;
	} else if (z <= 2.45e+181) {
		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 <= -1.25e+232:
		tmp = t_1
	elif z <= 2.45e+181:
		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 <= -1.25e+232)
		tmp = t_1;
	elseif (z <= 2.45e+181)
		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 <= -1.25e+232)
		tmp = t_1;
	elseif (z <= 2.45e+181)
		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, -1.25e+232], t$95$1, If[LessEqual[z, 2.45e+181], 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 < -1.24999999999999997e232 or 2.44999999999999991e181 < z

   1. Initial program 99.7%

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

      1. +-commutative 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 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 75.3%

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

   7. Simplified 75.3%

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

   if -1.24999999999999997e232 < z < 2.44999999999999991e181

   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 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+181}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.6% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := x + t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ x t_1)))
   (if (<= t_1 -5e+45) t_2 (if (<= t_1 4e+85) (+ x 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 + t_1;
	double tmp;
	if (t_1 <= -5e+45) {
		tmp = t_2;
	} else if (t_1 <= 4e+85) {
		tmp = x + 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 + t_1
    if (t_1 <= (-5d+45)) then
        tmp = t_2
    else if (t_1 <= 4d+85) then
        tmp = x + 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 + t_1;
	double tmp;
	if (t_1 <= -5e+45) {
		tmp = t_2;
	} else if (t_1 <= 4e+85) {
		tmp = x + 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 + t_1
	tmp = 0
	if t_1 <= -5e+45:
		tmp = t_2
	elif t_1 <= 4e+85:
		tmp = x + 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(x + t_1)
	tmp = 0.0
	if (t_1 <= -5e+45)
		tmp = t_2;
	elseif (t_1 <= 4e+85)
		tmp = Float64(x + 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 + t_1;
	tmp = 0.0;
	if (t_1 <= -5e+45)
		tmp = t_2;
	elseif (t_1 <= 4e+85)
		tmp = x + 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[(x + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+45], t$95$2, If[LessEqual[t$95$1, 4e+85], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5e45 or 4.0000000000000001e85 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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 83.4%

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

   if -5e45 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.0000000000000001e85

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. log-lowering-log.f64 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 56.3%

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

   10. Simplified 56.3%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+45}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+85}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+45}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+166}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -2e+45)
   (+ x (* a b))
   (if (<= (+ x y) 5e+166) (* (+ a -0.5) b) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -2e+45) {
		tmp = x + (a * b);
	} else if ((x + y) <= 5e+166) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-2d+45)) then
        tmp = x + (a * b)
    else if ((x + y) <= 5d+166) then
        tmp = (a + (-0.5d0)) * b
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -2e+45) {
		tmp = x + (a * b);
	} else if ((x + y) <= 5e+166) {
		tmp = (a + -0.5) * b;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -2e+45:
		tmp = x + (a * b)
	elif (x + y) <= 5e+166:
		tmp = (a + -0.5) * b
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -2e+45)
		tmp = Float64(x + Float64(a * b));
	elseif (Float64(x + y) <= 5e+166)
		tmp = Float64(Float64(a + -0.5) * b);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -2e+45)
		tmp = x + (a * b);
	elseif ((x + y) <= 5e+166)
		tmp = (a + -0.5) * b;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e+45], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+166], N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.9999999999999999e45

   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 60.3%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 48.3%

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

   8. Simplified 48.3%

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

   if -1.9999999999999999e45 < (+.f64 x y) < 5.0000000000000002e166

   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 56.7%

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

   7. Simplified 56.7%

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

   if 5.0000000000000002e166 < (+.f64 x y)

   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 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 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 72.0%

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

   10. Simplified 72.0%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{+45}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+166}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + -0.5\right) \cdot b\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ a -0.5) b)))
   (if (<= b -7.6e+81) t_1 (if (<= b 9e+43) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (b <= -7.6e+81) {
		tmp = t_1;
	} else if (b <= 9e+43) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + (-0.5d0)) * b
    if (b <= (-7.6d+81)) then
        tmp = t_1
    else if (b <= 9d+43) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + -0.5) * b;
	double tmp;
	if (b <= -7.6e+81) {
		tmp = t_1;
	} else if (b <= 9e+43) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + -0.5) * b
	tmp = 0
	if b <= -7.6e+81:
		tmp = t_1
	elif b <= 9e+43:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + -0.5) * b)
	tmp = 0.0
	if (b <= -7.6e+81)
		tmp = t_1;
	elseif (b <= 9e+43)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + -0.5) * b;
	tmp = 0.0;
	if (b <= -7.6e+81)
		tmp = t_1;
	elseif (b <= 9e+43)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -7.6e+81], t$95$1, If[LessEqual[b, 9e+43], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.599999999999999e81 or 9e43 < b

   1. Initial program 99.9%

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

      1. +-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 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 76.0%

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

   7. Simplified 76.0%

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

   if -7.599999999999999e81 < b < 9e43

   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 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 53.0%

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

   10. Simplified 53.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+81}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+43}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.7% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq 10^{-99}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) 1e-99) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e-99) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if ((x + y) <= 1d-99) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((x + y) <= 1e-99) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= 1e-99:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= 1e-99)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= 1e-99)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 1e-99], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1e-99

   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 60.6%

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

   if 1e-99 < (+.f64 x 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 56.2%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-99}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e+87) (* a b) (if (<= b 1.06e+54) (+ x y) (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+87) {
		tmp = a * b;
	} else if (b <= 1.06e+54) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.6d+87)) then
        tmp = a * b
    else if (b <= 1.06d+54) then
        tmp = x + y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+87) {
		tmp = a * b;
	} else if (b <= 1.06e+54) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e+87:
		tmp = a * b
	elif b <= 1.06e+54:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e+87)
		tmp = Float64(a * b);
	elseif (b <= 1.06e+54)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e+87)
		tmp = a * b;
	elseif (b <= 1.06e+54)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e+87], N[(a * b), $MachinePrecision], If[LessEqual[b, 1.06e+54], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6e87 or 1.06e54 < b

   1. Initial program 99.9%

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

      1. +-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 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 49.4%

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

   7. Simplified 49.4%

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

   if -1.6e87 < b < 1.06e54

   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 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 51.6%

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

   10. Simplified 51.6%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+54}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-150}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+160) x (if (<= x 1.5e-150) (* a b) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+160) {
		tmp = x;
	} else if (x <= 1.5e-150) {
		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 <= (-6d+160)) then
        tmp = x
    else if (x <= 1.5d-150) 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 <= -6e+160) {
		tmp = x;
	} else if (x <= 1.5e-150) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+160:
		tmp = x
	elif x <= 1.5e-150:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+160)
		tmp = x;
	elseif (x <= 1.5e-150)
		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 <= -6e+160)
		tmp = x;
	elseif (x <= 1.5e-150)
		tmp = a * b;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+160], x, If[LessEqual[x, 1.5e-150], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -5.9999999999999997e160

   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 60.3%

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

   if -5.9999999999999997e160 < x < 1.5000000000000001e-150

   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 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 33.9%

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

   7. Simplified 33.9%

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

   if 1.5000000000000001e-150 < 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 17.0%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-150}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 78.2% 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 78.1%

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

5. Simplified 78.1%

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

6. Final simplification 78.1%

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

Alternative 17: 27.7% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= x -2.75e-42) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.75e-42) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.75d-42)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.75e-42) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.75e-42:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.75e-42)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.75e-42)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.75e-42], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -2.75e-42

   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 38.6%

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

   if -2.75e-42 < 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 20.0%

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

Alternative 18: 22.2% 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 19.9%

   \[\leadsto \color{blue}{x} \]
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 2024160 
(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)))