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

Percentage Accurate: 99.8% → 99.9%

Time: 12.1s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (- 1.0 (log t))) (+ (+ (* b (+ a -0.5)) x) y)))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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))) + (((b * (a + (-0.5d0))) + x) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (z * (1.0 - log(t))) + (((b * (a + -0.5)) + x) + y);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $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. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate-+r+ N/A

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

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

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

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

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

   5. metadata-eval N/A

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

   6. sub-neg N/A

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

   7. *-commutative N/A

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

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

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

   9. sub-neg N/A

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

   10. metadata-eval N/A

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

   11. +-lowering-+.f64 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + y\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.05e+14)
   (+ (+ (* b (+ a -0.5)) x) y)
   (+ (- (+ z y) (* z (log t))) (* b (- a 0.5)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+14) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = ((z + y) - (z * log(t))) + (b * (a - 0.5));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.05d+14)) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = ((z + y) - (z * log(t))) + (b * (a - 0.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.05e+14) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = ((z + y) - (z * Math.log(t))) + (b * (a - 0.5));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.05e+14:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = ((z + y) - (z * math.log(t))) + (b * (a - 0.5))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.05e+14)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = Float64(Float64(Float64(z + y) - Float64(z * log(t))) + Float64(b * Float64(a - 0.5)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.05e+14)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = ((z + y) - (z * log(t))) + (b * (a - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.05e+14], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], N[(N[(N[(z + y), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e14

   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 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 87.7%

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

   5. Simplified 87.7%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 87.7%

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

   7. Applied egg-rr 87.7%

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

   if -1.05e14 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-lowering-+.f64 86.5%

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

   5. Simplified 86.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+14}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(\left(z + y\right) - z \cdot \log t\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.25e+119)
   (+ (* b (- a 0.5)) (- z (* z (log t))))
   (if (<= z 3.4e+226)
     (+ (+ (* b (+ a -0.5)) x) y)
     (+ (* z (- 1.0 (log t))) y))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e+119) {
		tmp = (b * (a - 0.5)) + (z - (z * log(t)));
	} else if (z <= 3.4e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = (z * (1.0 - log(t))) + y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.25d+119)) then
        tmp = (b * (a - 0.5d0)) + (z - (z * log(t)))
    else if (z <= 3.4d+226) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = (z * (1.0d0 - log(t))) + y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e+119) {
		tmp = (b * (a - 0.5)) + (z - (z * Math.log(t)));
	} else if (z <= 3.4e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = (z * (1.0 - Math.log(t))) + y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.25e+119:
		tmp = (b * (a - 0.5)) + (z - (z * math.log(t)))
	elif z <= 3.4e+226:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = (z * (1.0 - math.log(t))) + y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.25e+119)
		tmp = Float64(Float64(b * Float64(a - 0.5)) + Float64(z - Float64(z * log(t))));
	elseif (z <= 3.4e+226)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = Float64(Float64(z * Float64(1.0 - log(t))) + y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.25e+119)
		tmp = (b * (a - 0.5)) + (z - (z * log(t)));
	elseif (z <= 3.4e+226)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = (z * (1.0 - log(t))) + y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.25e+119], N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+226], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e119

   1. Initial program 99.6%

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

   3. Taylor expanded in 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 89.2%

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

   if -1.25e119 < z < 3.39999999999999979e226

   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 93.1%

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

   5. Simplified 93.1%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 93.1%

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

   7. Applied egg-rr 93.1%

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

   if 3.39999999999999979e226 < z

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 81.4%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(a - 0.5\right) + \left(z - z \cdot \log t\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+167}:\\ \;\;\;\;t\_1 + b \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -2.9e+167)
     (+ t_1 (* b a))
     (if (<= z 3.4e+226) (+ (+ (* b (+ a -0.5)) x) y) (+ t_1 y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - log(t));
	double tmp;
	if (z <= -2.9e+167) {
		tmp = t_1 + (b * a);
	} else if (z <= 3.4e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1 + y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - log(t))
    if (z <= (-2.9d+167)) then
        tmp = t_1 + (b * a)
    else if (z <= 3.4d+226) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = t_1 + y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - Math.log(t));
	double tmp;
	if (z <= -2.9e+167) {
		tmp = t_1 + (b * a);
	} else if (z <= 3.4e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1 + y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -2.9e+167:
		tmp = t_1 + (b * a)
	elif z <= 3.4e+226:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = t_1 + y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -2.9e+167)
		tmp = Float64(t_1 + Float64(b * a));
	elseif (z <= 3.4e+226)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = Float64(t_1 + y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -2.9e+167)
		tmp = t_1 + (b * a);
	elseif (z <= 3.4e+226)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = t_1 + y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+167], N[(t$95$1 + N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+226], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], N[(t$95$1 + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999975e167

   1. Initial program 99.6%

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

      1. +-commutative 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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 85.4%

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

   7. Simplified 85.4%

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

   if -2.89999999999999975e167 < z < 3.39999999999999979e226

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 91.2%

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

   5. Simplified 91.2%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.2%

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

   7. Applied egg-rr 91.2%

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

   if 3.39999999999999979e226 < z

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 81.4%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + b \cdot a\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right) + y\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (- 1.0 (log t))) y)))
   (if (<= z -1.85e+124)
     t_1
     (if (<= z 5.6e+226) (+ (+ (* b (+ a -0.5)) x) y) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - log(t))) + y;
	double tmp;
	if (z <= -1.85e+124) {
		tmp = t_1;
	} else if (z <= 5.6e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (1.0d0 - log(t))) + y
    if (z <= (-1.85d+124)) then
        tmp = t_1
    else if (z <= 5.6d+226) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - Math.log(t))) + y;
	double tmp;
	if (z <= -1.85e+124) {
		tmp = t_1;
	} else if (z <= 5.6e+226) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = (z * (1.0 - math.log(t))) + y
	tmp = 0
	if z <= -1.85e+124:
		tmp = t_1
	elif z <= 5.6e+226:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(1.0 - log(t))) + y)
	tmp = 0.0
	if (z <= -1.85e+124)
		tmp = t_1;
	elseif (z <= 5.6e+226)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (1.0 - log(t))) + y;
	tmp = 0.0;
	if (z <= -1.85e+124)
		tmp = t_1;
	elseif (z <= 5.6e+226)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -1.85e+124], t$95$1, If[LessEqual[z, 5.6e+226], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000004e124 or 5.6000000000000005e226 < z

   1. Initial program 99.6%

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

      1. +-commutative 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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 70.5%

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

   if -1.85000000000000004e124 < z < 5.6000000000000005e226

   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 92.7%

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

   5. Simplified 92.7%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 92.7%

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

   7. Applied egg-rr 92.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+226}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -1.34 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+254}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -1.34e+225)
     t_1
     (if (<= z 1.65e+254) (+ (+ (* b (+ a -0.5)) x) y) (+ t_1 x)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
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 <= -1.34e+225) {
		tmp = t_1;
	} else if (z <= 1.65e+254) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-1.34d+225)) then
        tmp = t_1
    else if (z <= 1.65d+254) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 <= -1.34e+225) {
		tmp = t_1;
	} else if (z <= 1.65e+254) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -1.34e+225:
		tmp = t_1
	elif z <= 1.65e+254:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = t_1 + x
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -1.34e+225)
		tmp = t_1;
	elseif (z <= 1.65e+254)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -1.34e+225)
		tmp = t_1;
	elseif (z <= 1.65e+254)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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, -1.34e+225], t$95$1, If[LessEqual[z, 1.65e+254], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.33999999999999995e225

   1. Initial program 99.6%

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

      1. +-commutative 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 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 84.9%

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

   7. Simplified 84.9%

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

   if -1.33999999999999995e225 < z < 1.64999999999999996e254

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 88.1%

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

   5. Simplified 88.1%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 88.1%

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

   7. Applied egg-rr 88.1%

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

   if 1.64999999999999996e254 < z

   1. Initial program 99.4%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. distribute-rgt1-in N/A

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

      9. *-commutative N/A

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

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

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

      11. +-commutative N/A

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

      12. unsub-neg N/A

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

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

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

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

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

      15. +-commutative N/A

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

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

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

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

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

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

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

      19. sub-neg N/A

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

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

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

      21. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 88.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.34 \cdot 10^{+225}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+254}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+254}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 (log t)))))
   (if (<= z -5.9e+225)
     t_1
     (if (<= z 9.2e+254) (+ (+ (* b (+ a -0.5)) x) y) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
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 <= -5.9e+225) {
		tmp = t_1;
	} else if (z <= 9.2e+254) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 <= (-5.9d+225)) then
        tmp = t_1
    else if (z <= 9.2d+254) then
        tmp = ((b * (a + (-0.5d0))) + x) + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 <= -5.9e+225) {
		tmp = t_1;
	} else if (z <= 9.2e+254) {
		tmp = ((b * (a + -0.5)) + x) + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - math.log(t))
	tmp = 0
	if z <= -5.9e+225:
		tmp = t_1
	elif z <= 9.2e+254:
		tmp = ((b * (a + -0.5)) + x) + y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (z <= -5.9e+225)
		tmp = t_1;
	elseif (z <= 9.2e+254)
		tmp = Float64(Float64(Float64(b * Float64(a + -0.5)) + x) + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - log(t));
	tmp = 0.0;
	if (z <= -5.9e+225)
		tmp = t_1;
	elseif (z <= 9.2e+254)
		tmp = ((b * (a + -0.5)) + x) + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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, -5.9e+225], t$95$1, If[LessEqual[z, 9.2e+254], N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8999999999999998e225 or 9.19999999999999994e254 < z

   1. Initial program 99.6%

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

      1. +-commutative 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 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{z \cdot \left(1 - \log t\right) + \left(\left(x + y\right) + \left(a + -0.5\right) \cdot b\right)} \]
   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 86.4%

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

   7. Simplified 86.4%

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

   if -5.8999999999999998e225 < z < 9.19999999999999994e254

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 88.1%

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

   5. Simplified 88.1%

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

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

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

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

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 88.1%

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

   7. Applied egg-rr 88.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+225}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+254}:\\ \;\;\;\;\left(b \cdot \left(a + -0.5\right) + x\right) + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (* z (- 1.0 (log t))) (+ (* b (+ a -0.5)) (+ x y))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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))) + ((b * (a + (-0.5d0))) + (x + y))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (z * (1.0 - log(t))) + ((b * (a + -0.5)) + (x + y));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. +-commutative 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. Final simplification 99.9%

   \[\leadsto z \cdot \left(1 - \log t\right) + \left(b \cdot \left(a + -0.5\right) + \left(x + y\right)\right) \]
6. Add Preprocessing

Alternative 9: 61.8% accurate, 7.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a + -0.5\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ a -0.5))))
   (if (<= b -8e+39) t_1 (if (<= b 2e+22) (+ x y) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a + -0.5);
	double tmp;
	if (b <= -8e+39) {
		tmp = t_1;
	} else if (b <= 2e+22) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 (b <= (-8d+39)) then
        tmp = t_1
    else if (b <= 2d+22) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 (b <= -8e+39) {
		tmp = t_1;
	} else if (b <= 2e+22) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a + -0.5)
	tmp = 0
	if b <= -8e+39:
		tmp = t_1
	elif b <= 2e+22:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a + -0.5))
	tmp = 0.0
	if (b <= -8e+39)
		tmp = t_1;
	elseif (b <= 2e+22)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a + -0.5);
	tmp = 0.0;
	if (b <= -8e+39)
		tmp = t_1;
	elseif (b <= 2e+22)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+39], t$95$1, If[LessEqual[b, 2e+22], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.99999999999999952e39 or 2e22 < 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 71.8%

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

   7. Simplified 71.8%

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

   if -7.99999999999999952e39 < b < 2e22

   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 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 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 62.1%

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

   8. Simplified 62.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(a + -0.5\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;x + y \leq -4 \cdot 10^{-85}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5)))) (if (<= (+ x y) -4e-85) (+ x t_1) (+ y t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
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) <= -4e-85) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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) <= (-4d-85)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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) <= -4e-85) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (x + y) <= -4e-85:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (Float64(x + y) <= -4e-85)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((x + y) <= -4e-85)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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], -4e-85], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.9999999999999999e-85

   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 57.9%

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

   if -3.9999999999999999e-85 < (+.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 61.2%

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

4. Final simplification 59.7%

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

Alternative 11: 50.9% accurate, 8.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+110}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -7.4e+110) (* b a) (if (<= a 1.36e+23) (+ x y) (* b a))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.4e+110) {
		tmp = b * a;
	} else if (a <= 1.36e+23) {
		tmp = x + y;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.4d+110)) then
        tmp = b * a
    else if (a <= 1.36d+23) then
        tmp = x + y
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.4e+110) {
		tmp = b * a;
	} else if (a <= 1.36e+23) {
		tmp = x + y;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.4e+110:
		tmp = b * a
	elif a <= 1.36e+23:
		tmp = x + y
	else:
		tmp = b * a
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.4e+110)
		tmp = Float64(b * a);
	elseif (a <= 1.36e+23)
		tmp = Float64(x + y);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.4e+110)
		tmp = b * a;
	elseif (a <= 1.36e+23)
		tmp = x + y;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.4e+110], N[(b * a), $MachinePrecision], If[LessEqual[a, 1.36e+23], N[(x + y), $MachinePrecision], N[(b * a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -7.40000000000000024e110 or 1.36e23 < a

   1. Initial program 99.9%

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

      1. +-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 63.1%

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

   7. Simplified 63.1%

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

   if -7.40000000000000024e110 < a < 1.36e23

   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 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+110}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.6% accurate, 8.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.72 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+56}:\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.72e-279) x (if (<= y 3.2e+56) (* b a) y)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.72e-279) {
		tmp = x;
	} else if (y <= 3.2e+56) {
		tmp = b * a;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.72d-279) then
        tmp = x
    else if (y <= 3.2d+56) then
        tmp = b * a
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.72e-279) {
		tmp = x;
	} else if (y <= 3.2e+56) {
		tmp = b * a;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.72e-279:
		tmp = x
	elif y <= 3.2e+56:
		tmp = b * a
	else:
		tmp = y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.72e-279)
		tmp = x;
	elseif (y <= 3.2e+56)
		tmp = Float64(b * a);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.72e-279)
		tmp = x;
	elseif (y <= 3.2e+56)
		tmp = b * a;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.72e-279], x, If[LessEqual[y, 3.2e+56], N[(b * a), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 1.7199999999999999e-279

   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 21.4%

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

   if 1.7199999999999999e-279 < y < 3.20000000000000003e56

   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 34.2%

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

   7. Simplified 34.2%

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

   if 3.20000000000000003e56 < y

   1. Initial program 99.9%

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

      1. +-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 y around inf

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

   7. Simplified 49.3%

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

Alternative 13: 70.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.15e+66) (+ x (* b (- a 0.5))) (+ y (* b a))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.15e+66) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 1.15d+66) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + (b * a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.15e+66) {
		tmp = x + (b * (a - 0.5));
	} else {
		tmp = y + (b * a);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.15e+66:
		tmp = x + (b * (a - 0.5))
	else:
		tmp = y + (b * a)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.15e+66)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	else
		tmp = Float64(y + Float64(b * a));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.15e+66)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (b * a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.15e+66], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(b * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.15e66

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.2%

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

   if 1.15e66 < 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 73.9%

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

   6. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y + b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 78.8% accurate, 12.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (+ (+ (* b (+ a -0.5)) x) y))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = ((b * (a + (-0.5d0))) + x) + y
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((b * (a + -0.5)) + x) + y;
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((b * (a + -0.5)) + x) + y;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + y), $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 79.8%

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

5. Simplified 79.8%

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

   1. +-commutative N/A

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

   2. associate-+r+ N/A

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

   3. +-commutative N/A

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

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

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

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

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

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

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

   7. sub-neg N/A

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

   8. metadata-eval N/A

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

   9. +-lowering-+.f64 79.8%

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

7. Applied egg-rr 79.8%

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

8. Final simplification 79.8%

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

Alternative 15: 78.8% accurate, 12.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (+ (* b (- a 0.5)) (+ x y)))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = (b * (a - 0.5d0)) + (x + y)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (b * (a - 0.5)) + (x + y);
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (b * (a - 0.5)) + (x + y);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(x + y), $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 79.8%

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

5. Simplified 79.8%

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

6. Final simplification 79.8%

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

Alternative 16: 36.5% accurate, 19.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (if (<= y 2.9e+43) x y))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.9e+43) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= 2.9d+43) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 2.9e+43) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 2.9e+43:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 2.9e+43)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 2.9e+43)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 2.9e+43], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.9000000000000002e43

   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 23.2%

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

   if 2.9000000000000002e43 < y

   1. Initial program 99.9%

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

      1. +-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 y around inf

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

   7. Simplified 47.6%

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

Alternative 17: 21.7% accurate, 115.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 x)

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return x

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return x
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 20.8%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024140 
(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)))