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, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b + 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. associate--l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. +-commutative 99.9%

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

   7. +-commutative 99.9%

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

   8. *-commutative 99.9%

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

   9. cancel-sign-sub-inv 99.9%

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

   10. distribute-rgt1-in 99.9%

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

   11. *-commutative 99.9%

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

   12. fma-def 99.9%

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

   13. +-commutative 99.9%

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

   14. unsub-neg 99.9%

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

   15. fma-def 99.9%

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

   16. sub-neg 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto x + \mathsf{fma}\left(z, 1 - \log t, \mathsf{fma}\left(a + -0.5, b, y\right)\right) \]

Alternative 2: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+189} \lor \neg \left(t_1 \leq 10^{+99}\right):\\ \;\;\;\;\left(z - z \cdot \log t\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 (or (<= t_1 -5e+189) (not (<= t_1 1e+99)))
     (+ (- z (* z (log t))) (* (+ a -0.5) b))
     (+ (+ x y) (* z (- 1.0 (log t)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+189) || !(t_1 <= 1e+99)) {
		tmp = (z - (z * log(t))) + ((a + -0.5) * b);
	} else {
		tmp = (x + y) + (z * (1.0 - log(t)));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((t_1 <= (-5d+189)) .or. (.not. (t_1 <= 1d+99))) then
        tmp = (z - (z * log(t))) + ((a + (-0.5d0)) * b)
    else
        tmp = (x + y) + (z * (1.0d0 - log(t)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -5e+189) || !(t_1 <= 1e+99)) {
		tmp = (z - (z * Math.log(t))) + ((a + -0.5) * b);
	} else {
		tmp = (x + y) + (z * (1.0 - Math.log(t)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -5e+189) or not (t_1 <= 1e+99):
		tmp = (z - (z * math.log(t))) + ((a + -0.5) * b)
	else:
		tmp = (x + y) + (z * (1.0 - math.log(t)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -5e+189) || !(t_1 <= 1e+99))
		tmp = Float64(Float64(z - Float64(z * log(t))) + Float64(Float64(a + -0.5) * b));
	else
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 - log(t))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -5e+189) || ~((t_1 <= 1e+99)))
		tmp = (z - (z * log(t))) + ((a + -0.5) * b);
	else
		tmp = (x + y) + (z * (1.0 - log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[Or[LessEqual[t$95$1, -5e+189], N[Not[LessEqual[t$95$1, 1e+99]], $MachinePrecision]], N[(N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5.0000000000000004e189 or 9.9999999999999997e98 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 94.1%

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

   5. Taylor expanded in z around inf 91.1%

      \[\leadsto \color{blue}{\left(1 - \log t\right) \cdot z} + \left(a + -0.5\right) \cdot b \]
   6. Step-by-step derivation

      1. sub-neg 91.1%

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

      2. log-rec 91.1%

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

      3. +-commutative 91.1%

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

      4. distribute-rgt1-in 91.1%

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

      5. log-rec 91.1%

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

      6. cancel-sign-sub-inv 91.1%

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

   7. Simplified 91.1%

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

   if -5.0000000000000004e189 < (*.f64 (-.f64 a 1/2) b) < 9.9999999999999997e98

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.8%

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

      11. *-commutative 99.8%

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

      12. fma-def 99.8%

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

      13. +-commutative 99.8%

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

      14. unsub-neg 99.8%

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

      15. fma-def 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 92.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+189} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+99}\right):\\ \;\;\;\;\left(z - z \cdot \log t\right) + \left(a + -0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \]

Alternative 3: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+159} \lor \neg \left(t_1 \leq 10^{+91}\right):\\ \;\;\;\;x + \left(y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 (or (<= t_1 -2e+159) (not (<= t_1 1e+91)))
     (+ x (+ y t_1))
     (+ (+ x y) (* z (- 1.0 (log t)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+159) || !(t_1 <= 1e+91)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (x + y) + (z * (1.0 - log(t)));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((t_1 <= (-2d+159)) .or. (.not. (t_1 <= 1d+91))) then
        tmp = x + (y + t_1)
    else
        tmp = (x + y) + (z * (1.0d0 - log(t)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -2e+159) || !(t_1 <= 1e+91)) {
		tmp = x + (y + t_1);
	} else {
		tmp = (x + y) + (z * (1.0 - Math.log(t)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -2e+159) or not (t_1 <= 1e+91):
		tmp = x + (y + t_1)
	else:
		tmp = (x + y) + (z * (1.0 - math.log(t)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -2e+159) || !(t_1 <= 1e+91))
		tmp = Float64(x + Float64(y + t_1));
	else
		tmp = Float64(Float64(x + y) + Float64(z * Float64(1.0 - log(t))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -2e+159) || ~((t_1 <= 1e+91)))
		tmp = x + (y + t_1);
	else
		tmp = (x + y) + (z * (1.0 - log(t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[Or[LessEqual[t$95$1, -2e+159], N[Not[LessEqual[t$95$1, 1e+91]], $MachinePrecision]], N[(x + N[(y + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.9999999999999999e159 or 1.00000000000000008e91 < (*.f64 (-.f64 a 1/2) b)

   1. Initial program 100.0%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 100.0%

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

      11. *-commutative 100.0%

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

      12. fma-def 100.0%

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

      13. +-commutative 100.0%

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

      14. unsub-neg 100.0%

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

      15. fma-def 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 88.7%

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

   if -1.9999999999999999e159 < (*.f64 (-.f64 a 1/2) b) < 1.00000000000000008e91

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.8%

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

      11. *-commutative 99.8%

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

      12. fma-def 99.8%

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

      13. +-commutative 99.8%

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

      14. unsub-neg 99.8%

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

      15. fma-def 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 93.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+159} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+91}\right):\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + z \cdot \left(1 - \log t\right)\\ \end{array} \]

Alternative 4: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+31}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(\left(x + z\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e+31)
   (+ (* (+ a -0.5) b) (- (+ x z) (* z (log t))))
   (+ x (+ y (* b (- a 0.5))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e+31) {
		tmp = ((a + -0.5) * b) + ((x + z) - (z * log(t)));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 + y) <= 1d+31) then
        tmp = ((a + (-0.5d0)) * b) + ((x + z) - (z * log(t)))
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e+31) {
		tmp = ((a + -0.5) * b) + ((x + z) - (z * Math.log(t)));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e+31:
		tmp = ((a + -0.5) * b) + ((x + z) - (z * math.log(t)))
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e+31)
		tmp = Float64(Float64(Float64(a + -0.5) * b) + Float64(Float64(x + z) - Float64(z * log(t))));
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 1e+31)
		tmp = ((a + -0.5) * b) + ((x + z) - (z * log(t)));
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e+31], N[(N[(N[(a + -0.5), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 9.9999999999999996e30

   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. associate--l+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 82.5%

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

   if 9.9999999999999996e30 < (+.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. Step-by-step derivation

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 86.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{+31}:\\ \;\;\;\;\left(a + -0.5\right) \cdot b + \left(\left(x + z\right) - z \cdot \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

assert(x < y);
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

NOTE: x and y 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 + y) + (z - (z * log(t)))) + ((a + (-0.5d0)) * b)
end function

Java

assert x < y;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x + y), $MachinePrecision] + N[(z - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + -0.5), $MachinePrecision] * b), $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. associate--l+ 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 6: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+171} \lor \neg \left(z \leq 3.15 \cdot 10^{+103}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e+171) (not (<= z 3.15e+103)))
   (+ x (* z (- 1.0 (log t))))
   (+ x (+ y (* b (- a 0.5))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+171) || !(z <= 3.15e+103)) {
		tmp = x + (z * (1.0 - log(t)));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-2.3d+171)) .or. (.not. (z <= 3.15d+103))) then
        tmp = x + (z * (1.0d0 - log(t)))
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+171) || !(z <= 3.15e+103)) {
		tmp = x + (z * (1.0 - Math.log(t)));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e+171) or not (z <= 3.15e+103):
		tmp = x + (z * (1.0 - math.log(t)))
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e+171) || !(z <= 3.15e+103))
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e+171) || ~((z <= 3.15e+103)))
		tmp = x + (z * (1.0 - log(t)));
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e+171], N[Not[LessEqual[z, 3.15e+103]], $MachinePrecision]], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000017e171 or 3.14999999999999985e103 < 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. associate--l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+r+ 99.6%

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

      6. +-commutative 99.6%

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

      7. +-commutative 99.6%

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

      8. *-commutative 99.6%

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

      9. cancel-sign-sub-inv 99.6%

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

      10. distribute-rgt1-in 99.7%

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

      11. *-commutative 99.7%

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

      12. fma-def 99.7%

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

      13. +-commutative 99.7%

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

      14. unsub-neg 99.7%

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

      15. fma-def 99.7%

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

      16. sub-neg 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 68.6%

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

   if -2.30000000000000017e171 < z < 3.14999999999999985e103

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. +-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. cancel-sign-sub-inv 100.0%

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

      10. distribute-rgt1-in 100.0%

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

      11. *-commutative 100.0%

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

      12. fma-def 100.0%

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

      13. +-commutative 100.0%

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

      14. unsub-neg 100.0%

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

      15. fma-def 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 94.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+171} \lor \neg \left(z \leq 3.15 \cdot 10^{+103}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+169}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) - z \cdot \log t\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.2e+169)
   (+ x (* z (- 1.0 (log t))))
   (if (<= z 3.5e+103) (+ x (+ y (* b (- a 0.5)))) (- (+ x z) (* z (log t))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.2e+169) {
		tmp = x + (z * (1.0 - log(t)));
	} else if (z <= 3.5e+103) {
		tmp = x + (y + (b * (a - 0.5)));
	} else {
		tmp = (x + z) - (z * log(t));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-9.2d+169)) then
        tmp = x + (z * (1.0d0 - log(t)))
    else if (z <= 3.5d+103) then
        tmp = x + (y + (b * (a - 0.5d0)))
    else
        tmp = (x + z) - (z * log(t))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.2e+169) {
		tmp = x + (z * (1.0 - Math.log(t)));
	} else if (z <= 3.5e+103) {
		tmp = x + (y + (b * (a - 0.5)));
	} else {
		tmp = (x + z) - (z * Math.log(t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9.2e+169:
		tmp = x + (z * (1.0 - math.log(t)))
	elif z <= 3.5e+103:
		tmp = x + (y + (b * (a - 0.5)))
	else:
		tmp = (x + z) - (z * math.log(t))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.2e+169)
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	elseif (z <= 3.5e+103)
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	else
		tmp = Float64(Float64(x + z) - Float64(z * log(t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9.2e+169)
		tmp = x + (z * (1.0 - log(t)));
	elseif (z <= 3.5e+103)
		tmp = x + (y + (b * (a - 0.5)));
	else
		tmp = (x + z) - (z * log(t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.2e+169], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+103], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999997e169

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-+l+ 99.5%

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

      3. associate-+l+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

      6. +-commutative 99.5%

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

      7. +-commutative 99.5%

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

      8. *-commutative 99.5%

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

      9. cancel-sign-sub-inv 99.5%

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

      10. distribute-rgt1-in 99.6%

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

      11. *-commutative 99.6%

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

      12. fma-def 99.6%

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

      13. +-commutative 99.6%

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

      14. unsub-neg 99.6%

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

      15. fma-def 99.6%

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

      16. sub-neg 99.6%

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

      17. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 72.4%

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

   if -9.1999999999999997e169 < z < 3.5e103

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. +-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. cancel-sign-sub-inv 100.0%

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

      10. distribute-rgt1-in 100.0%

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

      11. *-commutative 100.0%

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

      12. fma-def 100.0%

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

      13. +-commutative 100.0%

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

      14. unsub-neg 100.0%

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

      15. fma-def 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 94.5%

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

   if 3.5e103 < z

   1. Initial program 99.7%

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

      1. associate--l+ 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 86.6%

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

   5. Taylor expanded in b around 0 66.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+169}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+103}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) - z \cdot \log t\\ \end{array} \]

Alternative 8: 84.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+227} \lor \neg \left(z \leq 4.8 \cdot 10^{+189}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e+227) (not (<= z 4.8e+189)))
   (* z (- 1.0 (log t)))
   (+ x (+ y (* b (- a 0.5))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+227) || !(z <= 4.8e+189)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= (-3.2d+227)) .or. (.not. (z <= 4.8d+189))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = x + (y + (b * (a - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e+227) || !(z <= 4.8e+189)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = x + (y + (b * (a - 0.5)));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e+227) or not (z <= 4.8e+189):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = x + (y + (b * (a - 0.5)))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e+227) || !(z <= 4.8e+189))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(x + Float64(y + Float64(b * Float64(a - 0.5))));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e+227) || ~((z <= 4.8e+189)))
		tmp = z * (1.0 - log(t));
	else
		tmp = x + (y + (b * (a - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e+227], N[Not[LessEqual[z, 4.8e+189]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999988e227 or 4.8000000000000001e189 < z

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-+l+ 99.5%

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

      3. associate-+l+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+r+ 99.5%

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

      6. +-commutative 99.5%

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

      7. +-commutative 99.5%

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

      8. *-commutative 99.5%

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

      9. cancel-sign-sub-inv 99.5%

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

      10. distribute-rgt1-in 99.7%

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

      11. *-commutative 99.7%

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

      12. fma-def 99.7%

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

      13. +-commutative 99.7%

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

      14. unsub-neg 99.7%

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

      15. fma-def 99.7%

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

      16. sub-neg 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 79.6%

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

   5. Taylor expanded in z around inf 79.1%

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

   if -3.19999999999999988e227 < z < 4.8000000000000001e189

   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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 88.0%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+227} \lor \neg \left(z \leq 4.8 \cdot 10^{+189}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + b \cdot \left(a - 0.5\right)\right)\\ \end{array} \]

Alternative 9: 72.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+117} \lor \neg \left(t_1 \leq 10^{+99}\right):\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y 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 (or (<= t_1 -1e+117) (not (<= t_1 1e+99)))
     (+ x t_1)
     (+ x (+ y (* -0.5 b))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 1e+99)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Fortran

NOTE: x and y 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 ((t_1 <= (-1d+117)) .or. (.not. (t_1 <= 1d+99))) then
        tmp = x + t_1
    else
        tmp = x + (y + ((-0.5d0) * b))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if ((t_1 <= -1e+117) || !(t_1 <= 1e+99)) {
		tmp = x + t_1;
	} else {
		tmp = x + (y + (-0.5 * b));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if (t_1 <= -1e+117) or not (t_1 <= 1e+99):
		tmp = x + t_1
	else:
		tmp = x + (y + (-0.5 * b))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if ((t_1 <= -1e+117) || !(t_1 <= 1e+99))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x + Float64(y + Float64(-0.5 * b)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if ((t_1 <= -1e+117) || ~((t_1 <= 1e+99)))
		tmp = x + t_1;
	else
		tmp = x + (y + (-0.5 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y 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[Or[LessEqual[t$95$1, -1e+117], N[Not[LessEqual[t$95$1, 1e+99]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(x + N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.00000000000000005e117 or 9.9999999999999997e98 < (*.f64 (-.f64 a 1/2) 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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 79.4%

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

   if -1.00000000000000005e117 < (*.f64 (-.f64 a 1/2) b) < 9.9999999999999997e98

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.8%

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

      11. *-commutative 99.8%

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

      12. fma-def 99.8%

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

      13. +-commutative 99.8%

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

      14. unsub-neg 99.8%

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

      15. fma-def 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 69.2%

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

   5. Taylor expanded in a around 0 67.4%

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

      1. *-commutative 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+117} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 10^{+99}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + -0.5 \cdot b\right)\\ \end{array} \]

Alternative 10: 57.2% accurate, 10.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x + a \cdot b\\ \mathbf{if}\;a \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-280}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-24}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a b))))
   (if (<= a -2.75e-11)
     t_1
     (if (<= a 1.25e-280) (+ x y) (if (<= a 7.5e-24) (+ x (* -0.5 b)) t_1)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * b);
	double tmp;
	if (a <= -2.75e-11) {
		tmp = t_1;
	} else if (a <= 1.25e-280) {
		tmp = x + y;
	} else if (a <= 7.5e-24) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 = x + (a * b)
    if (a <= (-2.75d-11)) then
        tmp = t_1
    else if (a <= 1.25d-280) then
        tmp = x + y
    else if (a <= 7.5d-24) then
        tmp = x + ((-0.5d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * b);
	double tmp;
	if (a <= -2.75e-11) {
		tmp = t_1;
	} else if (a <= 1.25e-280) {
		tmp = x + y;
	} else if (a <= 7.5e-24) {
		tmp = x + (-0.5 * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	t_1 = x + (a * b)
	tmp = 0
	if a <= -2.75e-11:
		tmp = t_1
	elif a <= 1.25e-280:
		tmp = x + y
	elif a <= 7.5e-24:
		tmp = x + (-0.5 * b)
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * b))
	tmp = 0.0
	if (a <= -2.75e-11)
		tmp = t_1;
	elseif (a <= 1.25e-280)
		tmp = Float64(x + y);
	elseif (a <= 7.5e-24)
		tmp = Float64(x + Float64(-0.5 * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * b);
	tmp = 0.0;
	if (a <= -2.75e-11)
		tmp = t_1;
	elseif (a <= 1.25e-280)
		tmp = x + y;
	elseif (a <= 7.5e-24)
		tmp = x + (-0.5 * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.75e-11], t$95$1, If[LessEqual[a, 1.25e-280], N[(x + y), $MachinePrecision], If[LessEqual[a, 7.5e-24], N[(x + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.74999999999999987e-11 or 7.50000000000000007e-24 < 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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 62.9%

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

   if -2.74999999999999987e-11 < a < 1.25000000000000007e-280

   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. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 58.9%

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

   if 1.25000000000000007e-280 < a < 7.50000000000000007e-24

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.8%

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

      11. *-commutative 99.8%

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

      12. fma-def 99.8%

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

      13. +-commutative 99.8%

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

      14. unsub-neg 99.8%

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

      15. fma-def 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 70.4%

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

   5. Taylor expanded in a around 0 70.4%

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

      1. *-commutative 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in y around 0 51.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{-11}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-280}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-24}:\\ \;\;\;\;x + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot b\\ \end{array} \]

Alternative 11: 69.8% accurate, 10.4× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 5e+45) (+ x (* b (- a 0.5))) (+ y (* -0.5 b))))

C

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

Fortran

NOTE: x and y 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 + y) <= 5d+45) then
        tmp = x + (b * (a - 0.5d0))
    else
        tmp = y + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 5e+45)
		tmp = x + (b * (a - 0.5));
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+45], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5e45

   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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 55.7%

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

   if 5e45 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 86.2%

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

   5. Taylor expanded in a around 0 68.8%

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

      1. *-commutative 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in x around 0 41.2%

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

4. Final simplification 51.6%

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

Alternative 12: 57.6% accurate, 12.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 5e+45) (+ x (* a b)) (+ x y)))

C

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

Fortran

NOTE: x and y 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 + y) <= 5d+45) then
        tmp = x + (a * b)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 5e+45:
		tmp = x + (a * b)
	else:
		tmp = x + y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 5e+45)
		tmp = Float64(x + Float64(a * b));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 5e+45)
		tmp = x + (a * b);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 5e+45], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5e45

   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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 43.5%

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

   if 5e45 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.0%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+45}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 60.1% accurate, 12.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-52}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 1e-52) (+ x (* a b)) (+ y (* -0.5 b))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e-52) {
		tmp = x + (a * b);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Fortran

NOTE: x and y 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 + y) <= 1d-52) then
        tmp = x + (a * b)
    else
        tmp = y + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 1e-52) {
		tmp = x + (a * b);
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= 1e-52:
		tmp = x + (a * b)
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 1e-52)
		tmp = Float64(x + Float64(a * b));
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= 1e-52)
		tmp = x + (a * b);
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 1e-52], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1e-52

   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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 44.0%

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

   if 1e-52 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 81.4%

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

   5. Taylor expanded in a around 0 62.1%

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

      1. *-commutative 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in x around 0 38.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 10^{-52}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \]

Alternative 14: 79.1% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y 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 + (y + (b * (a - 0.5d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. +-commutative 99.9%

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

   7. +-commutative 99.9%

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

   8. *-commutative 99.9%

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

   9. cancel-sign-sub-inv 99.9%

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

   10. distribute-rgt1-in 99.9%

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

   11. *-commutative 99.9%

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

   12. fma-def 99.9%

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

   13. +-commutative 99.9%

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

   14. unsub-neg 99.9%

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

   15. fma-def 99.9%

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

   16. sub-neg 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around 0 76.9%

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

5. Final simplification 76.9%

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

Alternative 15: 47.0% accurate, 16.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+126}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e+126) (* -0.5 b) (if (<= b 4.6e+151) (+ x y) (* -0.5 b))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+126) {
		tmp = -0.5 * b;
	} else if (b <= 4.6e+151) {
		tmp = x + y;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 (b <= (-1.8d+126)) then
        tmp = (-0.5d0) * b
    else if (b <= 4.6d+151) then
        tmp = x + y
    else
        tmp = (-0.5d0) * b
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+126) {
		tmp = -0.5 * b;
	} else if (b <= 4.6e+151) {
		tmp = x + y;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e+126:
		tmp = -0.5 * b
	elif b <= 4.6e+151:
		tmp = x + y
	else:
		tmp = -0.5 * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e+126)
		tmp = Float64(-0.5 * b);
	elseif (b <= 4.6e+151)
		tmp = Float64(x + y);
	else
		tmp = Float64(-0.5 * b);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e+126)
		tmp = -0.5 * b;
	elseif (b <= 4.6e+151)
		tmp = x + y;
	else
		tmp = -0.5 * b;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e+126], N[(-0.5 * b), $MachinePrecision], If[LessEqual[b, 4.6e+151], N[(x + y), $MachinePrecision], N[(-0.5 * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8e126 or 4.6000000000000002e151 < 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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 86.9%

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

   5. Taylor expanded in a around 0 41.3%

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

      1. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   8. Taylor expanded in b around inf 34.4%

      \[\leadsto \color{blue}{-0.5 \cdot b} \]

   if -1.8e126 < b < 4.6000000000000002e151

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. +-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. cancel-sign-sub-inv 99.8%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 54.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+126}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+151}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]

Alternative 16: 37.0% accurate, 37.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (if (<= y 6.2e+42) x y))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e+42) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

NOTE: x and y 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 <= 6.2d+42) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.2e+42) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 6.2e+42:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.2e+42)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 6.2e+42)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.2e+42], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 6.2000000000000003e42

   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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 22.4%

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

   if 6.2000000000000003e42 < 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. associate--l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. +-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. cancel-sign-sub-inv 99.9%

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

      10. distribute-rgt1-in 99.9%

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

      11. *-commutative 99.9%

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

      12. fma-def 99.9%

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

      13. +-commutative 99.9%

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

      14. unsub-neg 99.9%

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

      15. fma-def 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 86.4%

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

   5. Taylor expanded in a around 0 70.4%

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

      1. *-commutative 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in y around inf 44.9%

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

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 22.0% accurate, 115.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y 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. associate--l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. +-commutative 99.9%

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

   7. +-commutative 99.9%

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

   8. *-commutative 99.9%

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

   9. cancel-sign-sub-inv 99.9%

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

   10. distribute-rgt1-in 99.9%

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

   11. *-commutative 99.9%

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

   12. fma-def 99.9%

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

   13. +-commutative 99.9%

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

   14. unsub-neg 99.9%

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

   15. fma-def 99.9%

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

   16. sub-neg 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 21.2%

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

5. Final simplification 21.2%

   \[\leadsto x \]

Developer target: 99.4% 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 2023238 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))