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

Percentage Accurate: 99.9% → 99.9%

Time: 12.2s

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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 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 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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. 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: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	return fma(Float64(a + -0.5), b, Float64(Float64(y + Float64(x + z)) - Float64(z * log(t))))
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[(a + -0.5), $MachinePrecision] * b + N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.9%

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

   3. sub-neg 99.9%

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

   4. metadata-eval 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \left(y + \left(x + z\right)\right) + t_1\\ t_3 := z \cdot \left(1 - \log t\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-250}:\\ \;\;\;\;x + t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-20}:\\ \;\;\;\;y + t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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)))
        (t_2 (+ (+ y (+ x z)) t_1))
        (t_3 (* z (- 1.0 (log t)))))
   (if (<= t_1 -5e+63)
     t_2
     (if (<= t_1 -4e-250) (+ x t_3) (if (<= t_1 2e-20) (+ y t_3) t_2)))))

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 t_2 = (y + (x + z)) + t_1;
	double t_3 = z * (1.0 - log(t));
	double tmp;
	if (t_1 <= -5e+63) {
		tmp = t_2;
	} else if (t_1 <= -4e-250) {
		tmp = x + t_3;
	} else if (t_1 <= 2e-20) {
		tmp = y + t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    t_2 = (y + (x + z)) + t_1
    t_3 = z * (1.0d0 - log(t))
    if (t_1 <= (-5d+63)) then
        tmp = t_2
    else if (t_1 <= (-4d-250)) then
        tmp = x + t_3
    else if (t_1 <= 2d-20) then
        tmp = y + t_3
    else
        tmp = t_2
    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 t_2 = (y + (x + z)) + t_1;
	double t_3 = z * (1.0 - Math.log(t));
	double tmp;
	if (t_1 <= -5e+63) {
		tmp = t_2;
	} else if (t_1 <= -4e-250) {
		tmp = x + t_3;
	} else if (t_1 <= 2e-20) {
		tmp = y + t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	t_2 = (y + (x + z)) + t_1
	t_3 = z * (1.0 - math.log(t))
	tmp = 0
	if t_1 <= -5e+63:
		tmp = t_2
	elif t_1 <= -4e-250:
		tmp = x + t_3
	elif t_1 <= 2e-20:
		tmp = y + t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(Float64(y + Float64(x + z)) + t_1)
	t_3 = Float64(z * Float64(1.0 - log(t)))
	tmp = 0.0
	if (t_1 <= -5e+63)
		tmp = t_2;
	elseif (t_1 <= -4e-250)
		tmp = Float64(x + t_3);
	elseif (t_1 <= 2e-20)
		tmp = Float64(y + t_3);
	else
		tmp = t_2;
	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);
	t_2 = (y + (x + z)) + t_1;
	t_3 = z * (1.0 - log(t));
	tmp = 0.0;
	if (t_1 <= -5e+63)
		tmp = t_2;
	elseif (t_1 <= -4e-250)
		tmp = x + t_3;
	elseif (t_1 <= 2e-20)
		tmp = y + t_3;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+63], t$95$2, If[LessEqual[t$95$1, -4e-250], N[(x + t$95$3), $MachinePrecision], If[LessEqual[t$95$1, 2e-20], N[(y + t$95$3), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -5.00000000000000011e63 or 1.99999999999999989e-20 < (*.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. add-sqr-sqrt 45.6%

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

      2. pow2 45.6%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   3. Applied egg-rr 45.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 90.5%

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

   if -5.00000000000000011e63 < (*.f64 (-.f64 a 1/2) b) < -4.0000000000000002e-250

   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. associate-+l+ 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. +-commutative 99.7%

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

      7. +-commutative 99.7%

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

      8. *-commutative 99.7%

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

      9. cancel-sign-sub-inv 99.7%

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

      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 inf 73.3%

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

   if -4.0000000000000002e-250 < (*.f64 (-.f64 a 1/2) b) < 1.99999999999999989e-20

   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. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 99.8%

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

      1. associate-+r- 99.8%

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

      2. associate--l+ 99.8%

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

      3. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 59.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+63}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{-250}:\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{-20}:\\ \;\;\;\;y + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 4: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+66}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + t_1\\ \mathbf{elif}\;t_1 \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;y + \left(z + \left(x - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + t_1\\ \end{array} \end{array} \]

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 (* b (- a 0.5))))
   (if (<= t_1 -2e+66)
     (+ (+ y (+ x z)) t_1)
     (if (<= t_1 1.4e+91) (+ y (+ z (- x (* z (log t))))) (+ (+ x y) t_1)))))

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+66) {
		tmp = (y + (x + z)) + t_1;
	} else if (t_1 <= 1.4e+91) {
		tmp = y + (z + (x - (z * log(t))));
	} else {
		tmp = (x + y) + 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 = b * (a - 0.5d0)
    if (t_1 <= (-2d+66)) then
        tmp = (y + (x + z)) + t_1
    else if (t_1 <= 1.4d+91) then
        tmp = y + (z + (x - (z * log(t))))
    else
        tmp = (x + y) + 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 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+66) {
		tmp = (y + (x + z)) + t_1;
	} else if (t_1 <= 1.4e+91) {
		tmp = y + (z + (x - (z * Math.log(t))));
	} else {
		tmp = (x + y) + t_1;
	}
	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+66:
		tmp = (y + (x + z)) + t_1
	elif t_1 <= 1.4e+91:
		tmp = y + (z + (x - (z * math.log(t))))
	else:
		tmp = (x + y) + t_1
	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+66)
		tmp = Float64(Float64(y + Float64(x + z)) + t_1);
	elseif (t_1 <= 1.4e+91)
		tmp = Float64(y + Float64(z + Float64(x - Float64(z * log(t)))));
	else
		tmp = Float64(Float64(x + y) + 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 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -2e+66)
		tmp = (y + (x + z)) + t_1;
	elseif (t_1 <= 1.4e+91)
		tmp = y + (z + (x - (z * log(t))));
	else
		tmp = (x + y) + 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[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+66], N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 1.4e+91], N[(y + N[(z + N[(x - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -1.99999999999999989e66

   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. add-sqr-sqrt 46.2%

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

      2. pow2 46.2%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   3. Applied egg-rr 46.2%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 88.6%

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

   if -1.99999999999999989e66 < (*.f64 (-.f64 a 1/2) b) < 1.3999999999999999e91

   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. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 94.1%

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

      1. associate-+r- 94.1%

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

      2. associate--l+ 94.1%

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

      3. *-commutative 94.1%

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

   6. Simplified 94.1%

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

   if 1.3999999999999999e91 < (*.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. Taylor expanded in z around 0 97.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+66}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 1.4 \cdot 10^{+91}:\\ \;\;\;\;y + \left(z + \left(x - z \cdot \log t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

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 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

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. Final simplification 99.8%

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

Alternative 7: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+93} \lor \neg \left(z \leq 2.8 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

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 -7.6e+93) (not (<= z 2.8e+68)))
   (+ 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 <= -7.6e+93) || !(z <= 2.8e+68)) {
		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 <= (-7.6d+93)) .or. (.not. (z <= 2.8d+68))) 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 <= -7.6e+93) || !(z <= 2.8e+68)) {
		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 <= -7.6e+93) or not (z <= 2.8e+68):
		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 <= -7.6e+93) || !(z <= 2.8e+68))
		tmp = Float64(x + Float64(z * Float64(1.0 - log(t))));
	else
		tmp = Float64(Float64(x + 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 <= -7.6e+93) || ~((z <= 2.8e+68)))
		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, -7.6e+93], N[Not[LessEqual[z, 2.8e+68]], $MachinePrecision]], N[(x + N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5999999999999996e93 or 2.8e68 < 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 69.8%

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

   if -7.5999999999999996e93 < z < 2.8e68

   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. Taylor expanded in z around 0 93.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+93} \lor \neg \left(z \leq 2.8 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 8: 81.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+94} \lor \neg \left(z \leq 2.05 \cdot 10^{+246}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \end{array} \]

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 -1.85e+94) (not (<= z 2.05e+246)))
   (* z (- 1.0 (log t)))
   (+ (+ y (+ x z)) (* 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 <= -1.85e+94) || !(z <= 2.05e+246)) {
		tmp = z * (1.0 - log(t));
	} else {
		tmp = (y + (x + z)) + (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 <= (-1.85d+94)) .or. (.not. (z <= 2.05d+246))) then
        tmp = z * (1.0d0 - log(t))
    else
        tmp = (y + (x + z)) + (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 <= -1.85e+94) || !(z <= 2.05e+246)) {
		tmp = z * (1.0 - Math.log(t));
	} else {
		tmp = (y + (x + z)) + (b * (a - 0.5));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.85e+94) or not (z <= 2.05e+246):
		tmp = z * (1.0 - math.log(t))
	else:
		tmp = (y + (x + z)) + (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 <= -1.85e+94) || !(z <= 2.05e+246))
		tmp = Float64(z * Float64(1.0 - log(t)));
	else
		tmp = Float64(Float64(y + Float64(x + z)) + 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 <= -1.85e+94) || ~((z <= 2.05e+246)))
		tmp = z * (1.0 - log(t));
	else
		tmp = (y + (x + z)) + (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, -1.85e+94], N[Not[LessEqual[z, 2.05e+246]], $MachinePrecision]], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e94 or 2.04999999999999988e246 < 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. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in b around 0 75.1%

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

      1. associate-+r- 75.1%

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

      2. associate--l+ 75.1%

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

      3. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in z around inf 60.5%

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

   8. Taylor expanded in z around inf 57.3%

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

   if -1.8500000000000001e94 < z < 2.04999999999999988e246

   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. add-sqr-sqrt 48.1%

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

      2. pow2 48.1%

         \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   3. Applied egg-rr 48.1%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

   4. Taylor expanded in z around 0 86.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+94} \lor \neg \left(z \leq 2.05 \cdot 10^{+246}\right):\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(x + z\right)\right) + b \cdot \left(a - 0.5\right)\\ \end{array} \]

Alternative 9: 71.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+205} \lor \neg \left(t_1 \leq 5 \cdot 10^{+217}\right):\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (or (<= t_1 -2e+205) (not (<= t_1 5e+217)))
     (+ 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 <= -2e+205) || !(t_1 <= 5e+217)) {
		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 <= (-2d+205)) .or. (.not. (t_1 <= 5d+217))) 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 <= -2e+205) || !(t_1 <= 5e+217)) {
		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 <= -2e+205) or not (t_1 <= 5e+217):
		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 <= -2e+205) || !(t_1 <= 5e+217))
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(x + 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 <= -2e+205) || ~((t_1 <= 5e+217)))
		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, -2e+205], N[Not[LessEqual[t$95$1, 5e+217]], $MachinePrecision]], N[(x + t$95$1), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a 1/2) b) < -2.00000000000000003e205 or 5.00000000000000041e217 < (*.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. 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 b around inf 92.2%

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

   if -2.00000000000000003e205 < (*.f64 (-.f64 a 1/2) b) < 5.00000000000000041e217

   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. Taylor expanded in z around 0 68.0%

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

   3. Taylor expanded in a around 0 61.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+205} \lor \neg \left(b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+217}\right):\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + -0.5 \cdot b\\ \end{array} \]

Alternative 10: 67.1% accurate, 10.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+84}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

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) 2e+84) (+ x (* b (- a 0.5))) (+ 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) <= 2e+84) {
		tmp = x + (b * (a - 0.5));
	} 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) <= 2d+84) then
        tmp = x + (b * (a - 0.5d0))
    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) <= 2e+84) {
		tmp = x + (b * (a - 0.5));
	} 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) <= 2e+84:
		tmp = x + (b * (a - 0.5))
	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) <= 2e+84)
		tmp = Float64(x + Float64(b * Float64(a - 0.5)));
	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) <= 2e+84)
		tmp = x + (b * (a - 0.5));
	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], 2e+84], N[(x + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2.00000000000000012e84

   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+ 99.9%

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

      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 2.00000000000000012e84 < (+.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+ 99.8%

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

      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 61.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+84}:\\ \;\;\;\;x + b \cdot \left(a - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 79.0% accurate, 10.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

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. add-sqr-sqrt 45.6%

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

   2. pow2 45.6%

      \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

3. Applied egg-rr 45.6%

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{{\left(\sqrt{z \cdot \log t}\right)}^{2}}\right) + \left(a - 0.5\right) \cdot b \]

4. Taylor expanded in z around 0 76.1%

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

5. Final simplification 76.1%

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

Alternative 12: 57.2% accurate, 12.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

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+75) (+ 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+75) {
		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+75) 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+75) {
		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+75:
		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+75)
		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+75)
		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+75], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5.0000000000000002e75

   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+ 99.9%

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

      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 44.1%

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

   if 5.0000000000000002e75 < (+.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+ 99.8%

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

      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 60.6%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 5 \cdot 10^{+75}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 13: 78.1% accurate, 12.8× speedup

Math

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

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(Float64(x + 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[(N[(x + y), $MachinePrecision] + N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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. Taylor expanded in z around 0 75.4%

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

3. Final simplification 75.4%

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

Alternative 14: 38.4% accurate, 16.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-150}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

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 (<= x -8e+181) x (if (<= x -8.2e-150) (* a b) y)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+181) {
		tmp = x;
	} else if (x <= -8.2e-150) {
		tmp = a * b;
	} 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 (x <= (-8d+181)) then
        tmp = x
    else if (x <= (-8.2d-150)) then
        tmp = a * b
    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 (x <= -8e+181) {
		tmp = x;
	} else if (x <= -8.2e-150) {
		tmp = a * b;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+181:
		tmp = x
	elif x <= -8.2e-150:
		tmp = a * b
	else:
		tmp = y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+181)
		tmp = x;
	elseif (x <= -8.2e-150)
		tmp = Float64(a * b);
	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 (x <= -8e+181)
		tmp = x;
	elseif (x <= -8.2e-150)
		tmp = a * b;
	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[x, -8e+181], x, If[LessEqual[x, -8.2e-150], N[(a * b), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999993e181

   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 x around inf 68.3%

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

   if -7.9999999999999993e181 < x < -8.1999999999999997e-150

   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 a around inf 42.0%

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

   5. Taylor expanded in x around 0 36.9%

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

   if -8.1999999999999997e-150 < x

   1. Initial program 99.9%

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

      1. 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 b around 0 71.6%

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

      1. associate-+r- 71.6%

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

      2. associate--l+ 71.6%

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

      3. *-commutative 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 20.6%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+181}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-150}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 50.7% accurate, 16.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+183}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

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 (<= a -4.1e+183) (* a b) (if (<= a 1.5e+50) (+ x y) (* a b))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.1e+183) {
		tmp = a * b;
	} else if (a <= 1.5e+50) {
		tmp = x + y;
	} else {
		tmp = a * 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 (a <= (-4.1d+183)) then
        tmp = a * b
    else if (a <= 1.5d+50) then
        tmp = x + y
    else
        tmp = a * 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 (a <= -4.1e+183) {
		tmp = a * b;
	} else if (a <= 1.5e+50) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.1e+183:
		tmp = a * b
	elif a <= 1.5e+50:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.1e+183)
		tmp = Float64(a * b);
	elseif (a <= 1.5e+50)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * 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 (a <= -4.1e+183)
		tmp = a * b;
	elseif (a <= 1.5e+50)
		tmp = x + y;
	else
		tmp = a * 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[a, -4.1e+183], N[(a * b), $MachinePrecision], If[LessEqual[a, 1.5e+50], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.10000000000000015e183 or 1.4999999999999999e50 < 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 73.2%

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

   5. Taylor expanded in x around 0 60.4%

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

   if -4.10000000000000015e183 < a < 1.4999999999999999e50

   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 51.1%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+183}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 16: 37.2% accurate, 37.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

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 (<= x -1.25e+57) x y))

C

assert(x < y);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+57) {
		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 (x <= (-1.25d+57)) 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 (x <= -1.25e+57) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e+57:
		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 (x <= -1.25e+57)
		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 (x <= -1.25e+57)
		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[x, -1.25e+57], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999993e57

   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 x around inf 43.6%

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

   if -1.24999999999999993e57 < x

   1. Initial program 99.8%

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

      1. 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. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in b around 0 66.5%

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

      1. associate-+r- 66.5%

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

      2. associate--l+ 66.5%

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

      3. *-commutative 66.5%

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

   6. Simplified 66.5%

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

   7. Taylor expanded in y around inf 22.2%

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

4. Final simplification 27.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 17: 21.5% 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 99.8%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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. sub-neg 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 24.3%

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

5. Final simplification 24.3%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023257 
(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)))