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

Percentage Accurate: 99.9% → 99.9%

Time: 11.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.8%

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

Alternative 2: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right) + \left(\left(z + \left(y + x\right)\right) - \log t \cdot z\right)\\ t_2 := 1 - \log t\\ \mathbf{if}\;t\_1 \leq 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, z, \mathsf{fma}\left(-0.5, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (- a 0.5)) (- (+ z (+ y x)) (* (log t) z))))
        (t_2 (- 1.0 (log t))))
   (if (<= t_1 1e-85)
     (fma t_2 z (fma (- a 0.5) b x))
     (if (<= t_1 2e+283)
       (fma t_2 z (fma -0.5 b y))
       (+ (fma (- a 0.5) b y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a - 0.5)) + ((z + (y + x)) - (log(t) * z));
	double t_2 = 1.0 - log(t);
	double tmp;
	if (t_1 <= 1e-85) {
		tmp = fma(t_2, z, fma((a - 0.5), b, x));
	} else if (t_1 <= 2e+283) {
		tmp = fma(t_2, z, fma(-0.5, b, y));
	} else {
		tmp = fma((a - 0.5), b, y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a - 0.5)) + Float64(Float64(z + Float64(y + x)) - Float64(log(t) * z)))
	t_2 = Float64(1.0 - log(t))
	tmp = 0.0
	if (t_1 <= 1e-85)
		tmp = fma(t_2, z, fma(Float64(a - 0.5), b, x));
	elseif (t_1 <= 2e+283)
		tmp = fma(t_2, z, fma(-0.5, b, y));
	else
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-85], N[(t$95$2 * z + N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+283], N[(t$95$2 * z + N[(-0.5 * b + y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < 9.9999999999999998e-86

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 81.9%

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

   if 9.9999999999999998e-86 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < 1.99999999999999991e283

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-lft-identity N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-in N/A

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

      13. log-rec N/A

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

      14. sub-neg N/A

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

   7. Applied rewrites 79.1%

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

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(\frac{-1}{2}, b, y\right)\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 71.5%

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

   if 1.99999999999999991e283 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) + \left(\left(z + \left(y + x\right)\right) - \log t \cdot z\right) \leq 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) + \left(\left(z + \left(y + x\right)\right) - \log t \cdot z\right) \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(-0.5, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (+ (fma (- a 0.5) b y) x)))
   (if (<= t_1 -5e+182)
     t_2
     (if (<= t_1 5e+128) (fma (- 1.0 (log t)) z (+ y x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = fma((a - 0.5), b, y) + x;
	double tmp;
	if (t_1 <= -5e+182) {
		tmp = t_2;
	} else if (t_1 <= 5e+128) {
		tmp = fma((1.0 - log(t)), z, (y + x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = Float64(fma(Float64(a - 0.5), b, y) + x)
	tmp = 0.0
	if (t_1 <= -5e+182)
		tmp = t_2;
	elseif (t_1 <= 5e+128)
		tmp = fma(Float64(1.0 - log(t)), z, Float64(y + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+182], t$95$2, If[LessEqual[t$95$1, 5e+128], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(y + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.99999999999999973e182 or 5e128 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 99.1

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

   5. Applied rewrites 99.1%

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

   if -4.99999999999999973e182 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5e128

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0

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

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

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

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

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

      5. *-rgt-identity N/A

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

      6. distribute-lft-out-- N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-log.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+182}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(z + \left(y + x\right)\right) - \log t \cdot z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ z (+ y x)) (* (log t) z)) -4e-86)
   (fma (- a 0.5) b x)
   (fma (- a 0.5) b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((z + (y + x)) - (log(t) * z)) <= -4e-86) {
		tmp = fma((a - 0.5), b, x);
	} else {
		tmp = fma((a - 0.5), b, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(z + Float64(y + x)) - Float64(log(t) * z)) <= -4e-86)
		tmp = fma(Float64(a - 0.5), b, x);
	else
		tmp = fma(Float64(a - 0.5), b, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], -4e-86], N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -4.00000000000000034e-86

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 77.1

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

   7. Applied rewrites 77.1%

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

   8. Taylor expanded in y around 0

      \[\leadsto x + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 58.4%

       \[\leadsto \mathsf{fma}\left(a - 0.5, \color{blue}{b}, x\right) \]

   if -4.00000000000000034e-86 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-lft-identity N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-in N/A

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

      13. log-rec N/A

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

      14. sub-neg N/A

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto y + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 61.9%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + \left(y + x\right)\right) - \log t \cdot z \leq -4 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(z + \left(y + x\right)\right) - \log t \cdot z \leq -4 \cdot 10^{+71}:\\ \;\;\;\;b \cdot a + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ z (+ y x)) (* (log t) z)) -4e+71)
   (+ (* b a) x)
   (fma (- a 0.5) b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((z + (y + x)) - (log(t) * z)) <= -4e+71) {
		tmp = (b * a) + x;
	} else {
		tmp = fma((a - 0.5), b, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(z + Float64(y + x)) - Float64(log(t) * z)) <= -4e+71)
		tmp = Float64(Float64(b * a) + x);
	else
		tmp = fma(Float64(a - 0.5), b, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], -4e+71], N[(N[(b * a), $MachinePrecision] + x), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -4.0000000000000002e71

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 76.8

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

   7. Applied rewrites 76.8%

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

   8. Taylor expanded in a around inf

      \[\leadsto a \cdot b + x \]
   9. Step-by-step derivation

   10. Applied rewrites 49.8%

       \[\leadsto a \cdot b + x \]

   if -4.0000000000000002e71 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-lft-identity N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-in N/A

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

      13. log-rec N/A

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

      14. sub-neg N/A

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto y + \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 60.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + \left(y + x\right)\right) - \log t \cdot z \leq -4 \cdot 10^{+71}:\\ \;\;\;\;b \cdot a + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;y + x \leq -1 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= (+ y x) -1e-94)
     (fma t_1 z (fma (- a 0.5) b x))
     (fma t_1 z (fma (- a 0.5) b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if ((y + x) <= -1e-94) {
		tmp = fma(t_1, z, fma((a - 0.5), b, x));
	} else {
		tmp = fma(t_1, z, fma((a - 0.5), b, y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (Float64(y + x) <= -1e-94)
		tmp = fma(t_1, z, fma(Float64(a - 0.5), b, x));
	else
		tmp = fma(t_1, z, fma(Float64(a - 0.5), b, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y + x), $MachinePrecision], -1e-94], N[(t$95$1 * z + N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z + N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.9999999999999996e-95

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 76.6%

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

   if -9.9999999999999996e-95 < (+.f64 x y)

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-lft-identity N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-in N/A

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

      13. log-rec N/A

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

      14. sub-neg N/A

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

   7. Applied rewrites 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -1 \cdot 10^{-94}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+238}:\\ \;\;\;\;z - \log t \cdot z\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\log t, z, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.2e+238)
   (- z (* (log t) z))
   (if (<= z 6.3e+127) (+ (fma (- a 0.5) b y) x) (fma (- (log t)) z z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.2e+238) {
		tmp = z - (log(t) * z);
	} else if (z <= 6.3e+127) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = fma(-log(t), z, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.2e+238)
		tmp = Float64(z - Float64(log(t) * z));
	elseif (z <= 6.3e+127)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = fma(Float64(-log(t)), z, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.2e+238], N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.3e+127], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], N[((-N[Log[t], $MachinePrecision]) * z + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999942e238

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. log-rec N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. log-rec N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-log.f64 86.4

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

   5. Applied rewrites 86.4%

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

   if -7.19999999999999942e238 < z < 6.30000000000000047e127

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if 6.30000000000000047e127 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. log-rec N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. log-rec N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-log.f64 61.4

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

   5. Applied rewrites 61.4%

      \[\leadsto \color{blue}{z - \log t \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 61.5%

      \[\leadsto \mathsf{fma}\left(-\log t, \color{blue}{z}, z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \log t \cdot z\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* (log t) z))))
   (if (<= z -7.2e+238)
     t_1
     (if (<= z 6.3e+127) (+ (fma (- a 0.5) b y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (log(t) * z);
	double tmp;
	if (z <= -7.2e+238) {
		tmp = t_1;
	} else if (z <= 6.3e+127) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(log(t) * z))
	tmp = 0.0
	if (z <= -7.2e+238)
		tmp = t_1;
	elseif (z <= 6.3e+127)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+238], t$95$1, If[LessEqual[z, 6.3e+127], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999942e238 or 6.30000000000000047e127 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. log-rec N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. log-rec N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-log.f64 66.8

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

   5. Applied rewrites 66.8%

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

   if -7.19999999999999942e238 < z < 6.30000000000000047e127

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 88.9

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

   5. Applied rewrites 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a - 0.5, b, y\right) + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 65.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+163}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -1e+196) t_1 (if (<= t_1 2e+163) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+196) {
		tmp = t_1;
	} else if (t_1 <= 2e+163) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-1d+196)) then
        tmp = t_1
    else if (t_1 <= 2d+163) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -1e+196) {
		tmp = t_1;
	} else if (t_1 <= 2e+163) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -1e+196:
		tmp = t_1
	elif t_1 <= 2e+163:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+196)
		tmp = t_1;
	elseif (t_1 <= 2e+163)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+196)
		tmp = t_1;
	elseif (t_1 <= 2e+163)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+196], t$95$1, If[LessEqual[t$95$1, 2e+163], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -9.9999999999999995e195 or 1.9999999999999999e163 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(a - \frac{1}{2}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.7

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

   5. Applied rewrites 84.7%

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

   if -9.9999999999999995e195 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.9999999999999999e163

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 66.0

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

   7. Applied rewrites 66.0%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 58.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -1 \cdot 10^{+196}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+163}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.2% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+223}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+229}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -4e+223) (* b a) (if (<= t_1 2e+229) (+ y x) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+223) {
		tmp = b * a;
	} else if (t_1 <= 2e+229) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-4d+223)) then
        tmp = b * a
    else if (t_1 <= 2d+229) then
        tmp = y + x
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -4e+223) {
		tmp = b * a;
	} else if (t_1 <= 2e+229) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -4e+223:
		tmp = b * a
	elif t_1 <= 2e+229:
		tmp = y + x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -4e+223)
		tmp = Float64(b * a);
	elseif (t_1 <= 2e+229)
		tmp = Float64(y + x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -4e+223)
		tmp = b * a;
	elseif (t_1 <= 2e+229)
		tmp = y + x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+223], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 2e+229], N[(y + x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.00000000000000019e223 or 2e229 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. lower-*.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -4.00000000000000019e223 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2e229

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. flip-+ N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-+ N/A

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

      7. lift-+.f64 N/A

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 69.0

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

   7. Applied rewrites 69.0%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 56.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -4 \cdot 10^{+223}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+229}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.5% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 77.8

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

5. Applied rewrites 77.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a - 0.5, b, y\right) + x} \]
6. Add Preprocessing

Alternative 12: 41.8% accurate, 31.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(y + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(y + x), $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. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. flip-+ N/A

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

   3. clear-num N/A

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

   4. lower-/.f64 N/A

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

   5. clear-num N/A

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

   6. flip-+ N/A

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

   7. lift-+.f64 N/A

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

4. Applied rewrites 99.7%

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

5. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + \left(y + b \cdot \left(a - \frac{1}{2}\right)\right)} \]
6. Step-by-step derivation

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 77.8

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

7. Applied rewrites 77.8%

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

8. Taylor expanded in b around 0

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

10. Applied rewrites 41.6%

    \[\leadsto y + \color{blue}{x} \]
11. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024278 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 1/2) b)))

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