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

Percentage Accurate: 99.9% → 99.9%

Time: 7.8s

Alternatives: 13

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. 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. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lift-+.f64 N/A

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

   5. associate--l+ N/A

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

   6. lower-+.f64 N/A

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

   7. lift-+.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lower--.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. fp-cancel-sub-sign-inv N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. distribute-lft-neg-out N/A

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

   17. *-commutative N/A

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

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

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

   19. lower-*.f64 N/A

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

   20. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in z around 0

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

   1. associate-*r* N/A

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

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

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

   3. mul-1-neg N/A

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

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

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

   5. *-commutative N/A

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

   6. +-commutative N/A

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

   7. mul-1-neg N/A

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

   8. fp-cancel-sub-sign N/A

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

   9. *-commutative N/A

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

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

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

   11. *-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lower--.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-*.f64 N/A

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

   16. lower-log.f64 99.9

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

7. Applied rewrites 99.9%

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

Alternative 2: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+57} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right) + \mathsf{fma}\left(-0.5, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -5e+57) (not (<= t_1 2e+127)))
     (+ (+ y x) (- z (* (- 0.5 a) b)))
     (+ (fma (- 1.0 (log t)) z y) (fma -0.5 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -5e+57) || !(t_1 <= 2e+127)) {
		tmp = (y + x) + (z - ((0.5 - a) * b));
	} else {
		tmp = fma((1.0 - log(t)), z, y) + fma(-0.5, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -5e+57) || !(t_1 <= 2e+127))
		tmp = Float64(Float64(y + x) + Float64(z - Float64(Float64(0.5 - a) * b)));
	else
		tmp = Float64(fma(Float64(1.0 - log(t)), z, y) + fma(-0.5, b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+57], N[Not[LessEqual[t$95$1, 2e+127]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] + N[(z - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision] + N[(-0.5 * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.99999999999999972e57 or 1.99999999999999991e127 < (*.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. 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. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. fp-cancel-sub-sign-inv N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. distribute-lft-neg-out N/A

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. fp-cancel-sub-sign N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-out-- N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 92.5

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

   7. Applied rewrites 92.5%

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

   if -4.99999999999999972e57 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999991e127

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. associate-+l+ N/A

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

      13. log-rec N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 97.3%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -5 \cdot 10^{+57} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right) + \mathsf{fma}\left(-0.5, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+57} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -5e+57) (not (<= t_1 2e+127)))
     (+ (+ y x) (- z (* (- 0.5 a) b)))
     (fma (- 1.0 (log t)) z (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -5e+57) || !(t_1 <= 2e+127)) {
		tmp = (y + x) + (z - ((0.5 - a) * b));
	} else {
		tmp = fma((1.0 - log(t)), z, (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -5e+57) || !(t_1 <= 2e+127))
		tmp = Float64(Float64(y + x) + Float64(z - Float64(Float64(0.5 - a) * b)));
	else
		tmp = fma(Float64(1.0 - log(t)), z, Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+57], N[Not[LessEqual[t$95$1, 2e+127]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] + N[(z - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.99999999999999972e57 or 1.99999999999999991e127 < (*.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. 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. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. fp-cancel-sub-sign-inv N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. distribute-lft-neg-out N/A

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. fp-cancel-sub-sign N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-out-- N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 92.5

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

   7. Applied rewrites 92.5%

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

   if -4.99999999999999972e57 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999991e127

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. associate-+l+ N/A

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

      13. log-rec N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \frac{-1}{2} \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 5.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 93.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -5 \cdot 10^{+57} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x + y\right) + z\right) - z \cdot \log t \leq -5 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ (+ x y) z) (* z (log t))) -5e-58)
   (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 ((((x + y) + z) - (z * log(t))) <= -5e-58) {
		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(Float64(x + y) + z) - Float64(z * log(t))) <= -5e-58)
		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[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-58], 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))) < -4.99999999999999977e-58

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 76.4

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

   5. Applied rewrites 76.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 54.7%

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

   if -4.99999999999999977e-58 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 80.7

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

   5. Applied rewrites 80.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.1%

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

Alternative 5: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a - 0.5, b, y\right)\\ \mathbf{if}\;x + y \leq -5 \cdot 10^{+52}:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- a 0.5) b y)))
   (if (<= (+ x y) -5e+52) (+ t_1 x) (fma (- 1.0 (log t)) z t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((a - 0.5), b, y);
	double tmp;
	if ((x + y) <= -5e+52) {
		tmp = t_1 + x;
	} else {
		tmp = fma((1.0 - log(t)), z, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(a - 0.5), b, y)
	tmp = 0.0
	if (Float64(x + y) <= -5e+52)
		tmp = Float64(t_1 + x);
	else
		tmp = fma(Float64(1.0 - log(t)), z, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], -5e+52], N[(t$95$1 + x), $MachinePrecision], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5e52

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   7. Applied rewrites 87.6%

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

   if -5e52 < (+.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. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate-+r- N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

Alternative 6: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+267} \lor \neg \left(z \leq 4.6 \cdot 10^{+97}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+267) (not (<= z 4.6e+97)))
   (fma (- 1.0 (log t)) z y)
   (+ (+ y x) (- z (* (- 0.5 a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+267) || !(z <= 4.6e+97)) {
		tmp = fma((1.0 - log(t)), z, y);
	} else {
		tmp = (y + x) + (z - ((0.5 - a) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e+267) || !(z <= 4.6e+97))
		tmp = fma(Float64(1.0 - log(t)), z, y);
	else
		tmp = Float64(Float64(y + x) + Float64(z - Float64(Float64(0.5 - a) * b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e+267], N[Not[LessEqual[z, 4.6e+97]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + N[(z - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000002e267 or 4.60000000000000011e97 < 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 x around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. associate-+r- N/A

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

      4. *-rgt-identity N/A

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

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

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-log.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 77.3%

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

   if -6.20000000000000002e267 < z < 4.60000000000000011e97

   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. 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. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. fp-cancel-sub-sign-inv N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. distribute-lft-neg-out N/A

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. fp-cancel-sub-sign N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-out-- N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 91.4

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

   7. Applied rewrites 91.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+267} \lor \neg \left(z \leq 4.6 \cdot 10^{+97}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+267} \lor \neg \left(z \leq 1.4 \cdot 10^{+103}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+267) (not (<= z 1.4e+103)))
   (* (- 1.0 (log t)) z)
   (+ (+ y x) (- z (* (- 0.5 a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+267) || !(z <= 1.4e+103)) {
		tmp = (1.0 - log(t)) * z;
	} else {
		tmp = (y + x) + (z - ((0.5 - a) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.2d+267)) .or. (.not. (z <= 1.4d+103))) then
        tmp = (1.0d0 - log(t)) * z
    else
        tmp = (y + x) + (z - ((0.5d0 - a) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+267) || !(z <= 1.4e+103)) {
		tmp = (1.0 - Math.log(t)) * z;
	} else {
		tmp = (y + x) + (z - ((0.5 - a) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e+267) or not (z <= 1.4e+103):
		tmp = (1.0 - math.log(t)) * z
	else:
		tmp = (y + x) + (z - ((0.5 - a) * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e+267) || !(z <= 1.4e+103))
		tmp = Float64(Float64(1.0 - log(t)) * z);
	else
		tmp = Float64(Float64(y + x) + Float64(z - Float64(Float64(0.5 - a) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e+267) || ~((z <= 1.4e+103)))
		tmp = (1.0 - log(t)) * z;
	else
		tmp = (y + x) + (z - ((0.5 - a) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e+267], N[Not[LessEqual[z, 1.4e+103]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + N[(z - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000002e267 or 1.40000000000000004e103 < 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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-log.f64 69.9

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

   5. Applied rewrites 69.9%

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

   if -6.20000000000000002e267 < z < 1.40000000000000004e103

   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. 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. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lift-+.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. fp-cancel-sub-sign-inv N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. distribute-lft-neg-out N/A

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

      17. *-commutative N/A

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

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

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

      19. lower-*.f64 N/A

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

      20. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

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

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

      3. mul-1-neg N/A

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

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

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

      5. *-commutative N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. fp-cancel-sub-sign N/A

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

      9. *-commutative N/A

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

      10. distribute-rgt-out-- N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 91.4

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

   7. Applied rewrites 91.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+267} \lor \neg \left(z \leq 1.4 \cdot 10^{+103}\right):\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - \left(0.5 - a\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.5% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -10 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- a 0.5) -10.0) (not (<= (- a 0.5) -0.4))) (* b a) (* -0.5 b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -10.0) || !((a - 0.5) <= -0.4)) {
		tmp = b * a;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((a - 0.5d0) <= (-10.0d0)) .or. (.not. ((a - 0.5d0) <= (-0.4d0)))) then
        tmp = b * a
    else
        tmp = (-0.5d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((a - 0.5) <= -10.0) || !((a - 0.5) <= -0.4)) {
		tmp = b * a;
	} else {
		tmp = -0.5 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((a - 0.5) <= -10.0) or not ((a - 0.5) <= -0.4):
		tmp = b * a
	else:
		tmp = -0.5 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(a - 0.5) <= -10.0) || !(Float64(a - 0.5) <= -0.4))
		tmp = Float64(b * a);
	else
		tmp = Float64(-0.5 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((a - 0.5) <= -10.0) || ~(((a - 0.5) <= -0.4)))
		tmp = b * a;
	else
		tmp = -0.5 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(a - 0.5), $MachinePrecision], -10.0], N[Not[LessEqual[N[(a - 0.5), $MachinePrecision], -0.4]], $MachinePrecision]], N[(b * a), $MachinePrecision], N[(-0.5 * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -10 or -0.40000000000000002 < (-.f64 a #s(literal 1/2 binary64))

   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. *-commutative N/A

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

      2. lower-*.f64 51.2

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

   5. Applied rewrites 51.2%

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

   if -10 < (-.f64 a #s(literal 1/2 binary64)) < -0.40000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

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

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

      3. mul-1-neg N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. log-rec N/A

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

      7. +-commutative N/A

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

      8. +-commutative N/A

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

      9. associate-+r+ N/A

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

      10. associate-+l+ N/A

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

      11. associate-+r+ N/A

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

      12. +-commutative N/A

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

      13. log-rec N/A

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

      14. mul-1-neg N/A

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

      15. *-commutative N/A

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

      16. mul-1-neg N/A

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

      17. fp-cancel-sub-sign-inv N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \frac{-1}{2} \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 25.5%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a - 0.5 \leq -10 \lor \neg \left(a - 0.5 \leq -0.4\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.6% accurate, 7.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (y + x) + (z - ((0.5 - a) * 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 = (y + x) + (z - ((0.5d0 - a) * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
2. 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. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lift-+.f64 N/A

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

   5. associate--l+ N/A

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

   6. lower-+.f64 N/A

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

   7. lift-+.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lower--.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. fp-cancel-sub-sign-inv N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. distribute-lft-neg-out N/A

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

   17. *-commutative N/A

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

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

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

   19. lower-*.f64 N/A

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

   20. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in z around 0

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

   1. associate-*r* N/A

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

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

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

   3. mul-1-neg N/A

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

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

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

   5. *-commutative N/A

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

   6. +-commutative N/A

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

   7. mul-1-neg N/A

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

   8. fp-cancel-sub-sign N/A

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

   9. *-commutative N/A

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

   10. distribute-rgt-out-- N/A

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

   11. *-commutative N/A

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

   12. lower-*.f64 N/A

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

   13. lower--.f64 79.0

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

7. Applied rewrites 79.0%

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

Alternative 10: 78.8% 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 99.9%

   \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
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. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 78.7

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

5. Applied rewrites 78.7%

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

7. Applied rewrites 78.7%

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

Alternative 11: 58.1% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 78.7

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

5. Applied rewrites 78.7%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 57.0%

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

Alternative 12: 38.0% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ \left(a - 0.5\right) \cdot b \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (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 = (a - 0.5d0) * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in 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 39.4

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

5. Applied rewrites 39.4%

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

Alternative 13: 14.0% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot b \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return -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 = (-0.5d0) * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.5 * b), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around 0

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

   1. *-commutative N/A

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

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

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

   3. mul-1-neg N/A

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

   4. *-commutative N/A

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

   5. mul-1-neg N/A

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

   6. log-rec N/A

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

   7. +-commutative N/A

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

   8. +-commutative N/A

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

   9. associate-+r+ N/A

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

   10. associate-+l+ N/A

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

   11. associate-+r+ N/A

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

   12. +-commutative N/A

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

   13. log-rec N/A

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

   14. mul-1-neg N/A

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

   15. *-commutative N/A

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

   16. mul-1-neg N/A

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

   17. fp-cancel-sub-sign-inv N/A

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

   18. *-commutative N/A

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

5. Applied rewrites 74.0%

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

6. Taylor expanded in b around inf

   \[\leadsto \frac{-1}{2} \cdot \color{blue}{b} \]
7. Step-by-step derivation

8. Applied rewrites 13.9%

   \[\leadsto -0.5 \cdot \color{blue}{b} \]
9. 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 2024320 
(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)))