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

Percentage Accurate: 99.9% → 99.9%

Time: 11.3s

Alternatives: 15

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.9

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

   5. lift--.f64 N/A

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

   6. sub-neg N/A

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

   7. +-commutative N/A

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

   8. lift-*.f64 N/A

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

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

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

   10. lower-fma.f64 N/A

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

   11. lower-neg.f64 99.9

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

   12. lift-+.f64 N/A

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

   13. +-commutative N/A

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

   14. lower-+.f64 99.9

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

   15. lift-+.f64 N/A

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

   16. +-commutative N/A

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

   17. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, b, \mathsf{fma}\left(1 - \log t, z, y\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+104)
     (fma (- a 0.5) b (+ x y))
     (if (<= t_1 4e+35)
       (+ (fma -0.5 b (fma (- 1.0 (log t)) z y)) x)
       (+ (fma (- a 0.5) b y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+104) {
		tmp = fma((a - 0.5), b, (x + y));
	} else if (t_1 <= 4e+35) {
		tmp = fma(-0.5, b, fma((1.0 - log(t)), z, y)) + x;
	} else {
		tmp = fma((a - 0.5), b, y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+104)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	elseif (t_1 <= 4e+35)
		tmp = Float64(fma(-0.5, b, fma(Float64(1.0 - log(t)), z, y)) + x);
	else
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+104], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+35], N[(N[(-0.5 * b + N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2e104

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 100.0

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 100.0

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.7

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

   7. Applied rewrites 94.7%

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

   if -2e104 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.9999999999999999e35

   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. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

   5. Applied rewrites 96.9%

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

   if 3.9999999999999999e35 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, b, \mathsf{fma}\left(1 - \log t, z, y\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -2e+104)
     (fma (- a 0.5) b (+ x y))
     (if (<= t_1 4e+35)
       (+ (fma (- 1.0 (log t)) z y) x)
       (+ (fma (- a 0.5) b y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -2e+104) {
		tmp = fma((a - 0.5), b, (x + y));
	} else if (t_1 <= 4e+35) {
		tmp = fma((1.0 - log(t)), z, y) + x;
	} else {
		tmp = fma((a - 0.5), b, y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -2e+104)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	elseif (t_1 <= 4e+35)
		tmp = Float64(fma(Float64(1.0 - log(t)), z, y) + x);
	else
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+104], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+35], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2e104

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 100.0

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 100.0

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 100.0

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.7

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

   7. Applied rewrites 94.7%

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

   if -2e104 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.9999999999999999e35

   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 inf

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

      1. lower-*.f64 4.8

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

   5. Applied rewrites 4.8%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 95.5%

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

   if 3.9999999999999999e35 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 4 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.25e+99)
   (fma (- 1.0 (log t)) z (fma (- a 0.5) b x))
   (+ (fma (- a 0.5) b y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.25e+99) {
		tmp = fma((1.0 - log(t)), z, fma((a - 0.5), b, x));
	} else {
		tmp = fma((a - 0.5), b, y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.25e+99)
		tmp = fma(Float64(1.0 - log(t)), z, fma(Float64(a - 0.5), b, x));
	else
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.25e+99], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25000000000000002e99

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 82.9%

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

   if 1.25000000000000002e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 90.2

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

   5. Applied rewrites 90.2%

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

Alternative 5: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, y\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -3.2e+159)
     (fma t_1 z y)
     (if (<= z 6.2e+177) (fma (- a 0.5) b (+ x y)) (fma t_1 z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= -3.2e+159) {
		tmp = fma(t_1, z, y);
	} else if (z <= 6.2e+177) {
		tmp = fma((a - 0.5), b, (x + y));
	} else {
		tmp = fma(t_1, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= -3.2e+159)
		tmp = fma(t_1, z, y);
	elseif (z <= 6.2e+177)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	else
		tmp = fma(t_1, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+159], N[(t$95$1 * z + y), $MachinePrecision], If[LessEqual[z, 6.2e+177], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999985e159

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 17.5

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

   5. Applied rewrites 17.5%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 77.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 70.1%

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

   if -3.19999999999999985e159 < z < 6.1999999999999998e177

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 99.9

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.9

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.1

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

   7. Applied rewrites 90.1%

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

   if 6.1999999999999998e177 < 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 y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 91.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, x\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z x)))
   (if (<= z -1.15e+159)
     t_1
     (if (<= z 6.2e+177) (fma (- a 0.5) b (+ x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, x);
	double tmp;
	if (z <= -1.15e+159) {
		tmp = t_1;
	} else if (z <= 6.2e+177) {
		tmp = fma((a - 0.5), b, (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, x)
	tmp = 0.0
	if (z <= -1.15e+159)
		tmp = t_1;
	elseif (z <= 6.2e+177)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -1.15e+159], t$95$1, If[LessEqual[z, 6.2e+177], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999998e159 or 6.1999999999999998e177 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 70.9%

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

   if -1.14999999999999998e159 < z < 6.1999999999999998e177

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 99.9

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.9

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.1

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

   7. Applied rewrites 90.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+177}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-\log t, z, z\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (log t)) z z)))
   (if (<= z -9.8e+160) t_1 (if (<= z 8e+178) (fma (- a 0.5) b (+ x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-log(t), z, z);
	double tmp;
	if (z <= -9.8e+160) {
		tmp = t_1;
	} else if (z <= 8e+178) {
		tmp = fma((a - 0.5), b, (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-log(t)), z, z)
	tmp = 0.0
	if (z <= -9.8e+160)
		tmp = t_1;
	elseif (z <= 8e+178)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[Log[t], $MachinePrecision]) * z + z), $MachinePrecision]}, If[LessEqual[z, -9.8e+160], t$95$1, If[LessEqual[z, 8e+178], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000005e160 or 8.0000000000000004e178 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. log-rec N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. log-rec N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-log.f64 68.5

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

   5. Applied rewrites 68.5%

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

   7. Applied rewrites 68.7%

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

   if -9.8000000000000005e160 < z < 8.0000000000000004e178

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 99.9

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.9

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.1

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

   7. Applied rewrites 90.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(-\log t, z, z\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\log t, z, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \log t \cdot z\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* (log t) z))))
   (if (<= z -9.8e+160)
     t_1
     (if (<= z 8.5e+178) (fma (- a 0.5) b (+ x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (log(t) * z);
	double tmp;
	if (z <= -9.8e+160) {
		tmp = t_1;
	} else if (z <= 8.5e+178) {
		tmp = fma((a - 0.5), b, (x + y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(log(t) * z))
	tmp = 0.0
	if (z <= -9.8e+160)
		tmp = t_1;
	elseif (z <= 8.5e+178)
		tmp = fma(Float64(a - 0.5), b, Float64(x + y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+160], t$95$1, If[LessEqual[z, 8.5e+178], N[(N[(a - 0.5), $MachinePrecision] * b + N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000005e160 or 8.49999999999999991e178 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. log-rec N/A

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

      3. distribute-lft-in N/A

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

      4. *-rgt-identity N/A

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

      5. remove-double-neg N/A

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. lower--.f64 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. log-rec N/A

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

      12. remove-double-neg N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lower-log.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -9.8000000000000005e160 < z < 8.49999999999999991e178

   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. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.9

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. lift-*.f64 N/A

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

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

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

      10. lower-fma.f64 N/A

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

      11. lower-neg.f64 99.9

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.9

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 90.1

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

   7. Applied rewrites 90.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+160}:\\ \;\;\;\;z - \log t \cdot z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+178}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - \log t \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+188}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+188)
     (* b a)
     (if (<= t_1 1e+238) (+ x y) (if (<= t_1 2e+303) (* -0.5 b) (* b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = b * a;
	} else if (t_1 <= 1e+238) {
		tmp = x + y;
	} else if (t_1 <= 2e+303) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-5d+188)) then
        tmp = b * a
    else if (t_1 <= 1d+238) then
        tmp = x + y
    else if (t_1 <= 2d+303) then
        tmp = (-0.5d0) * b
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = b * a;
	} else if (t_1 <= 1e+238) {
		tmp = x + y;
	} else if (t_1 <= 2e+303) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+188:
		tmp = b * a
	elif t_1 <= 1e+238:
		tmp = x + y
	elif t_1 <= 2e+303:
		tmp = -0.5 * b
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+188)
		tmp = Float64(b * a);
	elseif (t_1 <= 1e+238)
		tmp = Float64(x + y);
	elseif (t_1 <= 2e+303)
		tmp = Float64(-0.5 * b);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -5e+188)
		tmp = b * a;
	elseif (t_1 <= 1e+238)
		tmp = x + y;
	elseif (t_1 <= 2e+303)
		tmp = -0.5 * b;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+188], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+238], N[(x + y), $MachinePrecision], If[LessEqual[t$95$1, 2e+303], N[(-0.5 * b), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000001e188 or 2e303 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 77.6

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

   5. Applied rewrites 77.6%

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

   if -5.0000000000000001e188 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1e238

   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 inf

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

      1. lower-*.f64 11.4

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

   5. Applied rewrites 11.4%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 85.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 57.1%

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

   if 1e238 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2e303

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 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 81.7

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 70.7%

      \[\leadsto -0.5 \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+188}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 10^{+238}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ t_2 := \mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-24}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))) (t_2 (fma (- a 0.5) b x)))
   (if (<= t_1 -2e+104) t_2 (if (<= t_1 1e-24) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double t_2 = fma((a - 0.5), b, x);
	double tmp;
	if (t_1 <= -2e+104) {
		tmp = t_2;
	} else if (t_1 <= 1e-24) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	t_2 = fma(Float64(a - 0.5), b, x)
	tmp = 0.0
	if (t_1 <= -2e+104)
		tmp = t_2;
	elseif (t_1 <= 1e-24)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+104], t$95$2, If[LessEqual[t$95$1, 1e-24], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2e104 or 9.99999999999999924e-25 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

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

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

      3. log-rec N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. associate-+r+ N/A

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

      9. *-rgt-identity N/A

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

      10. distribute-lft-in N/A

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

      11. +-commutative N/A

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

      12. log-rec N/A

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

      13. sub-neg N/A

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

      14. *-commutative N/A

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

      15. sub-neg N/A

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.8%

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

   if -2e104 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.99999999999999924e-25

   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 inf

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

      1. lower-*.f64 3.9

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

   5. Applied rewrites 3.9%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 96.7%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 62.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 10^{-24}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+188) t_1 (if (<= t_1 2e+67) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = t_1;
	} else if (t_1 <= 2e+67) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-5d+188)) then
        tmp = t_1
    else if (t_1 <= 2d+67) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = t_1;
	} else if (t_1 <= 2e+67) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+188:
		tmp = t_1
	elif t_1 <= 2e+67:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+188)
		tmp = t_1;
	elseif (t_1 <= 2e+67)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -5e+188)
		tmp = t_1;
	elseif (t_1 <= 2e+67)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+188], t$95$1, If[LessEqual[t$95$1, 2e+67], N[(x + y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000001e188 or 1.99999999999999997e67 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   if -5.0000000000000001e188 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999997e67

   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 inf

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

      1. lower-*.f64 7.4

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

   5. Applied rewrites 7.4%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 90.2%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 60.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+188}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 2 \cdot 10^{+67}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.9% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+188}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+241}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- a 0.5))))
   (if (<= t_1 -5e+188) (* b a) (if (<= t_1 5e+241) (+ x y) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = b * a;
	} else if (t_1 <= 5e+241) {
		tmp = x + y;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a - 0.5d0)
    if (t_1 <= (-5d+188)) then
        tmp = b * a
    else if (t_1 <= 5d+241) then
        tmp = x + y
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (a - 0.5);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = b * a;
	} else if (t_1 <= 5e+241) {
		tmp = x + y;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (a - 0.5)
	tmp = 0
	if t_1 <= -5e+188:
		tmp = b * a
	elif t_1 <= 5e+241:
		tmp = x + y
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(a - 0.5))
	tmp = 0.0
	if (t_1 <= -5e+188)
		tmp = Float64(b * a);
	elseif (t_1 <= 5e+241)
		tmp = Float64(x + y);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (a - 0.5);
	tmp = 0.0;
	if (t_1 <= -5e+188)
		tmp = b * a;
	elseif (t_1 <= 5e+241)
		tmp = x + y;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+188], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 5e+241], N[(x + y), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000001e188 or 5.00000000000000025e241 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -5.0000000000000001e188 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000025e241

   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 inf

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

      1. lower-*.f64 11.3

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

   5. Applied rewrites 11.3%

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

   6. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r- N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

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

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

      7. log-rec N/A

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

      8. *-lft-identity N/A

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

      9. distribute-rgt-in N/A

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

      10. +-commutative N/A

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

      11. log-rec N/A

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

      12. mul-1-neg N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. associate-+r+ N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 N/A

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

   8. Applied rewrites 84.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 56.8%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a - 0.5\right) \leq -5 \cdot 10^{+188}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;b \cdot \left(a - 0.5\right) \leq 5 \cdot 10^{+241}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.9% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.9

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

   5. lift--.f64 N/A

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

   6. sub-neg N/A

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

   7. +-commutative N/A

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

   8. lift-*.f64 N/A

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

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

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

   10. lower-fma.f64 N/A

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

   11. lower-neg.f64 99.9

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

   12. lift-+.f64 N/A

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

   13. +-commutative N/A

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

   14. lower-+.f64 99.9

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

   15. lift-+.f64 N/A

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

   16. +-commutative N/A

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

   17. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 79.0

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

7. Applied rewrites 79.0%

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

8. Final simplification 79.0%

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

Alternative 14: 78.9% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 79.0

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

5. Applied rewrites 79.0%

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

Alternative 15: 42.0% accurate, 31.5× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around inf

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

   1. lower-*.f64 29.0

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

5. Applied rewrites 29.0%

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

6. Taylor expanded in b around 0

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

   1. associate-+r+ N/A

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

   2. associate-+r- N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

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

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

   7. log-rec N/A

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

   8. *-lft-identity N/A

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

   9. distribute-rgt-in N/A

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

   10. +-commutative N/A

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

   11. log-rec N/A

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

   12. mul-1-neg N/A

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

   13. mul-1-neg N/A

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

   14. sub-neg N/A

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

   15. associate-+r+ N/A

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

   16. +-commutative N/A

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

   17. lower-+.f64 N/A

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

8. Applied rewrites 61.8%

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

9. Taylor expanded in z around 0

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

11. Applied rewrites 41.3%

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

12. Final simplification 41.3%

    \[\leadsto x + y \]
13. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024268 
(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)))