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

Percentage Accurate: 99.8% → 99.8%

Time: 15.3s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (+ y (fma b (+ a -0.5) x))))
   (if (<= t_1 -2e+209)
     t_2
     (if (<= t_1 2e+90) (fma z (- 1.0 (log t)) (+ x y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = y + fma(b, (a + -0.5), x);
	double tmp;
	if (t_1 <= -2e+209) {
		tmp = t_2;
	} else if (t_1 <= 2e+90) {
		tmp = fma(z, (1.0 - log(t)), (x + y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(y + fma(b, Float64(a + -0.5), x))
	tmp = 0.0
	if (t_1 <= -2e+209)
		tmp = t_2;
	elseif (t_1 <= 2e+90)
		tmp = fma(z, Float64(1.0 - log(t)), Float64(x + y));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(b * N[(a + -0.5), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+209], t$95$2, If[LessEqual[t$95$1, 2e+90], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.0000000000000001e209 or 1.99999999999999993e90 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 96.3

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

   5. Simplified 96.3%

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

   if -2.0000000000000001e209 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.99999999999999993e90

   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 0

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

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

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

      2. associate-+r+ N/A

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

      3. associate-+l+ N/A

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

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

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

      5. *-rgt-identity N/A

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

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

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. *-commutative N/A

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

      12. accelerator-lowering-fma.f64 N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. log-lowering-log.f64 N/A

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

      17. +-commutative N/A

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

      18. +-lowering-+.f64 89.9

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

   5. Simplified 89.9%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+209}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{elif}\;\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, x + y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;\left(z + \left(x + y\right)\right) - z \cdot \log t \leq -5 \cdot 10^{-100}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= (- (+ z (+ x y)) (* z (log t))) -5e-100) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (((z + (x + y)) - (z * log(t))) <= -5e-100) {
		tmp = x + t_1;
	} else {
		tmp = y + 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 = (a - 0.5d0) * b
    if (((z + (x + y)) - (z * log(t))) <= (-5d-100)) then
        tmp = x + t_1
    else
        tmp = y + 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 = (a - 0.5) * b;
	double tmp;
	if (((z + (x + y)) - (z * Math.log(t))) <= -5e-100) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if ((z + (x + y)) - (z * math.log(t))) <= -5e-100:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) <= -5e-100)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (((z + (x + y)) - (z * log(t))) <= -5e-100)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-100], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -5.0000000000000001e-100

   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 x around inf

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

   5. Simplified 61.9%

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

   if -5.0000000000000001e-100 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 64.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z + \left(x + y\right)\right) - z \cdot \log t \leq -5 \cdot 10^{-100}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + \left(a - 0.5\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 21.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (- (+ z (+ x y)) (* z (log t))) (* (- a 0.5) b)) -5e-100) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((z + (x + y)) - (z * log(t))) + ((a - 0.5) * b)) <= -5e-100) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((((z + (x + y)) - (z * log(t))) + ((a - 0.5d0) * b)) <= (-5d-100)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((z + (x + y)) - (z * Math.log(t))) + ((a - 0.5) * b)) <= -5e-100) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (((z + (x + y)) - (z * math.log(t))) + ((a - 0.5) * b)) <= -5e-100:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(z + Float64(x + y)) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b)) <= -5e-100)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((((z + (x + y)) - (z * log(t))) + ((a - 0.5) * b)) <= -5e-100)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], -5e-100], x, y]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)) < -5.0000000000000001e-100

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 20.6%

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

   if -5.0000000000000001e-100 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   4. Step-by-step derivation

   5. Simplified 26.9%

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

4. Final simplification 24.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(z + \left(x + y\right)\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{if}\;x + y \leq 2 \cdot 10^{-99}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ a -0.5) x)))
   (if (<= (+ x y) 2e-99) (fma z (- 1.0 (log t)) t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, (a + -0.5), x);
	double tmp;
	if ((x + y) <= 2e-99) {
		tmp = fma(z, (1.0 - log(t)), t_1);
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, Float64(a + -0.5), x)
	tmp = 0.0
	if (Float64(x + y) <= 2e-99)
		tmp = fma(z, Float64(1.0 - log(t)), t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(a + -0.5), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[N[(x + y), $MachinePrecision], 2e-99], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2e-99

   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. +-commutative N/A

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

      10. *-rgt-identity N/A

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

      11. distribute-lft-in N/A

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

      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. mul-1-neg N/A

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

      14. +-commutative N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 84.2%

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

   if 2e-99 < (+.f64 x 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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 88.0

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

   5. Simplified 88.0%

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

Alternative 6: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - \log t, a \cdot b\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+173}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 (log t)) (* a b))))
   (if (<= z -2.2e+235)
     t_1
     (if (<= z 1.55e+173) (+ y (fma b (+ a -0.5) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - log(t)), (a * b));
	double tmp;
	if (z <= -2.2e+235) {
		tmp = t_1;
	} else if (z <= 1.55e+173) {
		tmp = y + fma(b, (a + -0.5), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - log(t)), Float64(a * b))
	tmp = 0.0
	if (z <= -2.2e+235)
		tmp = t_1;
	elseif (z <= 1.55e+173)
		tmp = Float64(y + fma(b, Float64(a + -0.5), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+235], t$95$1, If[LessEqual[z, 1.55e+173], N[(y + N[(b * N[(a + -0.5), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e235 or 1.55e173 < z

   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. +-commutative N/A

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

      10. *-rgt-identity N/A

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

      11. distribute-lft-in N/A

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

      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. mul-1-neg N/A

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

      14. +-commutative N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 93.8%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(z, 1 - \log t, \color{blue}{a \cdot b}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 89.1

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

   8. Simplified 89.1%

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

   if -2.2e235 < z < 1.55e173

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 93.6

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

   5. Simplified 93.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+235}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+173}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{+179}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - \log t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3e+179) (+ y (fma b (+ a -0.5) x)) (fma z (- 1.0 (log t)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3e+179) {
		tmp = y + fma(b, (a + -0.5), x);
	} else {
		tmp = fma(z, (1.0 - log(t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3e+179)
		tmp = Float64(y + fma(b, Float64(a + -0.5), x));
	else
		tmp = fma(z, Float64(1.0 - log(t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3e+179], N[(y + N[(b * N[(a + -0.5), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.9999999999999998e179

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.1

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

   5. Simplified 91.1%

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

   if 2.9999999999999998e179 < z

   1. Initial program 99.7%

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

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

      10. *-rgt-identity N/A

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

      11. distribute-lft-in N/A

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

      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. mul-1-neg N/A

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

      14. +-commutative N/A

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

      15. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 94.1%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 77.4%

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

Alternative 8: 82.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.38 \cdot 10^{+178}:\\ \;\;\;\;y + \mathsf{fma}\left(b, a + -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \log t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.38e+178) (+ y (fma b (+ a -0.5) x)) (* z (- 1.0 (log t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 1.38e+178) {
		tmp = y + fma(b, (a + -0.5), x);
	} else {
		tmp = z * (1.0 - log(t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 1.38e+178)
		tmp = Float64(y + fma(b, Float64(a + -0.5), x));
	else
		tmp = Float64(z * Float64(1.0 - log(t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 1.38e+178], N[(y + N[(b * N[(a + -0.5), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.37999999999999994e178

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 91.1

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

   5. Simplified 91.1%

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

   if 1.37999999999999994e178 < z

   1. Initial program 99.7%

      \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \]
   2. 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. mul-1-neg N/A

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

      3. *-lowering-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. --lowering--.f64 N/A

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

      7. log-lowering-log.f64 73.3

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

   5. Simplified 73.3%

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

Alternative 9: 70.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := b \cdot \left(a + -0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;y + \mathsf{fma}\left(b, -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (* b (+ a -0.5))))
   (if (<= t_1 -2e+218) t_2 (if (<= t_1 2e+167) (+ y (fma b -0.5 x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = b * (a + -0.5);
	double tmp;
	if (t_1 <= -2e+218) {
		tmp = t_2;
	} else if (t_1 <= 2e+167) {
		tmp = y + fma(b, -0.5, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(b * Float64(a + -0.5))
	tmp = 0.0
	if (t_1 <= -2e+218)
		tmp = t_2;
	elseif (t_1 <= 2e+167)
		tmp = Float64(y + fma(b, -0.5, x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+218], t$95$2, If[LessEqual[t$95$1, 2e+167], N[(y + N[(b * -0.5 + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.00000000000000017e218 or 2.0000000000000001e167 < (*.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 b around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. +-lowering-+.f64 90.4

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

   5. Simplified 90.4%

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

   if -2.00000000000000017e218 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000001e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 75.1

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

   5. Simplified 75.1%

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

   6. Taylor expanded in a around 0

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

   8. Simplified 69.0%

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

Alternative 10: 65.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := b \cdot \left(a + -0.5\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (* b (+ a -0.5))))
   (if (<= t_1 -2e+212) t_2 (if (<= t_1 2e+167) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = b * (a + -0.5);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = t_2;
	} else if (t_1 <= 2e+167) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = b * (a + (-0.5d0))
    if (t_1 <= (-2d+212)) then
        tmp = t_2
    else if (t_1 <= 2d+167) then
        tmp = x + y
    else
        tmp = t_2
    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 = (a - 0.5) * b;
	double t_2 = b * (a + -0.5);
	double tmp;
	if (t_1 <= -2e+212) {
		tmp = t_2;
	} else if (t_1 <= 2e+167) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = b * (a + -0.5)
	tmp = 0
	if t_1 <= -2e+212:
		tmp = t_2
	elif t_1 <= 2e+167:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(b * Float64(a + -0.5))
	tmp = 0.0
	if (t_1 <= -2e+212)
		tmp = t_2;
	elseif (t_1 <= 2e+167)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = b * (a + -0.5);
	tmp = 0.0;
	if (t_1 <= -2e+212)
		tmp = t_2;
	elseif (t_1 <= 2e+167)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a + -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+212], t$95$2, If[LessEqual[t$95$1, 2e+167], 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) < -1.9999999999999998e212 or 2.0000000000000001e167 < (*.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 b around inf

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

      1. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. +-lowering-+.f64 89.5

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

   5. Simplified 89.5%

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

   if -1.9999999999999998e212 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000001e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 74.8

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

   5. Simplified 74.8%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 62.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+212}:\\ \;\;\;\;b \cdot \left(a + -0.5\right)\\ \mathbf{elif}\;\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+167}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a + -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+218}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+167}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -2e+218) (* a b) (if (<= t_1 2e+167) (+ x y) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -2e+218) {
		tmp = a * b;
	} else if (t_1 <= 2e+167) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-2d+218)) then
        tmp = a * b
    else if (t_1 <= 2d+167) then
        tmp = x + y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -2e+218) {
		tmp = a * b;
	} else if (t_1 <= 2e+167) {
		tmp = x + y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -2e+218:
		tmp = a * b
	elif t_1 <= 2e+167:
		tmp = x + y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -2e+218)
		tmp = Float64(a * b);
	elseif (t_1 <= 2e+167)
		tmp = Float64(x + y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -2e+218)
		tmp = a * b;
	elseif (t_1 <= 2e+167)
		tmp = x + y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+218], N[(a * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+167], N[(x + y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.00000000000000017e218 or 2.0000000000000001e167 < (*.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. *-commutative N/A

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

      2. *-lowering-*.f64 72.0

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

   5. Simplified 72.0%

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

   if -2.00000000000000017e218 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.0000000000000001e167

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 75.1

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

   5. Simplified 75.1%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 62.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+218}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;\left(a - 0.5\right) \cdot b \leq 2 \cdot 10^{+167}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \mathsf{fma}\left(b, a, x\right)\\ \mathbf{if}\;a - 0.5 \leq -0.502:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a - 0.5 \leq -0.5:\\ \;\;\;\;y + \mathsf{fma}\left(b, -0.5, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (fma b a x))))
   (if (<= (- a 0.5) -0.502)
     t_1
     (if (<= (- a 0.5) -0.5) (+ y (fma b -0.5 x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + fma(b, a, x);
	double tmp;
	if ((a - 0.5) <= -0.502) {
		tmp = t_1;
	} else if ((a - 0.5) <= -0.5) {
		tmp = y + fma(b, -0.5, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + fma(b, a, x))
	tmp = 0.0
	if (Float64(a - 0.5) <= -0.502)
		tmp = t_1;
	elseif (Float64(a - 0.5) <= -0.5)
		tmp = Float64(y + fma(b, -0.5, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(b * a + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.502], t$95$1, If[LessEqual[N[(a - 0.5), $MachinePrecision], -0.5], N[(y + N[(b * -0.5 + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 a #s(literal 1/2 binary64)) < -0.502 or -0.5 < (-.f64 a #s(literal 1/2 binary64))

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 86.3

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

   5. Simplified 86.3%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 85.2%

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

   if -0.502 < (-.f64 a #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 78.7

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

   5. Simplified 78.7%

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

   6. Taylor expanded in a around 0

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

   8. Simplified 77.9%

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

Alternative 13: 45.8% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-44}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -4e+49) (+ x y) (if (<= (+ x y) 2e-44) (* b -0.5) (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+49) {
		tmp = x + y;
	} else if ((x + y) <= 2e-44) {
		tmp = b * -0.5;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((x + y) <= (-4d+49)) then
        tmp = x + y
    else if ((x + y) <= 2d-44) then
        tmp = b * (-0.5d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -4e+49) {
		tmp = x + y;
	} else if ((x + y) <= 2e-44) {
		tmp = b * -0.5;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -4e+49:
		tmp = x + y
	elif (x + y) <= 2e-44:
		tmp = b * -0.5
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -4e+49)
		tmp = Float64(x + y);
	elseif (Float64(x + y) <= 2e-44)
		tmp = Float64(b * -0.5);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -4e+49)
		tmp = x + y;
	elseif ((x + y) <= 2e-44)
		tmp = b * -0.5;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e+49], N[(x + y), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e-44], N[(b * -0.5), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.99999999999999979e49 or 1.99999999999999991e-44 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-lowering-+.f64 86.4

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

   5. Simplified 86.4%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 57.7%

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

   if -3.99999999999999979e49 < (+.f64 x y) < 1.99999999999999991e-44

   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. *-lowering-*.f64 N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. +-lowering-+.f64 69.4

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

   5. Simplified 69.4%

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

   6. Taylor expanded in a around 0

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

   8. Simplified 28.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-44}:\\ \;\;\;\;b \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 79.6% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

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

   5. +-commutative N/A

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

   6. accelerator-lowering-fma.f64 N/A

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

   7. sub-neg N/A

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

   8. metadata-eval N/A

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

   9. +-lowering-+.f64 82.9

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

5. Simplified 82.9%

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

Alternative 15: 42.5% 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 99.9%

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

3. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

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

   5. +-commutative N/A

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

   6. accelerator-lowering-fma.f64 N/A

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

   7. sub-neg N/A

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

   8. metadata-eval N/A

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

   9. +-lowering-+.f64 82.9

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

5. Simplified 82.9%

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

6. Taylor expanded in b around 0

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

8. Simplified 43.8%

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

9. Final simplification 43.8%

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

Alternative 16: 22.3% accurate, 126.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 20.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024196 
(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)))