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

Percentage Accurate: 99.9% → 99.9%

Time: 4.8s

Alternatives: 19

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 N/A

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

   5. +-commutative N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. lift--.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 57.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x + y\right) + z\right) - z \cdot \log t \leq -5 \cdot 10^{-120}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a - 0.5, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ (+ x y) z) (* z (log t))) -5e-120)
   (+ x (* (- a 0.5) b))
   (fma b (- a 0.5) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((x + y) + z) - (z * log(t))) <= -5e-120) {
		tmp = x + ((a - 0.5) * b);
	} else {
		tmp = fma(b, (a - 0.5), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) <= -5e-120)
		tmp = Float64(x + Float64(Float64(a - 0.5) * b));
	else
		tmp = fma(b, Float64(a - 0.5), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-120], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(b * N[(a - 0.5), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -5.00000000000000007e-120

   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. Taylor expanded in x around inf

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

   4. Applied rewrites 57.2%

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

   if -5.00000000000000007e-120 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 77.9

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

   4. Applied rewrites 77.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 58.1

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

   7. Applied rewrites 58.1%

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

Alternative 3: 21.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -4 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)) -4e-125) x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((((x + y) + z) - (z * log(t))) + ((a - 0.5) * b)) <= -4e-125) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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) + z) - (z * log(t))) + ((a - 0.5d0) * b)) <= (-4d-125)) 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 (((((x + y) + z) - (z * Math.log(t))) + ((a - 0.5) * b)) <= -4e-125) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((((x + y) + z) - (z * math.log(t))) + ((a - 0.5) * b)) <= -4e-125:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) + Float64(Float64(a - 0.5) * b)) <= -4e-125)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((((x + y) + z) - (z * log(t))) + ((a - 0.5) * b)) <= -4e-125)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], -4e-125], 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)) < -4.00000000000000005e-125

   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. Taylor expanded in x around inf

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

   4. Applied rewrites 21.5%

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

   if -4.00000000000000005e-125 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 22.4%

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

Alternative 4: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(b, a - 0.5, y\right)\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z (fma b (- a 0.5) y))))
   (if (<= z -1.35e+39)
     t_1
     (if (<= z 7.5e+176) (+ (fma (- a 0.5) b y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, fma(b, (a - 0.5), y));
	double tmp;
	if (z <= -1.35e+39) {
		tmp = t_1;
	} else if (z <= 7.5e+176) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, fma(b, Float64(a - 0.5), y))
	tmp = 0.0
	if (z <= -1.35e+39)
		tmp = t_1;
	elseif (z <= 7.5e+176)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(b * N[(a - 0.5), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+39], t$95$1, If[LessEqual[z, 7.5e+176], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000002e39 or 7.499999999999999e176 < 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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 87.3

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

   7. Applied rewrites 87.3%

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

   if -1.35000000000000002e39 < z < 7.499999999999999e176

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 92.7

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

   4. Applied rewrites 92.7%

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

Alternative 5: 87.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, b \cdot a\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(-0.5, b, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -1.52e+174)
     (fma t_1 z (* b a))
     (if (<= z 8.6e+192)
       (+ (fma (- a 0.5) b y) x)
       (fma t_1 z (fma -0.5 b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= -1.52e+174) {
		tmp = fma(t_1, z, (b * a));
	} else if (z <= 8.6e+192) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = fma(t_1, z, fma(-0.5, b, y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= -1.52e+174)
		tmp = fma(t_1, z, Float64(b * a));
	elseif (z <= 8.6e+192)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = fma(t_1, z, fma(-0.5, b, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+174], N[(t$95$1 * z + N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+192], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 * z + N[(-0.5 * b + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52000000000000004e174

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 91.4

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

   7. Applied rewrites 91.4%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.5

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

   10. Applied rewrites 78.5%

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

   if -1.52000000000000004e174 < z < 8.59999999999999952e192

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 89.6

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

   4. Applied rewrites 89.6%

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

   if 8.59999999999999952e192 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 92.4

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

   7. Applied rewrites 92.4%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 77.6

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

   10. Applied rewrites 77.6%

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

Alternative 6: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, b \cdot a\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -1.52e+174)
     (fma t_1 z (* b a))
     (if (<= z 1.35e+193) (+ (fma (- a 0.5) b y) x) (fma t_1 z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - log(t);
	double tmp;
	if (z <= -1.52e+174) {
		tmp = fma(t_1, z, (b * a));
	} else if (z <= 1.35e+193) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = fma(t_1, z, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - log(t))
	tmp = 0.0
	if (z <= -1.52e+174)
		tmp = fma(t_1, z, Float64(b * a));
	elseif (z <= 1.35e+193)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = fma(t_1, z, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+174], N[(t$95$1 * z + N[(b * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+193], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 * z + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52000000000000004e174

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 91.4

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

   7. Applied rewrites 91.4%

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

   8. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.5

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

   10. Applied rewrites 78.5%

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

   if -1.52000000000000004e174 < z < 1.35e193

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 89.6

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

   4. Applied rewrites 89.6%

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

   if 1.35e193 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 92.4

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

   7. Applied rewrites 92.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 73.0%

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

Alternative 7: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+196}:\\ \;\;\;\;t\_1 + x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z y)))
   (if (<= z -2.25e+196)
     (+ t_1 x)
     (if (<= z 1.35e+193) (+ (fma (- a 0.5) b y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, y);
	double tmp;
	if (z <= -2.25e+196) {
		tmp = t_1 + x;
	} else if (z <= 1.35e+193) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, y)
	tmp = 0.0
	if (z <= -2.25e+196)
		tmp = Float64(t_1 + x);
	elseif (z <= 1.35e+193)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[z, -2.25e+196], N[(t$95$1 + x), $MachinePrecision], If[LessEqual[z, 1.35e+193], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.24999999999999989e196

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in b around 0

      \[\leadsto \left(y + z \cdot \left(1 - \log t\right)\right) + x \]
   6. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 81.4

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

   7. Applied rewrites 81.4%

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

   if -2.24999999999999989e196 < z < 1.35e193

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 88.9

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

   4. Applied rewrites 88.9%

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

   if 1.35e193 < z

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 92.4

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

   7. Applied rewrites 92.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 73.0%

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

Alternative 8: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \log t, z, y\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+193}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (log t)) z y)))
   (if (<= z -1.7e+199)
     t_1
     (if (<= z 1.35e+193) (+ (fma (- a 0.5) b y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - log(t)), z, y);
	double tmp;
	if (z <= -1.7e+199) {
		tmp = t_1;
	} else if (z <= 1.35e+193) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - log(t)), z, y)
	tmp = 0.0
	if (z <= -1.7e+199)
		tmp = t_1;
	elseif (z <= 1.35e+193)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision]}, If[LessEqual[z, -1.7e+199], t$95$1, If[LessEqual[z, 1.35e+193], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e199 or 1.35e193 < 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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift--.f64 92.4

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

   7. Applied rewrites 92.4%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 73.6%

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

   if -1.7e199 < z < 1.35e193

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 9: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -3 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+216}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (log t)) z)))
   (if (<= z -3e+218) t_1 (if (<= z 1.5e+216) (+ (fma (- a 0.5) b y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - log(t)) * z;
	double tmp;
	if (z <= -3e+218) {
		tmp = t_1;
	} else if (z <= 1.5e+216) {
		tmp = fma((a - 0.5), b, y) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - log(t)) * z)
	tmp = 0.0
	if (z <= -3e+218)
		tmp = t_1;
	elseif (z <= 1.5e+216)
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -3e+218], t$95$1, If[LessEqual[z, 1.5e+216], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e218 or 1.4999999999999999e216 < z

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(1 - \log t\right) \cdot z \]

      4. lift-log.f64 70.6

         \[\leadsto \left(1 - \log t\right) \cdot z \]

   4. Applied rewrites 70.6%

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

   if -3.0000000000000001e218 < z < 1.4999999999999999e216

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 87.2

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

   4. Applied rewrites 87.2%

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

Alternative 10: 63.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -1e+145)
     t_1
     (if (<= t_1 1e+35)
       (+ y x)
       (if (<= t_1 5e+88) t_1 (if (<= t_1 2e+199) (fma b a 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 (t_1 <= -1e+145) {
		tmp = t_1;
	} else if (t_1 <= 1e+35) {
		tmp = y + x;
	} else if (t_1 <= 5e+88) {
		tmp = t_1;
	} else if (t_1 <= 2e+199) {
		tmp = fma(b, a, y);
	} else {
		tmp = 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 (t_1 <= -1e+145)
		tmp = t_1;
	elseif (t_1 <= 1e+35)
		tmp = Float64(y + x);
	elseif (t_1 <= 5e+88)
		tmp = t_1;
	elseif (t_1 <= 2e+199)
		tmp = fma(b, a, y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+145], t$95$1, If[LessEqual[t$95$1, 1e+35], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 5e+88], t$95$1, If[LessEqual[t$95$1, 2e+199], N[(b * a + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -9.9999999999999999e144 or 9.9999999999999997e34 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.99999999999999997e88 or 2.00000000000000019e199 < (*.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. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 72.4

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

   4. Applied rewrites 72.4%

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

   if -9.9999999999999999e144 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.9999999999999997e34

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto y + x \]
   6. Step-by-step derivation

   7. Applied rewrites 60.8%

      \[\leadsto y + x \]

   if 4.99999999999999997e88 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000019e199

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 77.5

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 58.4

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

   7. Applied rewrites 58.4%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(b, a, y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 39.0%

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

Alternative 11: 58.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+274}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+261}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -4e+274)
     (* b a)
     (if (<= t_1 -5e+38)
       (fma b -0.5 y)
       (if (<= t_1 1e+35)
         (+ y x)
         (if (<= t_1 4e+261) (fma b -0.5 y) (* b a)))))))

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 <= -4e+274) {
		tmp = b * a;
	} else if (t_1 <= -5e+38) {
		tmp = fma(b, -0.5, y);
	} else if (t_1 <= 1e+35) {
		tmp = y + x;
	} else if (t_1 <= 4e+261) {
		tmp = fma(b, -0.5, y);
	} else {
		tmp = b * a;
	}
	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 <= -4e+274)
		tmp = Float64(b * a);
	elseif (t_1 <= -5e+38)
		tmp = fma(b, -0.5, y);
	elseif (t_1 <= 1e+35)
		tmp = Float64(y + x);
	elseif (t_1 <= 4e+261)
		tmp = fma(b, -0.5, y);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+274], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, -5e+38], N[(b * -0.5 + y), $MachinePrecision], If[LessEqual[t$95$1, 1e+35], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+261], N[(b * -0.5 + y), $MachinePrecision], N[(b * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -3.99999999999999969e274 or 3.9999999999999997e261 < (*.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. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 80.8

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

   4. Applied rewrites 80.8%

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

   if -3.99999999999999969e274 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -4.9999999999999997e38 or 9.9999999999999997e34 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.9999999999999997e261

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 79.9

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

   4. Applied rewrites 79.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 62.1

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 41.7%

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

   if -4.9999999999999997e38 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.9999999999999997e34

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto y + x \]
   6. Step-by-step derivation

   7. Applied rewrites 63.2%

      \[\leadsto y + x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 57.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+199}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+261}:\\ \;\;\;\;-0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -2e+250)
     (* b a)
     (if (<= t_1 2e+199) (+ y x) (if (<= t_1 4e+261) (* -0.5 b) (* b a))))))

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+250) {
		tmp = b * a;
	} else if (t_1 <= 2e+199) {
		tmp = y + x;
	} else if (t_1 <= 4e+261) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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+250)) then
        tmp = b * a
    else if (t_1 <= 2d+199) then
        tmp = y + x
    else if (t_1 <= 4d+261) 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 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -2e+250) {
		tmp = b * a;
	} else if (t_1 <= 2e+199) {
		tmp = y + x;
	} else if (t_1 <= 4e+261) {
		tmp = -0.5 * b;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -2e+250:
		tmp = b * a
	elif t_1 <= 2e+199:
		tmp = y + x
	elif t_1 <= 4e+261:
		tmp = -0.5 * b
	else:
		tmp = b * a
	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+250)
		tmp = Float64(b * a);
	elseif (t_1 <= 2e+199)
		tmp = Float64(y + x);
	elseif (t_1 <= 4e+261)
		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 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -2e+250)
		tmp = b * a;
	elseif (t_1 <= 2e+199)
		tmp = y + x;
	elseif (t_1 <= 4e+261)
		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[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+250], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 2e+199], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+261], 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) < -1.9999999999999998e250 or 3.9999999999999997e261 < (*.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. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.6

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

   4. Applied rewrites 76.6%

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

   if -1.9999999999999998e250 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 2.00000000000000019e199

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto y + x \]
   6. Step-by-step derivation

   7. Applied rewrites 54.3%

      \[\leadsto y + x \]

   if 2.00000000000000019e199 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.9999999999999997e261

   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. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 64.2

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

   4. Applied rewrites 64.2%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 35.3%

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

Alternative 13: 57.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+250}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+212}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -2e+250) (* b a) (if (<= t_1 4e+212) (+ y x) (* b a)))))

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+250) {
		tmp = b * a;
	} else if (t_1 <= 4e+212) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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+250)) then
        tmp = b * a
    else if (t_1 <= 4d+212) then
        tmp = y + x
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -2e+250) {
		tmp = b * a;
	} else if (t_1 <= 4e+212) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -2e+250:
		tmp = b * a
	elif t_1 <= 4e+212:
		tmp = y + x
	else:
		tmp = b * a
	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+250)
		tmp = Float64(b * a);
	elseif (t_1 <= 4e+212)
		tmp = Float64(y + x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -2e+250)
		tmp = b * a;
	elseif (t_1 <= 4e+212)
		tmp = y + x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+250], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 4e+212], N[(y + x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1.9999999999999998e250 or 3.9999999999999996e212 < (*.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. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 69.1

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

   4. Applied rewrites 69.1%

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

   if -1.9999999999999998e250 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 3.9999999999999996e212

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto y + x \]
   6. Step-by-step derivation

   7. Applied rewrites 53.7%

      \[\leadsto y + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 49.8% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot a + x\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{-22}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e+71)
   (+ (* b a) x)
   (if (<= (+ x y) 2e-22) (* (- a 0.5) b) (fma b a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e+71) {
		tmp = (b * a) + x;
	} else if ((x + y) <= 2e-22) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = fma(b, a, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e+71)
		tmp = Float64(Float64(b * a) + x);
	elseif (Float64(x + y) <= 2e-22)
		tmp = Float64(Float64(a - 0.5) * b);
	else
		tmp = fma(b, a, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+71], N[(N[(b * a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e-22], N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision], N[(b * a + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -4.99999999999999972e71

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 48.8

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

   7. Applied rewrites 48.8%

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

   if -4.99999999999999972e71 < (+.f64 x y) < 2.0000000000000001e-22

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 53.6

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

   4. Applied rewrites 53.6%

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

   if 2.0000000000000001e-22 < (+.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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 83.3

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

   4. Applied rewrites 83.3%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 58.1

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

   7. Applied rewrites 58.1%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(b, a, y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 47.8%

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

Alternative 15: 57.1% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.5:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-111}:\\ \;\;\;\;\mathsf{fma}\left(b, -0.5, y\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -0.5)
   (fma b a y)
   (if (<= a -2.3e-111)
     (fma b -0.5 y)
     (if (<= a 1.25e-5) (+ y x) (fma b a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -0.5) {
		tmp = fma(b, a, y);
	} else if (a <= -2.3e-111) {
		tmp = fma(b, -0.5, y);
	} else if (a <= 1.25e-5) {
		tmp = y + x;
	} else {
		tmp = fma(b, a, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -0.5)
		tmp = fma(b, a, y);
	elseif (a <= -2.3e-111)
		tmp = fma(b, -0.5, y);
	elseif (a <= 1.25e-5)
		tmp = Float64(y + x);
	else
		tmp = fma(b, a, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -0.5], N[(b * a + y), $MachinePrecision], If[LessEqual[a, -2.3e-111], N[(b * -0.5 + y), $MachinePrecision], If[LessEqual[a, 1.25e-5], N[(y + x), $MachinePrecision], N[(b * a + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.5 or 1.25000000000000006e-5 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 66.2

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

   7. Applied rewrites 66.2%

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

   8. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(b, a, y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 65.3%

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

   if -0.5 < a < -2.3e-111

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 73.7

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

   4. Applied rewrites 73.7%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 50.4

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

   7. Applied rewrites 50.4%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 48.5%

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

   if -2.3e-111 < a < 1.25000000000000006e-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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto y + x \]
   6. Step-by-step derivation

   7. Applied rewrites 49.3%

      \[\leadsto y + x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 55.5% accurate, 6.6× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e+71) (+ (* b a) x) (fma b (- a 0.5) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e+71) {
		tmp = (b * a) + x;
	} else {
		tmp = fma(b, (a - 0.5), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e+71)
		tmp = Float64(Float64(b * a) + x);
	else
		tmp = fma(b, Float64(a - 0.5), y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e+71], N[(N[(b * a), $MachinePrecision] + x), $MachinePrecision], N[(b * N[(a - 0.5), $MachinePrecision] + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.99999999999999972e71

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. *-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 48.8

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

   7. Applied rewrites 48.8%

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

   if -4.99999999999999972e71 < (+.f64 x y)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 74.9

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

   4. Applied rewrites 74.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 58.6

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

   7. Applied rewrites 58.6%

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

Alternative 17: 78.2% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lift--.f64 78.2

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

4. Applied rewrites 78.2%

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

Alternative 18: 42.3% accurate, 31.5× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 N/A

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

   5. +-commutative N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lift-log.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-*.f64 N/A

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

   12. lift--.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in y around inf

   \[\leadsto y + x \]
6. Step-by-step derivation

7. Applied rewrites 42.3%

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

Alternative 19: 21.7% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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. Taylor expanded in x around inf

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

4. Applied rewrites 21.7%

   \[\leadsto \color{blue}{x} \]
5. 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 2025103 
(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)))