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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

Alternatives: 17

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. lift-*.f64 N/A

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

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

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

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

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

   17. lift-*.f64 N/A

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

   18. lower-neg.f64 99.9

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 21.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -1 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)) -1e-119) 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)) <= -1e-119) {
		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)) <= (-1d-119)) 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)) <= -1e-119) {
		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)) <= -1e-119:
		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)) <= -1e-119)
		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)) <= -1e-119)
		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], -1e-119], 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)) < -1.00000000000000001e-119

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 20.9%

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

   if -1.00000000000000001e-119 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 22.4%

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

Alternative 3: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.7 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e-12) (not (<= z 4.7e+36)))
   (fma (- 1.0 (log t)) z (fma (- a 0.5) b y))
   (fma (- a 0.5) b (+ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e-12) || !(z <= 4.7e+36)) {
		tmp = fma((1.0 - log(t)), z, fma((a - 0.5), b, y));
	} else {
		tmp = fma((a - 0.5), b, (y + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e-12) || !(z <= 4.7e+36))
		tmp = fma(Float64(1.0 - log(t)), z, fma(Float64(a - 0.5), b, y));
	else
		tmp = fma(Float64(a - 0.5), b, Float64(y + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e-12], N[Not[LessEqual[z, 4.7e+36]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999998e-12 or 4.69999999999999989e36 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.2%

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

   if -2.6999999999999998e-12 < z < 4.69999999999999989e36

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 99.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-12} \lor \neg \left(z \leq 4.7 \cdot 10^{+36}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a - 0.5, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x + y\right) + z\right) - z \cdot \log t \leq -5 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- (+ (+ x y) z) (* z (log t))) -5e-79)
   (fma (- a 0.5) b x)
   (fma (- a 0.5) b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((x + y) + z) - (z * log(t))) <= -5e-79) {
		tmp = fma((a - 0.5), b, x);
	} else {
		tmp = fma((a - 0.5), b, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) <= -5e-79)
		tmp = fma(Float64(a - 0.5), b, x);
	else
		tmp = fma(Float64(a - 0.5), b, y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-79], N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision], N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -4.99999999999999999e-79

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 58.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 58.2

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

   7. Applied rewrites 58.2%

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

   if -4.99999999999999999e-79 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 68.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 68.5

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

   7. Applied rewrites 68.5%

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

Alternative 5: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+58} \lor \neg \left(z \leq 2 \cdot 10^{+154}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+58) (not (<= z 2e+154)))
   (fma (- 1.0 (log t)) z (fma a b y))
   (- (+ z (+ y x)) (* (- 0.5 a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+58) || !(z <= 2e+154)) {
		tmp = fma((1.0 - log(t)), z, fma(a, b, y));
	} else {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+58) || !(z <= 2e+154))
		tmp = fma(Float64(1.0 - log(t)), z, fma(a, b, y));
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+58], N[Not[LessEqual[z, 2e+154]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + N[(a * b + y), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000001e58 or 2.00000000000000007e154 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 86.0%

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

   if -1.15000000000000001e58 < z < 2.00000000000000007e154

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. lift-*.f64 N/A

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

      18. lower-neg.f64 100.0

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 97.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+58} \lor \neg \left(z \leq 2 \cdot 10^{+154}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, \mathsf{fma}\left(a, b, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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]

Derivation

1. Initial program 99.9%

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

Alternative 7: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+224} \lor \neg \left(z \leq 2.9 \cdot 10^{+150}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+224) (not (<= z 2.9e+150)))
   (+ (fma (- 1.0 (log t)) z x) y)
   (- (+ z (+ y x)) (* (- 0.5 a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+224) || !(z <= 2.9e+150)) {
		tmp = fma((1.0 - log(t)), z, x) + y;
	} else {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+224) || !(z <= 2.9e+150))
		tmp = Float64(fma(Float64(1.0 - log(t)), z, x) + y);
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+224], N[Not[LessEqual[z, 2.9e+150]], $MachinePrecision]], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision] + y), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000025e224 or 2.90000000000000011e150 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 88.2%

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

   7. Applied rewrites 88.2%

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

   if -3.80000000000000025e224 < z < 2.90000000000000011e150

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. lift-*.f64 N/A

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

      18. lower-neg.f64 99.9

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 94.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+224} \lor \neg \left(z \leq 2.9 \cdot 10^{+150}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right) + y\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+224} \lor \neg \left(z \leq 5.7 \cdot 10^{+181}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+224) (not (<= z 5.7e+181)))
   (fma (- 1.0 (log t)) z x)
   (- (+ z (+ y x)) (* (- 0.5 a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+224) || !(z <= 5.7e+181)) {
		tmp = fma((1.0 - log(t)), z, x);
	} else {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+224) || !(z <= 5.7e+181))
		tmp = fma(Float64(1.0 - log(t)), z, x);
	else
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+224], N[Not[LessEqual[z, 5.7e+181]], $MachinePrecision]], N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000025e224 or 5.7000000000000002e181 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 75.4%

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

   if -3.80000000000000025e224 < z < 5.7000000000000002e181

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. lift-*.f64 N/A

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

      18. lower-neg.f64 99.9

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 93.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+224} \lor \neg \left(z \leq 5.7 \cdot 10^{+181}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \log t\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+154}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (log t))))
   (if (<= z -3.8e+224)
     (fma t_1 z x)
     (if (<= z 3.8e+154) (- (+ z (+ y x)) (* (- 0.5 a) b)) (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 <= -3.8e+224) {
		tmp = fma(t_1, z, x);
	} else if (z <= 3.8e+154) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} 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 <= -3.8e+224)
		tmp = fma(t_1, z, x);
	elseif (z <= 3.8e+154)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	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, -3.8e+224], N[(t$95$1 * z + x), $MachinePrecision], If[LessEqual[z, 3.8e+154], N[(N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000025e224

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 84.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 63.5%

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

   if -3.80000000000000025e224 < z < 3.7999999999999998e154

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. lift-*.f64 N/A

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

      18. lower-neg.f64 99.9

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 94.4%

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

   if 3.7999999999999998e154 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 84.2%

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

Alternative 10: 81.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+182}:\\ \;\;\;\;\left(z + \left(y + x\right)\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log t\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 2e+182) (- (+ z (+ y x)) (* (- 0.5 a) b)) (* (- 1.0 (log t)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e+182) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else {
		tmp = (1.0 - log(t)) * z;
	}
	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 (z <= 2d+182) then
        tmp = (z + (y + x)) - ((0.5d0 - a) * b)
    else
        tmp = (1.0d0 - log(t)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 2e+182) {
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	} else {
		tmp = (1.0 - Math.log(t)) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 2e+182:
		tmp = (z + (y + x)) - ((0.5 - a) * b)
	else:
		tmp = (1.0 - math.log(t)) * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 2e+182)
		tmp = Float64(Float64(z + Float64(y + x)) - Float64(Float64(0.5 - a) * b));
	else
		tmp = Float64(Float64(1.0 - log(t)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 2e+182)
		tmp = (z + (y + x)) - ((0.5 - a) * b);
	else
		tmp = (1.0 - log(t)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 2.0000000000000001e182

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

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

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

      17. lift-*.f64 N/A

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

      18. lower-neg.f64 99.9

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 89.7%

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

   if 2.0000000000000001e182 < z

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 83.4%

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

Alternative 11: 65.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+130} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+138}\right):\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -2e+130) (not (<= t_1 5e+138))) (* (+ -0.5 a) b) (+ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -2e+130) || !(t_1 <= 5e+138)) {
		tmp = (-0.5 + a) * b;
	} else {
		tmp = y + x;
	}
	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+130)) .or. (.not. (t_1 <= 5d+138))) then
        tmp = ((-0.5d0) + a) * b
    else
        tmp = y + x
    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+130) || !(t_1 <= 5e+138)) {
		tmp = (-0.5 + a) * b;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -2e+130) or not (t_1 <= 5e+138):
		tmp = (-0.5 + a) * b
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -2e+130) || !(t_1 <= 5e+138))
		tmp = Float64(Float64(-0.5 + a) * b);
	else
		tmp = Float64(y + x);
	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+130) || ~((t_1 <= 5e+138)))
		tmp = (-0.5 + a) * b;
	else
		tmp = y + x;
	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[Or[LessEqual[t$95$1, -2e+130], N[Not[LessEqual[t$95$1, 5e+138]], $MachinePrecision]], N[(N[(-0.5 + a), $MachinePrecision] * b), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.0000000000000001e130 or 5.00000000000000016e138 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 82.1%

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

   if -2.0000000000000001e130 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 5.00000000000000016e138

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.9%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+130} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+138}\right):\\ \;\;\;\;\left(-0.5 + a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.6% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+130} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+209}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (or (<= t_1 -2e+130) (not (<= t_1 5e+209))) (* b a) (+ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((t_1 <= -2e+130) || !(t_1 <= 5e+209)) {
		tmp = b * a;
	} else {
		tmp = y + x;
	}
	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+130)) .or. (.not. (t_1 <= 5d+209))) then
        tmp = b * a
    else
        tmp = y + x
    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+130) || !(t_1 <= 5e+209)) {
		tmp = b * a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (t_1 <= -2e+130) or not (t_1 <= 5e+209):
		tmp = b * a
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if ((t_1 <= -2e+130) || !(t_1 <= 5e+209))
		tmp = Float64(b * a);
	else
		tmp = Float64(y + x);
	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+130) || ~((t_1 <= 5e+209)))
		tmp = b * a;
	else
		tmp = y + x;
	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[Or[LessEqual[t$95$1, -2e+130], N[Not[LessEqual[t$95$1, 5e+209]], $MachinePrecision]], N[(b * a), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -2.0000000000000001e130 or 4.99999999999999964e209 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 67.7%

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

   if -2.0000000000000001e130 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 4.99999999999999964e209

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{+130} \lor \neg \left(\left(a - 0.5\right) \cdot b \leq 5 \cdot 10^{+209}\right):\\ \;\;\;\;b \cdot a\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 50000:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) 50000.0) (fma (- a 0.5) b x) (+ y (* a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= 50000.0) {
		tmp = fma((a - 0.5), b, x);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= 50000.0)
		tmp = fma(Float64(a - 0.5), b, x);
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], 50000.0], N[(N[(a - 0.5), $MachinePrecision] * b + x), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 5e4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 65.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 65.3

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

   7. Applied rewrites 65.3%

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

   if 5e4 < (+.f64 x y)

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 55.9%

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

Alternative 14: 79.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift--.f64 N/A

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

   3. associate-+l- N/A

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

   4. lower--.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-+.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 N/A

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

   11. lift-*.f64 N/A

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

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

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 N/A

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

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

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

   17. lift-*.f64 N/A

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

   18. lower-neg.f64 99.9

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. lower-*.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in b around inf

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

7. Applied rewrites 82.4%

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

Alternative 15: 78.6% accurate, 9.7× speedup

Math

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

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 fma(Float64(a - 0.5), b, Float64(y + x))
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 81.7%

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

Alternative 16: 41.9% 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. Add Preprocessing

3. Taylor expanded in z around 0

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

5. Applied rewrites 81.7%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 39.6%

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

Alternative 17: 21.8% 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. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 21.7%

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

Developer Target 1: 99.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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 2025019 
(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)))