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

Percentage Accurate: 99.9% → 99.9%

Time: 4.9s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision] + x), $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. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lift-log.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 46.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y\right) + z\right) - z \cdot \log t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-42}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;t\_1 \leq 10^{+44}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 10^{+165}:\\ \;\;\;\;y + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ (+ x y) z) (* z (log t)))))
   (if (<= t_1 -5e-42)
     (+ x (* a b))
     (if (<= t_1 1e+44)
       (* (- a 0.5) b)
       (if (<= t_1 1e+165) (+ y (* -0.5 b)) (+ y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + y) + z) - (z * log(t));
	double tmp;
	if (t_1 <= -5e-42) {
		tmp = x + (a * b);
	} else if (t_1 <= 1e+44) {
		tmp = (a - 0.5) * b;
	} else if (t_1 <= 1e+165) {
		tmp = y + (-0.5 * b);
	} else {
		tmp = y + (a * b);
	}
	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 = ((x + y) + z) - (z * log(t))
    if (t_1 <= (-5d-42)) then
        tmp = x + (a * b)
    else if (t_1 <= 1d+44) then
        tmp = (a - 0.5d0) * b
    else if (t_1 <= 1d+165) then
        tmp = y + ((-0.5d0) * b)
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + y) + z) - (z * Math.log(t));
	double tmp;
	if (t_1 <= -5e-42) {
		tmp = x + (a * b);
	} else if (t_1 <= 1e+44) {
		tmp = (a - 0.5) * b;
	} else if (t_1 <= 1e+165) {
		tmp = y + (-0.5 * b);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + y) + z) - (z * math.log(t))
	tmp = 0
	if t_1 <= -5e-42:
		tmp = x + (a * b)
	elif t_1 <= 1e+44:
		tmp = (a - 0.5) * b
	elif t_1 <= 1e+165:
		tmp = y + (-0.5 * b)
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + y) + z) - Float64(z * log(t)))
	tmp = 0.0
	if (t_1 <= -5e-42)
		tmp = Float64(x + Float64(a * b));
	elseif (t_1 <= 1e+44)
		tmp = Float64(Float64(a - 0.5) * b);
	elseif (t_1 <= 1e+165)
		tmp = Float64(y + Float64(-0.5 * b));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + y) + z) - (z * log(t));
	tmp = 0.0;
	if (t_1 <= -5e-42)
		tmp = x + (a * b);
	elseif (t_1 <= 1e+44)
		tmp = (a - 0.5) * b;
	elseif (t_1 <= 1e+165)
		tmp = y + (-0.5 * b);
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-42], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+44], N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t$95$1, 1e+165], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -5.00000000000000003e-42

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 55.4%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 44.9%

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

   if -5.00000000000000003e-42 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < 1.0000000000000001e44

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 72.6

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

   4. Applied rewrites 72.6%

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

   if 1.0000000000000001e44 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < 9.99999999999999899e164

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 34.2%

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

   if 9.99999999999999899e164 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 49.3%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 43.5%

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

Alternative 3: 52.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y\right) + z\right) - z \cdot \log t\\ \mathbf{if}\;t\_1 \leq 10^{+44}:\\ \;\;\;\;x + \left(a - 0.5\right) \cdot b\\ \mathbf{elif}\;t\_1 \leq 10^{+165}:\\ \;\;\;\;y + -0.5 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ (+ x y) z) (* z (log t)))))
   (if (<= t_1 1e+44)
     (+ x (* (- a 0.5) b))
     (if (<= t_1 1e+165) (+ y (* -0.5 b)) (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + y) + z) - (z * log(t));
	double tmp;
	if (t_1 <= 1e+44) {
		tmp = x + ((a - 0.5) * b);
	} else if (t_1 <= 1e+165) {
		tmp = y + (-0.5 * b);
	} else {
		tmp = y + (a * b);
	}
	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 = ((x + y) + z) - (z * log(t))
    if (t_1 <= 1d+44) then
        tmp = x + ((a - 0.5d0) * b)
    else if (t_1 <= 1d+165) then
        tmp = y + ((-0.5d0) * b)
    else
        tmp = y + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + y) + z) - (z * Math.log(t));
	double tmp;
	if (t_1 <= 1e+44) {
		tmp = x + ((a - 0.5) * b);
	} else if (t_1 <= 1e+165) {
		tmp = y + (-0.5 * b);
	} else {
		tmp = y + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + y) + z) - (z * math.log(t))
	tmp = 0
	if t_1 <= 1e+44:
		tmp = x + ((a - 0.5) * b)
	elif t_1 <= 1e+165:
		tmp = y + (-0.5 * b)
	else:
		tmp = y + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + y) + z) - Float64(z * log(t)))
	tmp = 0.0
	if (t_1 <= 1e+44)
		tmp = Float64(x + Float64(Float64(a - 0.5) * b));
	elseif (t_1 <= 1e+165)
		tmp = Float64(y + Float64(-0.5 * b));
	else
		tmp = Float64(y + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + y) + z) - (z * log(t));
	tmp = 0.0;
	if (t_1 <= 1e+44)
		tmp = x + ((a - 0.5) * b);
	elseif (t_1 <= 1e+165)
		tmp = y + (-0.5 * b);
	else
		tmp = y + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+44], N[(x + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+165], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision], N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < 1.0000000000000001e44

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 61.3%

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

   if 1.0000000000000001e44 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < 9.99999999999999899e164

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 34.2%

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

   if 9.99999999999999899e164 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 49.3%

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

   8. Taylor expanded in a around inf

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

   10. Applied rewrites 43.5%

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

Alternative 4: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ t_2 := \left(\left(y + x\right) + z\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+130}:\\ \;\;\;\;\left(y + x\right) + \left(z - \log t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)) (t_2 (- (+ (+ y x) z) (* (- 0.5 a) b))))
   (if (<= t_1 -1e+27)
     t_2
     (if (<= t_1 1e+130) (+ (+ y x) (- z (* (log t) z))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = ((y + x) + z) - ((0.5 - a) * b);
	double tmp;
	if (t_1 <= -1e+27) {
		tmp = t_2;
	} else if (t_1 <= 1e+130) {
		tmp = (y + x) + (z - (log(t) * z));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    t_2 = ((y + x) + z) - ((0.5d0 - a) * b)
    if (t_1 <= (-1d+27)) then
        tmp = t_2
    else if (t_1 <= 1d+130) then
        tmp = (y + x) + (z - (log(t) * z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double t_2 = ((y + x) + z) - ((0.5 - a) * b);
	double tmp;
	if (t_1 <= -1e+27) {
		tmp = t_2;
	} else if (t_1 <= 1e+130) {
		tmp = (y + x) + (z - (Math.log(t) * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	t_2 = ((y + x) + z) - ((0.5 - a) * b)
	tmp = 0
	if t_1 <= -1e+27:
		tmp = t_2
	elif t_1 <= 1e+130:
		tmp = (y + x) + (z - (math.log(t) * z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	t_2 = Float64(Float64(Float64(y + x) + z) - Float64(Float64(0.5 - a) * b))
	tmp = 0.0
	if (t_1 <= -1e+27)
		tmp = t_2;
	elseif (t_1 <= 1e+130)
		tmp = Float64(Float64(y + x) + Float64(z - Float64(log(t) * z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	t_2 = ((y + x) + z) - ((0.5 - a) * b);
	tmp = 0.0;
	if (t_1 <= -1e+27)
		tmp = t_2;
	elseif (t_1 <= 1e+130)
		tmp = (y + x) + (z - (log(t) * z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+27], t$95$2, If[LessEqual[t$95$1, 1e+130], N[(N[(y + x), $MachinePrecision] + N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -1e27 or 1.0000000000000001e130 < (*.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. 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. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. *-commutative N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 88.5

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

   6. Applied rewrites 88.5%

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

   if -1e27 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 1.0000000000000001e130

   1. Initial program 99.8%

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

   2. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. lower--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-log.f64 90.7

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

   4. Applied rewrites 90.7%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lower--.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-log.f64 N/A

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

      15. lift-*.f64 90.7

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

   6. Applied rewrites 90.7%

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

Alternative 5: 58.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;\left(\left(x + y\right) + z\right) - z \cdot \log t \leq -2 \cdot 10^{-157}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;y + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= (- (+ (+ x y) z) (* z (log t))) -2e-157) (+ x t_1) (+ y t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((((x + y) + z) - (z * log(t))) <= -2e-157) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	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 ((((x + y) + z) - (z * log(t))) <= (-2d-157)) then
        tmp = x + t_1
    else
        tmp = y + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if ((((x + y) + z) - (z * Math.log(t))) <= -2e-157) {
		tmp = x + t_1;
	} else {
		tmp = y + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if (((x + y) + z) - (z * math.log(t))) <= -2e-157:
		tmp = x + t_1
	else:
		tmp = y + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) + z) - Float64(z * log(t))) <= -2e-157)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(y + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if ((((x + y) + z) - (z * log(t))) <= -2e-157)
		tmp = x + t_1;
	else
		tmp = y + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] + z), $MachinePrecision] - N[(z * N[Log[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e-157], N[(x + t$95$1), $MachinePrecision], N[(y + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) < -1.99999999999999989e-157

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 57.3%

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

   if -1.99999999999999989e-157 < (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t)))

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 59.4%

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

Alternative 6: 21.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b \leq -2 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)) -2e-157) 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)) <= -2e-157) {
		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)) <= (-2d-157)) 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)) <= -2e-157) {
		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)) <= -2e-157:
		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)) <= -2e-157)
		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)) <= -2e-157)
		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], -2e-157], 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)) < -1.99999999999999989e-157

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 20.1%

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

   if -1.99999999999999989e-157 < (+.f64 (-.f64 (+.f64 (+.f64 x y) z) (*.f64 z (log.f64 t))) (*.f64 (-.f64 a #s(literal 1/2 binary64)) b))

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 21.9%

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

Alternative 7: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8 \cdot 10^{+70}:\\ \;\;\;\;\mathsf{fma}\left(1 - \log t, z, x\right) + \left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a - 0.5, b, y\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 6.8e+70)
   (+ (fma (- 1.0 (log t)) z x) (* (- a 0.5) b))
   (+ (fma (- a 0.5) b y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 6.8e+70) {
		tmp = fma((1.0 - log(t)), z, x) + ((a - 0.5) * b);
	} else {
		tmp = fma((a - 0.5), b, y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 6.8e+70)
		tmp = Float64(fma(Float64(1.0 - log(t)), z, x) + Float64(Float64(a - 0.5) * b));
	else
		tmp = Float64(fma(Float64(a - 0.5), b, y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 6.8e+70], N[(N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision] + N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - 0.5), $MachinePrecision] * b + y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.8000000000000002e70

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 84.9

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

   7. Applied rewrites 84.9%

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

   if 6.8000000000000002e70 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 87.3

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

   4. Applied rewrites 87.3%

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

Alternative 8: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t \cdot z\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;y + \left(z - t\_1\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+78}:\\ \;\;\;\;\left(\left(y + x\right) + z\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log t) z)))
   (if (<= z -6.2e+109)
     (+ y (- z t_1))
     (if (<= z 8.5e+78) (- (+ (+ y x) z) (* (- 0.5 a) b)) (- (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(t) * z;
	double tmp;
	if (z <= -6.2e+109) {
		tmp = y + (z - t_1);
	} else if (z <= 8.5e+78) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = (x + z) - t_1;
	}
	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 = log(t) * z
    if (z <= (-6.2d+109)) then
        tmp = y + (z - t_1)
    else if (z <= 8.5d+78) then
        tmp = ((y + x) + z) - ((0.5d0 - a) * b)
    else
        tmp = (x + z) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(t) * z;
	double tmp;
	if (z <= -6.2e+109) {
		tmp = y + (z - t_1);
	} else if (z <= 8.5e+78) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = (x + z) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(t) * z
	tmp = 0
	if z <= -6.2e+109:
		tmp = y + (z - t_1)
	elif z <= 8.5e+78:
		tmp = ((y + x) + z) - ((0.5 - a) * b)
	else:
		tmp = (x + z) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(t) * z)
	tmp = 0.0
	if (z <= -6.2e+109)
		tmp = Float64(y + Float64(z - t_1));
	elseif (z <= 8.5e+78)
		tmp = Float64(Float64(Float64(y + x) + z) - Float64(Float64(0.5 - a) * b));
	else
		tmp = Float64(Float64(x + z) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(t) * z;
	tmp = 0.0;
	if (z <= -6.2e+109)
		tmp = y + (z - t_1);
	elseif (z <= 8.5e+78)
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	else
		tmp = (x + z) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -6.2e+109], N[(y + N[(z - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+78], N[(N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(x + z), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.19999999999999985e109

   1. Initial program 99.6%

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

   2. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. lower--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-log.f64 74.0

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

   4. Applied rewrites 74.0%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lower--.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-log.f64 N/A

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

      15. lift-*.f64 74.0

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

   6. Applied rewrites 74.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 63.4%

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

   if -6.19999999999999985e109 < z < 8.50000000000000079e78

   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. 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. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. *-commutative N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift--.f64 100.0

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 94.9

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

   6. Applied rewrites 94.9%

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

   if 8.50000000000000079e78 < 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. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. lower--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-log.f64 70.9

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

   4. Applied rewrites 70.9%

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

   5. Taylor expanded in x around inf

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

      1. +-commutative 58.9

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

   7. Applied rewrites 58.9%

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

Alternative 9: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - \log t \cdot z\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;\left(\left(y + x\right) + z\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (- z (* (log t) z)))))
   (if (<= z -6.2e+109)
     t_1
     (if (<= z 1.55e+122) (- (+ (+ y x) z) (* (- 0.5 a) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z - (log(t) * z));
	double tmp;
	if (z <= -6.2e+109) {
		tmp = t_1;
	} else if (z <= 1.55e+122) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	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 = y + (z - (log(t) * z))
    if (z <= (-6.2d+109)) then
        tmp = t_1
    else if (z <= 1.55d+122) then
        tmp = ((y + x) + z) - ((0.5d0 - a) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z - (Math.log(t) * z));
	double tmp;
	if (z <= -6.2e+109) {
		tmp = t_1;
	} else if (z <= 1.55e+122) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z - (math.log(t) * z))
	tmp = 0
	if z <= -6.2e+109:
		tmp = t_1
	elif z <= 1.55e+122:
		tmp = ((y + x) + z) - ((0.5 - a) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z - Float64(log(t) * z)))
	tmp = 0.0
	if (z <= -6.2e+109)
		tmp = t_1;
	elseif (z <= 1.55e+122)
		tmp = Float64(Float64(Float64(y + x) + z) - Float64(Float64(0.5 - a) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z - (log(t) * z));
	tmp = 0.0;
	if (z <= -6.2e+109)
		tmp = t_1;
	elseif (z <= 1.55e+122)
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z - N[(N[Log[t], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+109], t$95$1, If[LessEqual[z, 1.55e+122], N[(N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999985e109 or 1.54999999999999999e122 < 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. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. lower--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lift-log.f64 73.4

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

   4. Applied rewrites 73.4%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-+.f64 N/A

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

      12. lower--.f64 N/A

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

      13. *-commutative N/A

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

      14. lift-log.f64 N/A

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

      15. lift-*.f64 73.4

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

   6. Applied rewrites 73.4%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 63.1%

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

   if -6.19999999999999985e109 < z < 1.54999999999999999e122

   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. 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. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. *-commutative N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift--.f64 100.0

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 94.0

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

   6. Applied rewrites 94.0%

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

Alternative 10: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - \log t\right) \cdot z\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+255}:\\ \;\;\;\;\left(\left(y + x\right) + z\right) - \left(0.5 - a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 (log t)) z)))
   (if (<= z -8.5e+176)
     t_1
     (if (<= z 2.6e+255) (- (+ (+ y x) z) (* (- 0.5 a) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - log(t)) * z;
	double tmp;
	if (z <= -8.5e+176) {
		tmp = t_1;
	} else if (z <= 2.6e+255) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	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 = (1.0d0 - log(t)) * z
    if (z <= (-8.5d+176)) then
        tmp = t_1
    else if (z <= 2.6d+255) then
        tmp = ((y + x) + z) - ((0.5d0 - a) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - Math.log(t)) * z;
	double tmp;
	if (z <= -8.5e+176) {
		tmp = t_1;
	} else if (z <= 2.6e+255) {
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - math.log(t)) * z
	tmp = 0
	if z <= -8.5e+176:
		tmp = t_1
	elif z <= 2.6e+255:
		tmp = ((y + x) + z) - ((0.5 - a) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - log(t)) * z)
	tmp = 0.0
	if (z <= -8.5e+176)
		tmp = t_1;
	elseif (z <= 2.6e+255)
		tmp = Float64(Float64(Float64(y + x) + z) - Float64(Float64(0.5 - a) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - log(t)) * z;
	tmp = 0.0;
	if (z <= -8.5e+176)
		tmp = t_1;
	elseif (z <= 2.6e+255)
		tmp = ((y + x) + z) - ((0.5 - a) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - N[Log[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8.5e+176], t$95$1, If[LessEqual[z, 2.6e+255], N[(N[(N[(y + x), $MachinePrecision] + z), $MachinePrecision] - N[(N[(0.5 - a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999995e176 or 2.6000000000000001e255 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 66.0

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

   4. Applied rewrites 66.0%

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

   if -8.4999999999999995e176 < z < 2.6000000000000001e255

   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. 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. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-+l- N/A

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

      10. lower--.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 N/A

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

      14. *-commutative N/A

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

      15. lower--.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-log.f64 N/A

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

      19. *-commutative N/A

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

      20. lift-*.f64 N/A

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

      21. lift--.f64 99.9

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.6

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

   6. Applied rewrites 87.6%

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

Alternative 11: 65.5% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -5e+159) t_1 (if (<= t_1 1e+157) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -5e+159) {
		tmp = t_1;
	} else if (t_1 <= 1e+157) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	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 <= (-5d+159)) then
        tmp = t_1
    else if (t_1 <= 1d+157) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -5e+159) {
		tmp = t_1;
	} else if (t_1 <= 1e+157) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -5e+159:
		tmp = t_1
	elif t_1 <= 1e+157:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -5e+159)
		tmp = t_1;
	elseif (t_1 <= 1e+157)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -5e+159)
		tmp = t_1;
	elseif (t_1 <= 1e+157)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+159], t$95$1, If[LessEqual[t$95$1, 1e+157], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.00000000000000003e159 or 9.99999999999999983e156 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 78.9

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

   4. Applied rewrites 78.9%

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

   if -5.00000000000000003e159 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.99999999999999983e156

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 70.7

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

   4. Applied rewrites 70.7%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 57.4%

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

Alternative 12: 57.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a - 0.5\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+187}:\\ \;\;\;\;b \cdot a\\ \mathbf{elif}\;t\_1 \leq 10^{+157}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a 0.5) b)))
   (if (<= t_1 -5e+187) (* b a) (if (<= t_1 1e+157) (+ y x) (* b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -5e+187) {
		tmp = b * a;
	} else if (t_1 <= 1e+157) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - 0.5d0) * b
    if (t_1 <= (-5d+187)) then
        tmp = b * a
    else if (t_1 <= 1d+157) then
        tmp = y + x
    else
        tmp = b * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - 0.5) * b;
	double tmp;
	if (t_1 <= -5e+187) {
		tmp = b * a;
	} else if (t_1 <= 1e+157) {
		tmp = y + x;
	} else {
		tmp = b * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - 0.5) * b
	tmp = 0
	if t_1 <= -5e+187:
		tmp = b * a
	elif t_1 <= 1e+157:
		tmp = y + x
	else:
		tmp = b * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - 0.5) * b)
	tmp = 0.0
	if (t_1 <= -5e+187)
		tmp = Float64(b * a);
	elseif (t_1 <= 1e+157)
		tmp = Float64(y + x);
	else
		tmp = Float64(b * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - 0.5) * b;
	tmp = 0.0;
	if (t_1 <= -5e+187)
		tmp = b * a;
	elseif (t_1 <= 1e+157)
		tmp = y + x;
	else
		tmp = b * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+187], N[(b * a), $MachinePrecision], If[LessEqual[t$95$1, 1e+157], N[(y + x), $MachinePrecision], N[(b * a), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < -5.0000000000000001e187 or 9.99999999999999983e156 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b)

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 60.1

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

   4. Applied rewrites 60.1%

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

   if -5.0000000000000001e187 < (*.f64 (-.f64 a #s(literal 1/2 binary64)) b) < 9.99999999999999983e156

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 71.1

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 56.3%

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

Alternative 13: 46.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-42}:\\ \;\;\;\;x + a \cdot b\\ \mathbf{elif}\;x + y \leq 10^{+44}:\\ \;\;\;\;\left(a - 0.5\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y + -0.5 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ x y) -5e-42)
   (+ x (* a b))
   (if (<= (+ x y) 1e+44) (* (- a 0.5) b) (+ y (* -0.5 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e-42) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e+44) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = y + (-0.5 * b);
	}
	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) <= (-5d-42)) then
        tmp = x + (a * b)
    else if ((x + y) <= 1d+44) then
        tmp = (a - 0.5d0) * b
    else
        tmp = y + ((-0.5d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + y) <= -5e-42) {
		tmp = x + (a * b);
	} else if ((x + y) <= 1e+44) {
		tmp = (a - 0.5) * b;
	} else {
		tmp = y + (-0.5 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + y) <= -5e-42:
		tmp = x + (a * b)
	elif (x + y) <= 1e+44:
		tmp = (a - 0.5) * b
	else:
		tmp = y + (-0.5 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + y) <= -5e-42)
		tmp = Float64(x + Float64(a * b));
	elseif (Float64(x + y) <= 1e+44)
		tmp = Float64(Float64(a - 0.5) * b);
	else
		tmp = Float64(y + Float64(-0.5 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + y) <= -5e-42)
		tmp = x + (a * b);
	elseif ((x + y) <= 1e+44)
		tmp = (a - 0.5) * b;
	else
		tmp = y + (-0.5 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-42], N[(x + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 1e+44], N[(N[(a - 0.5), $MachinePrecision] * b), $MachinePrecision], N[(y + N[(-0.5 * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -5.00000000000000003e-42

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 57.0%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 46.8%

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

   if -5.00000000000000003e-42 < (+.f64 x y) < 1.0000000000000001e44

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 56.2

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

   4. Applied rewrites 56.2%

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

   if 1.0000000000000001e44 < (+.f64 x y)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lift-log.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 58.3%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 37.3%

       \[\leadsto y + \color{blue}{-0.5} \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 79.7% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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) + z) - ((0.5d0 - a) * b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(y + x), $MachinePrecision] + z), $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. 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. lift-+.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. associate-+l- N/A

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

   10. lower--.f64 N/A

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

   11. lift-+.f64 N/A

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

   12. +-commutative N/A

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

   13. lower-+.f64 N/A

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

   14. *-commutative N/A

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

   15. lower--.f64 N/A

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

   16. *-commutative N/A

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

   17. lower-*.f64 N/A

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

   18. lift-log.f64 N/A

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

   19. *-commutative N/A

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

   20. lift-*.f64 N/A

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

   21. lift--.f64 99.9

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

3. Applied rewrites 99.9%

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

4. Taylor expanded in b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 79.7

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

6. Applied rewrites 79.7%

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

Alternative 15: 78.8% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lift--.f64 78.8

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

4. Applied rewrites 78.8%

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

Alternative 16: 41.1% accurate, 31.5× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lift--.f64 78.8

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

4. Applied rewrites 78.8%

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

5. Taylor expanded in y around inf

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

7. Applied rewrites 41.1%

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

Alternative 17: 20.7% accurate, 126.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 20.7%

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

Developer Target 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025093 
(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)))