AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 59.6% → 98.7%

Time: 14.9s

Alternatives: 18

Speedup: 1.5×

Specification

Math

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

FPCore

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

C

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

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) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) + x\\ \mathsf{fma}\left(-b, \frac{y}{t\_1}, \frac{y + x}{t\_1} \cdot z\right) - \frac{\left(-t\right) - y}{t\_1} \cdot a \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t y) x)))
   (- (fma (- b) (/ y t_1) (* (/ (+ y x) t_1) z)) (* (/ (- (- t) y) t_1) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) + x;
	return fma(-b, (y / t_1), (((y + x) / t_1) * z)) - (((-t - y) / t_1) * a);
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) + x)
	return Float64(fma(Float64(-b), Float64(y / t_1), Float64(Float64(Float64(y + x) / t_1) * z)) - Float64(Float64(Float64(Float64(-t) - y) / t_1) * a))
end

Wolfram

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

Derivation

1. Initial program 59.6%

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

3. Applied rewrites 98.7%

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

Alternative 2: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(t + y\right) + x\\ t_4 := \mathsf{fma}\left(-b, \frac{y}{t\_3}, z\right) - \frac{\left(-t\right) - y}{t\_3} \cdot a\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+89}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (+ (+ t y) x))
        (t_4 (- (fma (- b) (/ y t_3) z) (* (/ (- (- t) y) t_3) a))))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 5e+89) (/ (fma (- (+ a z) b) y (fma a t (* z x))) t_1) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = (t + y) + x;
	double t_4 = fma(-b, (y / t_3), z) - (((-t - y) / t_3) * a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= 5e+89) {
		tmp = fma(((a + z) - b), y, fma(a, t, (z * x))) / t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(t + y) + x)
	t_4 = Float64(fma(Float64(-b), Float64(y / t_3), z) - Float64(Float64(Float64(Float64(-t) - y) / t_3) * a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= 5e+89)
		tmp = Float64(fma(Float64(Float64(a + z) - b), y, fma(a, t, Float64(z * x))) / t_1);
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$4 = N[(N[((-b) * N[(y / t$95$3), $MachinePrecision] + z), $MachinePrecision] - N[(N[(N[((-t) - y), $MachinePrecision] / t$95$3), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$4, If[LessEqual[t$95$2, 5e+89], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y + N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 4.99999999999999983e89 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 23.3%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 90.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.99999999999999983e89

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.4

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

   4. Applied rewrites 99.4%

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

Alternative 3: 92.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \mathsf{fma}\left(-b, \frac{y}{\left(t + y\right) + x}, z\right) - \left(-a\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+246}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(a + z\right) - b, y, \mathsf{fma}\left(a, t, z \cdot x\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (fma (- b) (/ y (+ (+ t y) x)) z) (- a))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+246)
       (/ (fma (- (+ a z) b) y (fma a t (* z x))) t_1)
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = fma(-b, (y / ((t + y) + x)), z) - -a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+246) {
		tmp = fma(((a + z) - b), y, fma(a, t, (z * x))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(fma(Float64(-b), Float64(y / Float64(Float64(t + y) + x)), z) - Float64(-a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+246)
		tmp = Float64(fma(Float64(Float64(a + z) - b), y, fma(a, t, Float64(z * x))) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[((-b) * N[(y / N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - (-a)), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+246], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y + N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 2.00000000000000014e246 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.6%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 91.8%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.5

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

   9. Applied rewrites 83.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000014e246

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 99.4

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

   4. Applied rewrites 99.4%

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

Alternative 4: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \mathsf{fma}\left(-b, \frac{y}{\left(t + y\right) + x}, z\right) - \left(-a\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+125}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+132}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t + y, a, y \cdot \left(z - b\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- (fma (- b) (/ y (+ (+ t y) x)) z) (- a))))
   (if (<= t_2 -2e+125)
     t_3
     (if (<= t_2 5e+132) (/ (fma (+ t y) a (* y (- z b))) t_1) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = fma(-b, (y / ((t + y) + x)), z) - -a;
	double tmp;
	if (t_2 <= -2e+125) {
		tmp = t_3;
	} else if (t_2 <= 5e+132) {
		tmp = fma((t + y), a, (y * (z - b))) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(fma(Float64(-b), Float64(y / Float64(Float64(t + y) + x)), z) - Float64(-a))
	tmp = 0.0
	if (t_2 <= -2e+125)
		tmp = t_3;
	elseif (t_2 <= 5e+132)
		tmp = Float64(fma(Float64(t + y), a, Float64(y * Float64(z - b))) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[((-b) * N[(y / N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] - (-a)), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+125], t$95$3, If[LessEqual[t$95$2, 5e+132], N[(N[(N[(t + y), $MachinePrecision] * a + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.9999999999999998e125 or 5.0000000000000001e132 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.1%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 91.0%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.8

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

   9. Applied rewrites 81.8%

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

   if -1.9999999999999998e125 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e132

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 72.7

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

   4. Applied rewrites 72.7%

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

Alternative 5: 76.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) + x\\ t_2 := z - \frac{\left(-t\right) - y}{t\_1} \cdot a\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(-b, \frac{y}{t\_1}, z\right) - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t y) x)) (t_2 (- z (* (/ (- (- t) y) t_1) a))))
   (if (<= a -8.5e+100)
     t_2
     (if (<= a 1.5e-23) (- (fma (- b) (/ y t_1) z) (- a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) + x;
	double t_2 = z - (((-t - y) / t_1) * a);
	double tmp;
	if (a <= -8.5e+100) {
		tmp = t_2;
	} else if (a <= 1.5e-23) {
		tmp = fma(-b, (y / t_1), z) - -a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) + x)
	t_2 = Float64(z - Float64(Float64(Float64(Float64(-t) - y) / t_1) * a))
	tmp = 0.0
	if (a <= -8.5e+100)
		tmp = t_2;
	elseif (a <= 1.5e-23)
		tmp = Float64(fma(Float64(-b), Float64(y / t_1), z) - Float64(-a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(z - N[(N[(N[((-t) - y), $MachinePrecision] / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+100], t$95$2, If[LessEqual[a, 1.5e-23], N[(N[((-b) * N[(y / t$95$1), $MachinePrecision] + z), $MachinePrecision] - (-a)), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000043e100 or 1.50000000000000001e-23 < a

   1. Initial program 46.5%

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 79.8%

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

   if -8.50000000000000043e100 < a < 1.50000000000000001e-23

   1. Initial program 70.0%

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

   3. Applied rewrites 98.3%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 79.6%

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

   7. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 73.2

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

   9. Applied rewrites 73.2%

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

Alternative 6: 66.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) + x\\ \mathbf{if}\;b \leq -6.1 \cdot 10^{+190}:\\ \;\;\;\;\left(-b\right) \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+231}:\\ \;\;\;\;z - \frac{\left(-t\right) - y}{t\_1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t y) x)))
   (if (<= b -6.1e+190)
     (* (- b) (/ y t_1))
     (if (<= b 1.3e+231)
       (- z (* (/ (- (- t) y) t_1) a))
       (/ (- (* z x) (* y b)) (+ (+ x t) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) + x;
	double tmp;
	if (b <= -6.1e+190) {
		tmp = -b * (y / t_1);
	} else if (b <= 1.3e+231) {
		tmp = z - (((-t - y) / t_1) * a);
	} else {
		tmp = ((z * x) - (y * b)) / ((x + t) + 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) :: t_1
    real(8) :: tmp
    t_1 = (t + y) + x
    if (b <= (-6.1d+190)) then
        tmp = -b * (y / t_1)
    else if (b <= 1.3d+231) then
        tmp = z - (((-t - y) / t_1) * a)
    else
        tmp = ((z * x) - (y * b)) / ((x + t) + 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 t_1 = (t + y) + x;
	double tmp;
	if (b <= -6.1e+190) {
		tmp = -b * (y / t_1);
	} else if (b <= 1.3e+231) {
		tmp = z - (((-t - y) / t_1) * a);
	} else {
		tmp = ((z * x) - (y * b)) / ((x + t) + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + y) + x
	tmp = 0
	if b <= -6.1e+190:
		tmp = -b * (y / t_1)
	elif b <= 1.3e+231:
		tmp = z - (((-t - y) / t_1) * a)
	else:
		tmp = ((z * x) - (y * b)) / ((x + t) + y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) + x)
	tmp = 0.0
	if (b <= -6.1e+190)
		tmp = Float64(Float64(-b) * Float64(y / t_1));
	elseif (b <= 1.3e+231)
		tmp = Float64(z - Float64(Float64(Float64(Float64(-t) - y) / t_1) * a));
	else
		tmp = Float64(Float64(Float64(z * x) - Float64(y * b)) / Float64(Float64(x + t) + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + y) + x;
	tmp = 0.0;
	if (b <= -6.1e+190)
		tmp = -b * (y / t_1);
	elseif (b <= 1.3e+231)
		tmp = z - (((-t - y) / t_1) * a);
	else
		tmp = ((z * x) - (y * b)) / ((x + t) + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -6.1e+190], N[((-b) * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e+231], N[(z - N[(N[(N[((-t) - y), $MachinePrecision] / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.1000000000000004e190

   1. Initial program 43.8%

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

   2. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{b \cdot y}{t + \left(x + y\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{neg}\left(b \cdot \frac{y}{t + \left(x + y\right)}\right) \]

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

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. lower-+.f64 N/A

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

      10. lift-+.f64 57.1

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

   4. Applied rewrites 57.1%

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

   if -6.1000000000000004e190 < b < 1.2999999999999999e231

   1. Initial program 62.5%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.7%

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

   if 1.2999999999999999e231 < b

   1. Initial program 45.1%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 35.5

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

   4. Applied rewrites 35.5%

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

Alternative 7: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := z - \left(b - a\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-24}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+97}:\\ \;\;\;\;\frac{a \cdot t - y \cdot b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- z (- b a))))
   (if (<= t_2 -5e+144)
     t_3
     (if (<= t_2 -1e-24)
       (/ (* (- (+ a z) b) y) t_1)
       (if (<= t_2 2e+97) (/ (- (* a t) (* y b)) t_1) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = z - (b - a);
	double tmp;
	if (t_2 <= -5e+144) {
		tmp = t_3;
	} else if (t_2 <= -1e-24) {
		tmp = (((a + z) - b) * y) / t_1;
	} else if (t_2 <= 2e+97) {
		tmp = ((a * t) - (y * b)) / t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1
    t_3 = z - (b - a)
    if (t_2 <= (-5d+144)) then
        tmp = t_3
    else if (t_2 <= (-1d-24)) then
        tmp = (((a + z) - b) * y) / t_1
    else if (t_2 <= 2d+97) then
        tmp = ((a * t) - (y * b)) / t_1
    else
        tmp = t_3
    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 + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = z - (b - a);
	double tmp;
	if (t_2 <= -5e+144) {
		tmp = t_3;
	} else if (t_2 <= -1e-24) {
		tmp = (((a + z) - b) * y) / t_1;
	} else if (t_2 <= 2e+97) {
		tmp = ((a * t) - (y * b)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1
	t_3 = z - (b - a)
	tmp = 0
	if t_2 <= -5e+144:
		tmp = t_3
	elif t_2 <= -1e-24:
		tmp = (((a + z) - b) * y) / t_1
	elif t_2 <= 2e+97:
		tmp = ((a * t) - (y * b)) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (t_2 <= -5e+144)
		tmp = t_3;
	elseif (t_2 <= -1e-24)
		tmp = Float64(Float64(Float64(Float64(a + z) - b) * y) / t_1);
	elseif (t_2 <= 2e+97)
		tmp = Float64(Float64(Float64(a * t) - Float64(y * b)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	t_3 = z - (b - a);
	tmp = 0.0;
	if (t_2 <= -5e+144)
		tmp = t_3;
	elseif (t_2 <= -1e-24)
		tmp = (((a + z) - b) * y) / t_1;
	elseif (t_2 <= 2e+97)
		tmp = ((a * t) - (y * b)) / t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+144], t$95$3, If[LessEqual[t$95$2, -1e-24], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+97], N[(N[(N[(a * t), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999999e144 or 2.0000000000000001e97 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 30.3%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 70.0

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

   6. Applied rewrites 70.0%

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

   if -4.9999999999999999e144 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999924e-25

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 51.1

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

   4. Applied rewrites 51.1%

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

   if -9.99999999999999924e-25 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e97

   1. Initial program 99.2%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 52.4

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

   4. Applied rewrites 52.4%

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

Alternative 8: 66.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := z - \left(b - a\right)\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) t_1))
        (t_3 (- z (- b a))))
   (if (<= t_2 -5e+144)
     t_3
     (if (<= t_2 -2e-6)
       (/ (* (- (+ a z) b) y) t_1)
       (if (<= t_2 2e+178) (/ (fma a t (* z x)) (+ t x)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / t_1;
	double t_3 = z - (b - a);
	double tmp;
	if (t_2 <= -5e+144) {
		tmp = t_3;
	} else if (t_2 <= -2e-6) {
		tmp = (((a + z) - b) * y) / t_1;
	} else if (t_2 <= 2e+178) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (t_2 <= -5e+144)
		tmp = t_3;
	elseif (t_2 <= -2e-6)
		tmp = Float64(Float64(Float64(Float64(a + z) - b) * y) / t_1);
	elseif (t_2 <= 2e+178)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+144], t$95$3, If[LessEqual[t$95$2, -2e-6], N[(N[(N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision] * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+178], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999999e144 or 2.0000000000000001e178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 23.6%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 71.8

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

   6. Applied rewrites 71.8%

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

   if -4.9999999999999999e144 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1.99999999999999991e-6

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 51.0

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

   4. Applied rewrites 51.0%

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

   if -1.99999999999999991e-6 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e178

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 62.3

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

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 62.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \frac{\left(-t\right) - y}{y + x} \cdot a\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;z - \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* (/ (- (- t) y) (+ y x)) a))))
   (if (<= x -1.4e+45)
     t_1
     (if (<= x -2.4e-36)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= x 3.5e-41) (- z (- b a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (((-t - y) / (y + x)) * a);
	double tmp;
	if (x <= -1.4e+45) {
		tmp = t_1;
	} else if (x <= -2.4e-36) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (x <= 3.5e-41) {
		tmp = z - (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(Float64(Float64(Float64(-t) - y) / Float64(y + x)) * a))
	tmp = 0.0
	if (x <= -1.4e+45)
		tmp = t_1;
	elseif (x <= -2.4e-36)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (x <= 3.5e-41)
		tmp = Float64(z - Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(N[(N[((-t) - y), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+45], t$95$1, If[LessEqual[x, -2.4e-36], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-41], N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4e45 or 3.5e-41 < x

   1. Initial program 53.4%

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

   3. Applied rewrites 98.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 71.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 61.6%

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

   if -1.4e45 < x < -2.4e-36

   1. Initial program 64.8%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 47.3

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

   4. Applied rewrites 47.3%

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

   if -2.4e-36 < x < 3.5e-41

   1. Initial program 65.8%

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

   3. Applied rewrites 98.6%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 65.2

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

   6. Applied rewrites 65.2%

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

Alternative 10: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+237}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+178}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (- z (- b a))))
   (if (<= t_1 -1e+237)
     t_2
     (if (<= t_1 2e+178) (/ (fma a t (* z x)) (+ t x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = z - (b - a);
	double tmp;
	if (t_1 <= -1e+237) {
		tmp = t_2;
	} else if (t_1 <= 2e+178) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (t_1 <= -1e+237)
		tmp = t_2;
	elseif (t_1 <= 2e+178)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+237], t$95$2, If[LessEqual[t$95$1, 2e+178], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e236 or 2.0000000000000001e178 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 16.9%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 73.1

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

   6. Applied rewrites 73.1%

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

   if -9.9999999999999994e236 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e178

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 61.1

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

   4. Applied rewrites 61.1%

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

Alternative 11: 60.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot \left(-b\right)}{x} + z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;z - \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(a - z\right) \cdot t}{x} + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.8e+158)
   (+ (/ (* y (- b)) x) z)
   (if (<= x 2.9e+38) (- z (- b a)) (+ (/ (* (- a z) t) x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+158) {
		tmp = ((y * -b) / x) + z;
	} else if (x <= 2.9e+38) {
		tmp = z - (b - a);
	} else {
		tmp = (((a - z) * t) / x) + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.8d+158)) then
        tmp = ((y * -b) / x) + z
    else if (x <= 2.9d+38) then
        tmp = z - (b - a)
    else
        tmp = (((a - z) * t) / x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+158) {
		tmp = ((y * -b) / x) + z;
	} else if (x <= 2.9e+38) {
		tmp = z - (b - a);
	} else {
		tmp = (((a - z) * t) / x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+158:
		tmp = ((y * -b) / x) + z
	elif x <= 2.9e+38:
		tmp = z - (b - a)
	else:
		tmp = (((a - z) * t) / x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+158)
		tmp = Float64(Float64(Float64(y * Float64(-b)) / x) + z);
	elseif (x <= 2.9e+38)
		tmp = Float64(z - Float64(b - a));
	else
		tmp = Float64(Float64(Float64(Float64(a - z) * t) / x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.8e+158)
		tmp = ((y * -b) / x) + z;
	elseif (x <= 2.9e+38)
		tmp = z - (b - a);
	else
		tmp = (((a - z) * t) / x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+158], N[(N[(N[(y * (-b)), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 2.9e+38], N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(a - z), $MachinePrecision] * t), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999994e158

   1. Initial program 43.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 54.3%

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

   5. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(b \cdot y\right)}{x} + z \]

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

         \[\leadsto \frac{\left(\mathsf{neg}\left(b\right)\right) \cdot y}{x} + z \]

      3. lift-neg.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 58.4

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

   7. Applied rewrites 58.4%

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

   if -1.79999999999999994e158 < x < 2.90000000000000007e38

   1. Initial program 64.8%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 62.0

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

   6. Applied rewrites 62.0%

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

   if 2.90000000000000007e38 < x

   1. Initial program 53.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 49.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \frac{a \cdot t - t \cdot z}{x} + z \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{a \cdot t - z \cdot t}{x} + z \]

      2. distribute-rgt-out-- N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 45.0

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

   7. Applied rewrites 45.0%

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

Alternative 12: 59.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot \left(-b\right)}{x} + z\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+60}:\\ \;\;\;\;z - \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t + x} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.8e+158)
   (+ (/ (* y (- b)) x) z)
   (if (<= x 4.9e+60) (- z (- b a)) (* (/ x (+ t x)) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+158) {
		tmp = ((y * -b) / x) + z;
	} else if (x <= 4.9e+60) {
		tmp = z - (b - a);
	} else {
		tmp = (x / (t + x)) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.8d+158)) then
        tmp = ((y * -b) / x) + z
    else if (x <= 4.9d+60) then
        tmp = z - (b - a)
    else
        tmp = (x / (t + x)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.8e+158) {
		tmp = ((y * -b) / x) + z;
	} else if (x <= 4.9e+60) {
		tmp = z - (b - a);
	} else {
		tmp = (x / (t + x)) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.8e+158:
		tmp = ((y * -b) / x) + z
	elif x <= 4.9e+60:
		tmp = z - (b - a)
	else:
		tmp = (x / (t + x)) * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.8e+158)
		tmp = Float64(Float64(Float64(y * Float64(-b)) / x) + z);
	elseif (x <= 4.9e+60)
		tmp = Float64(z - Float64(b - a));
	else
		tmp = Float64(Float64(x / Float64(t + x)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.8e+158)
		tmp = ((y * -b) / x) + z;
	elseif (x <= 4.9e+60)
		tmp = z - (b - a);
	else
		tmp = (x / (t + x)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.8e+158], N[(N[(N[(y * (-b)), $MachinePrecision] / x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 4.9e+60], N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999994e158

   1. Initial program 43.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 54.3%

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

   5. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(b \cdot y\right)}{x} + z \]

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

         \[\leadsto \frac{\left(\mathsf{neg}\left(b\right)\right) \cdot y}{x} + z \]

      3. lift-neg.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 58.4

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

   7. Applied rewrites 58.4%

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

   if -1.79999999999999994e158 < x < 4.9000000000000003e60

   1. Initial program 64.7%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

   if 4.9000000000000003e60 < x

   1. Initial program 52.4%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 39.0

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

   4. Applied rewrites 39.0%

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

   5. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

         \[\leadsto \frac{x}{t + x} \cdot z \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{x}{t + x} \cdot z \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{x}{t + x} \cdot z \]

      4. lift-+.f64 50.6

         \[\leadsto \frac{x}{t + x} \cdot z \]

   7. Applied rewrites 50.6%

      \[\leadsto \frac{x}{t + x} \cdot \color{blue}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 57.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (- b a))))
   (if (<= y -5.8e-120) t_1 (if (<= y 8.2e+23) (* (/ t (+ t x)) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b - a);
	double tmp;
	if (y <= -5.8e-120) {
		tmp = t_1;
	} else if (y <= 8.2e+23) {
		tmp = (t / (t + x)) * a;
	} 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 = z - (b - a)
    if (y <= (-5.8d-120)) then
        tmp = t_1
    else if (y <= 8.2d+23) then
        tmp = (t / (t + x)) * a
    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 = z - (b - a);
	double tmp;
	if (y <= -5.8e-120) {
		tmp = t_1;
	} else if (y <= 8.2e+23) {
		tmp = (t / (t + x)) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (b - a)
	tmp = 0
	if y <= -5.8e-120:
		tmp = t_1
	elif y <= 8.2e+23:
		tmp = (t / (t + x)) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (y <= -5.8e-120)
		tmp = t_1;
	elseif (y <= 8.2e+23)
		tmp = Float64(Float64(t / Float64(t + x)) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (b - a);
	tmp = 0.0;
	if (y <= -5.8e-120)
		tmp = t_1;
	elseif (y <= 8.2e+23)
		tmp = (t / (t + x)) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-120], t$95$1, If[LessEqual[y, 8.2e+23], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8e-120 or 8.19999999999999992e23 < y

   1. Initial program 46.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 68.8

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

   6. Applied rewrites 68.8%

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

   if -5.8e-120 < y < 8.19999999999999992e23

   1. Initial program 77.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{a \cdot t + x \cdot z}{\color{blue}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 58.1

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

   4. Applied rewrites 58.1%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

         \[\leadsto \frac{t \cdot a}{t + x} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{t}{t + x} \cdot a \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{t}{t + x} \cdot a \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{t}{t + x} \cdot a \]

      5. lift-+.f64 41.4

         \[\leadsto \frac{t}{t + x} \cdot a \]

   7. Applied rewrites 41.4%

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

Alternative 14: 57.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -1700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (- b a))))
   (if (<= y -1700.0) t_1 (if (<= y 2.6e+44) (+ a z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (b - a);
	double tmp;
	if (y <= -1700.0) {
		tmp = t_1;
	} else if (y <= 2.6e+44) {
		tmp = a + z;
	} 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 = z - (b - a)
    if (y <= (-1700.0d0)) then
        tmp = t_1
    else if (y <= 2.6d+44) then
        tmp = a + z
    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 = z - (b - a);
	double tmp;
	if (y <= -1700.0) {
		tmp = t_1;
	} else if (y <= 2.6e+44) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (b - a)
	tmp = 0
	if y <= -1700.0:
		tmp = t_1
	elif y <= 2.6e+44:
		tmp = a + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(b - a))
	tmp = 0.0
	if (y <= -1700.0)
		tmp = t_1;
	elseif (y <= 2.6e+44)
		tmp = Float64(a + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (b - a);
	tmp = 0.0;
	if (y <= -1700.0)
		tmp = t_1;
	elseif (y <= 2.6e+44)
		tmp = a + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1700.0], t$95$1, If[LessEqual[y, 2.6e+44], N[(a + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1700 or 2.5999999999999999e44 < y

   1. Initial program 40.0%

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 74.2

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

   6. Applied rewrites 74.2%

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

   if -1700 < y < 2.5999999999999999e44

   1. Initial program 77.2%

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

   3. Applied rewrites 97.6%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 40.1

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

   6. Applied rewrites 40.1%

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

   7. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   8. Step-by-step derivation

      1. lower-+.f64 48.5

         \[\leadsto a + z \]

   9. Applied rewrites 48.5%

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

Alternative 15: 52.9% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{+191}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.3e+191) (- a b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.3e+191) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.3d+191)) then
        tmp = a - b
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.3e+191) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.3e+191:
		tmp = a - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.3e+191)
		tmp = Float64(a - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.3e+191)
		tmp = a - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.3e+191], N[(a - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.30000000000000031e191

   1. Initial program 43.8%

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

   3. Applied rewrites 96.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 44.1

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

   6. Applied rewrites 44.1%

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

   7. Taylor expanded in z around 0

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

      1. lower--.f64 38.4

         \[\leadsto a - b \]

   9. Applied rewrites 38.4%

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

   if -5.30000000000000031e191 < b

   1. Initial program 61.3%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 57.5

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

   6. Applied rewrites 57.5%

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

   7. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   8. Step-by-step derivation

      1. lower-+.f64 54.5

         \[\leadsto a + z \]

   9. Applied rewrites 54.5%

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

Alternative 16: 47.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3650000:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3650000.0) z (if (<= x 2.9e-27) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3650000.0) {
		tmp = z;
	} else if (x <= 2.9e-27) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3650000.0d0)) then
        tmp = z
    else if (x <= 2.9d-27) then
        tmp = a - b
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3650000.0) {
		tmp = z;
	} else if (x <= 2.9e-27) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3650000.0:
		tmp = z
	elif x <= 2.9e-27:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3650000.0)
		tmp = z;
	elseif (x <= 2.9e-27)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3650000.0)
		tmp = z;
	elseif (x <= 2.9e-27)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3650000.0], z, If[LessEqual[x, 2.9e-27], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.65e6 or 2.90000000000000004e-27 < x

   1. Initial program 53.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 43.1%

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

   if -3.65e6 < x < 2.90000000000000004e-27

   1. Initial program 66.0%

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

   3. Applied rewrites 98.7%

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

   4. Taylor expanded in y around inf

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

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

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

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

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

      3. metadata-eval N/A

         \[\leadsto \left(z - 1 \cdot b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      4. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot a \]

      5. metadata-eval N/A

         \[\leadsto \left(z - b\right) + 1 \cdot a \]

      6. *-lft-identity N/A

         \[\leadsto \left(z - b\right) + a \]

      7. associate-+l- N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 64.6

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

   6. Applied rewrites 64.6%

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

   7. Taylor expanded in z around 0

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

      1. lower--.f64 52.2

         \[\leadsto a - b \]

   9. Applied rewrites 52.2%

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

Alternative 17: 44.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.8e+20) z (if (<= x 2.9e-27) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.8e+20) {
		tmp = z;
	} else if (x <= 2.9e-27) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.8d+20)) then
        tmp = z
    else if (x <= 2.9d-27) then
        tmp = a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.8e+20) {
		tmp = z;
	} else if (x <= 2.9e-27) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.8e+20:
		tmp = z
	elif x <= 2.9e-27:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.8e+20)
		tmp = z;
	elseif (x <= 2.9e-27)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.8e+20)
		tmp = z;
	elseif (x <= 2.9e-27)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.8e+20], z, If[LessEqual[x, 2.9e-27], a, z]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8e20 or 2.90000000000000004e-27 < x

   1. Initial program 53.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 43.4%

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

   if -3.8e20 < x < 2.90000000000000004e-27

   1. Initial program 66.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 44.9%

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

Alternative 18: 32.8% accurate, 29.5× speedup

Math

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

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.6%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 32.8%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64
  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))