Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.5% → 98.2%

Time: 3.7s

Alternatives: 16

Speedup: 0.5×

• 35.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) a)) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= (+ (- (- x (* (- y 1.0) z)) t_1) t_2) INFINITY)
     (+ (- (- x (fma z y (- z))) t_1) t_2)
     (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * a;
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if ((((x - ((y - 1.0) * z)) - t_1) + t_2) <= ((double) INFINITY)) {
		tmp = ((x - fma(z, y, -z)) - t_1) + t_2;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * a)
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - t_1) + t_2) <= Inf)
		tmp = Float64(Float64(Float64(x - fma(z, y, Float64(-z))) - t_1) + t_2);
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], Infinity], N[(N[(N[(x - N[(z * y + (-z)), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

Alternative 2: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 INFINITY) t_1 (* y (- b z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

Alternative 3: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \mathsf{fma}\left(z, y, -z\right)\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;\left(x + \left(z + b \cdot \left(t - 2\right)\right)\right) - a \cdot \left(t - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (- x (fma z y (- z))) (* (- t 1.0) a)) (* b y))))
   (if (<= y -6e+17)
     t_1
     (if (<= y 2.5e+59) (- (+ x (+ z (* b (- t 2.0)))) (* a (- t 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - fma(z, y, -z)) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (y <= -6e+17) {
		tmp = t_1;
	} else if (y <= 2.5e+59) {
		tmp = (x + (z + (b * (t - 2.0)))) - (a * (t - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - fma(z, y, Float64(-z))) - Float64(Float64(t - 1.0) * a)) + Float64(b * y))
	tmp = 0.0
	if (y <= -6e+17)
		tmp = t_1;
	elseif (y <= 2.5e+59)
		tmp = Float64(Float64(x + Float64(z + Float64(b * Float64(t - 2.0)))) - Float64(a * Float64(t - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(z * y + (-z)), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+17], t$95$1, If[LessEqual[y, 2.5e+59], N[(N[(x + N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6e17 or 2.4999999999999999e59 < y

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 78.5

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

   6. Applied rewrites 78.5%

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

   if -6e17 < y < 2.4999999999999999e59

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   4. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 69.6

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

   6. Applied rewrites 69.6%

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

Alternative 4: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - a \cdot \left(t - 1\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;a \leq -1.72 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-38}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- x (* a (- t 1.0))) (* (- (+ y t) 2.0) b))))
   (if (<= a -1.72e+27)
     t_1
     (if (<= a 1.1e-38) (- (+ x (* b (- (+ t y) 2.0))) (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b);
	double tmp;
	if (a <= -1.72e+27) {
		tmp = t_1;
	} else if (a <= 1.1e-38) {
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	} 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 = (x - (a * (t - 1.0d0))) + (((y + t) - 2.0d0) * b)
    if (a <= (-1.72d+27)) then
        tmp = t_1
    else if (a <= 1.1d-38) then
        tmp = (x + (b * ((t + y) - 2.0d0))) - (z * (y - 1.0d0))
    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 = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b);
	double tmp;
	if (a <= -1.72e+27) {
		tmp = t_1;
	} else if (a <= 1.1e-38) {
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b)
	tmp = 0
	if a <= -1.72e+27:
		tmp = t_1
	elif a <= 1.1e-38:
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (a <= -1.72e+27)
		tmp = t_1;
	elseif (a <= 1.1e-38)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (a <= -1.72e+27)
		tmp = t_1;
	elseif (a <= 1.1e-38)
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.72e+27], t$95$1, If[LessEqual[a, 1.1e-38], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7199999999999999e27 or 1.10000000000000004e-38 < a

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   if -1.7199999999999999e27 < a < 1.10000000000000004e-38

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.0

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

   4. Applied rewrites 73.0%

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

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (+ x z) (* (- t 1.0) a)) (* b y))))
   (if (<= a -1.85e-17)
     t_1
     (if (<= a 1.45e+91)
       (- (+ x (* b (- (+ t y) 2.0))) (* z (- y 1.0)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (a <= -1.85e-17) {
		tmp = t_1;
	} else if (a <= 1.45e+91) {
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	} 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 = ((x + z) - ((t - 1.0d0) * a)) + (b * y)
    if (a <= (-1.85d-17)) then
        tmp = t_1
    else if (a <= 1.45d+91) then
        tmp = (x + (b * ((t + y) - 2.0d0))) - (z * (y - 1.0d0))
    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 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (a <= -1.85e-17) {
		tmp = t_1;
	} else if (a <= 1.45e+91) {
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y)
	tmp = 0
	if a <= -1.85e-17:
		tmp = t_1
	elif a <= 1.45e+91:
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + z) - Float64(Float64(t - 1.0) * a)) + Float64(b * y))
	tmp = 0.0
	if (a <= -1.85e-17)
		tmp = t_1;
	elseif (a <= 1.45e+91)
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	tmp = 0.0;
	if (a <= -1.85e-17)
		tmp = t_1;
	elseif (a <= 1.45e+91)
		tmp = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + z), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.85e-17], t$95$1, If[LessEqual[a, 1.45e+91], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8499999999999999e-17 or 1.45000000000000007e91 < a

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 78.5

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

   6. Applied rewrites 78.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-+.f64 65.6

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

   9. Applied rewrites 65.6%

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

   if -1.8499999999999999e-17 < a < 1.45000000000000007e91

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      4. lower--.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right) \]

      6. lower-*.f64 N/A

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

      7. lower--.f64 73.0

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

   4. Applied rewrites 73.0%

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

Alternative 6: 78.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+40}:\\ \;\;\;\;\left(x - z \cdot \left(y - 1\right)\right) + b \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+59}:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + \left(t - 2\right) \cdot b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+40)
   (+ (- x (* z (- y 1.0))) (* b y))
   (if (<= y 3.5e+59)
     (+ (- x (* a (- t 1.0))) (* (- t 2.0) b))
     (if (<= y 2e+168) (+ (fma (- 1.0 t) a x) (* b y)) (* y (- b z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+40) {
		tmp = (x - (z * (y - 1.0))) + (b * y);
	} else if (y <= 3.5e+59) {
		tmp = (x - (a * (t - 1.0))) + ((t - 2.0) * b);
	} else if (y <= 2e+168) {
		tmp = fma((1.0 - t), a, x) + (b * y);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+40)
		tmp = Float64(Float64(x - Float64(z * Float64(y - 1.0))) + Float64(b * y));
	elseif (y <= 3.5e+59)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(Float64(t - 2.0) * b));
	elseif (y <= 2e+168)
		tmp = Float64(fma(Float64(1.0 - t), a, x) + Float64(b * y));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+40], N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+59], N[(N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+168], N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.90000000000000017e40

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 56.3

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

   7. Applied rewrites 56.3%

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

   8. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.7

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

   10. Applied rewrites 53.7%

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

   if -2.90000000000000017e40 < y < 3.5e59

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 60.0%

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

   if 3.5e59 < y < 1.9999999999999999e168

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 56.3

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

   7. Applied rewrites 56.3%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

          \[\leadsto \left(\left(1 - t\right) \cdot a + x\right) + b \cdot y \]

      11. lower-fma.f64 N/A

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

      12. lower--.f64 56.3

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

   9. Applied rewrites 56.3%

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

   if 1.9999999999999999e168 < y

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

Alternative 7: 73.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{+90}:\\ \;\;\;\;\left(x - z \cdot \left(y - 1\right)\right) + \left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (- (+ x z) (* (- t 1.0) a)) (* b y))))
   (if (<= a -1.7e-18)
     t_1
     (if (<= a 3.35e+90) (+ (- x (* z (- y 1.0))) (* (- t 2.0) b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (a <= -1.7e-18) {
		tmp = t_1;
	} else if (a <= 3.35e+90) {
		tmp = (x - (z * (y - 1.0))) + ((t - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + z) - ((t - 1.0d0) * a)) + (b * y)
    if (a <= (-1.7d-18)) then
        tmp = t_1
    else if (a <= 3.35d+90) then
        tmp = (x - (z * (y - 1.0d0))) + ((t - 2.0d0) * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	double tmp;
	if (a <= -1.7e-18) {
		tmp = t_1;
	} else if (a <= 3.35e+90) {
		tmp = (x - (z * (y - 1.0))) + ((t - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y)
	tmp = 0
	if a <= -1.7e-18:
		tmp = t_1
	elif a <= 3.35e+90:
		tmp = (x - (z * (y - 1.0))) + ((t - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + z) - Float64(Float64(t - 1.0) * a)) + Float64(b * y))
	tmp = 0.0
	if (a <= -1.7e-18)
		tmp = t_1;
	elseif (a <= 3.35e+90)
		tmp = Float64(Float64(x - Float64(z * Float64(y - 1.0))) + Float64(Float64(t - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + z) - ((t - 1.0) * a)) + (b * y);
	tmp = 0.0;
	if (a <= -1.7e-18)
		tmp = t_1;
	elseif (a <= 3.35e+90)
		tmp = (x - (z * (y - 1.0))) + ((t - 2.0) * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + z), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e-18], t$95$1, If[LessEqual[a, 3.35e+90], N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.70000000000000001e-18 or 3.3500000000000001e90 < a

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 78.5

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

   6. Applied rewrites 78.5%

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

   7. Taylor expanded in y around 0

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

      1. lower-+.f64 65.6

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

   9. Applied rewrites 65.6%

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

   if -1.70000000000000001e-18 < a < 3.3500000000000001e90

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.7

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

   4. Applied rewrites 49.7%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.0

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

   7. Applied rewrites 73.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 62.8%

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

Alternative 8: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right) + b \cdot y\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{+90}:\\ \;\;\;\;\left(x - z \cdot \left(y - 1\right)\right) + b \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- 1.0 t) a x) (* b y))))
   (if (<= a -1.7e-18)
     t_1
     (if (<= a 3.35e+90) (+ (- x (* z (- y 1.0))) (* b t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, x) + (b * y);
	double tmp;
	if (a <= -1.7e-18) {
		tmp = t_1;
	} else if (a <= 3.35e+90) {
		tmp = (x - (z * (y - 1.0))) + (b * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(1.0 - t), a, x) + Float64(b * y))
	tmp = 0.0
	if (a <= -1.7e-18)
		tmp = t_1;
	elseif (a <= 3.35e+90)
		tmp = Float64(Float64(x - Float64(z * Float64(y - 1.0))) + Float64(b * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e-18], t$95$1, If[LessEqual[a, 3.35e+90], N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.70000000000000001e-18 or 3.3500000000000001e90 < a

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 56.3

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

   7. Applied rewrites 56.3%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

          \[\leadsto \left(\left(1 - t\right) \cdot a + x\right) + b \cdot y \]

      11. lower-fma.f64 N/A

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

      12. lower--.f64 56.3

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

   9. Applied rewrites 56.3%

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

   if -1.70000000000000001e-18 < a < 3.3500000000000001e90

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.7

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

   4. Applied rewrites 49.7%

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

   5. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.0

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

   7. Applied rewrites 73.0%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 56.7

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

   10. Applied rewrites 56.7%

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

Alternative 9: 62.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.8e+108)
     t_1
     (if (<= t 3.4e+134) (+ (fma (- 1.0 t) a x) (* b y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.8e+108) {
		tmp = t_1;
	} else if (t <= 3.4e+134) {
		tmp = fma((1.0 - t), a, x) + (b * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.8e+108)
		tmp = t_1;
	elseif (t <= 3.4e+134)
		tmp = Float64(fma(Float64(1.0 - t), a, x) + Float64(b * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+108], t$95$1, If[LessEqual[t, 3.4e+134], N[(N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e108 or 3.40000000000000018e134 < t

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.6

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

   4. Applied rewrites 32.6%

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

   if -1.8e108 < t < 3.40000000000000018e134

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 56.3

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

   7. Applied rewrites 56.3%

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

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

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

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

          \[\leadsto \left(\left(1 - t\right) \cdot a + x\right) + b \cdot y \]

      11. lower-fma.f64 N/A

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

      12. lower--.f64 56.3

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

   9. Applied rewrites 56.3%

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

Alternative 10: 58.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;\left(x - a \cdot -1\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.85e+92)
     t_1
     (if (<= t 2.6e+54) (+ (- x (* a -1.0)) (* b y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.85e+92) {
		tmp = t_1;
	} else if (t <= 2.6e+54) {
		tmp = (x - (a * -1.0)) + (b * y);
	} 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 = t * (b - a)
    if (t <= (-1.85d+92)) then
        tmp = t_1
    else if (t <= 2.6d+54) then
        tmp = (x - (a * (-1.0d0))) + (b * y)
    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 = t * (b - a);
	double tmp;
	if (t <= -1.85e+92) {
		tmp = t_1;
	} else if (t <= 2.6e+54) {
		tmp = (x - (a * -1.0)) + (b * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.85e+92:
		tmp = t_1
	elif t <= 2.6e+54:
		tmp = (x - (a * -1.0)) + (b * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.85e+92)
		tmp = t_1;
	elseif (t <= 2.6e+54)
		tmp = Float64(Float64(x - Float64(a * -1.0)) + Float64(b * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.85e+92)
		tmp = t_1;
	elseif (t <= 2.6e+54)
		tmp = (x - (a * -1.0)) + (b * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+92], t$95$1, If[LessEqual[t, 2.6e+54], N[(N[(x - N[(a * -1.0), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.84999999999999999e92 or 2.60000000000000007e54 < t

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.6

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

   4. Applied rewrites 32.6%

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

   if -1.84999999999999999e92 < t < 2.60000000000000007e54

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 56.3

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

   7. Applied rewrites 56.3%

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

   8. Taylor expanded in t around 0

      \[\leadsto \left(x - a \cdot -1\right) + b \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 40.0%

       \[\leadsto \left(x - a \cdot -1\right) + b \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 48.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9.7 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1e+91)
     t_2
     (if (<= t 3.35e-158)
       t_1
       (if (<= t 6.8e-56) a (if (<= t 9.7e+36) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1e+91) {
		tmp = t_2;
	} else if (t <= 3.35e-158) {
		tmp = t_1;
	} else if (t <= 6.8e-56) {
		tmp = a;
	} else if (t <= 9.7e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-1d+91)) then
        tmp = t_2
    else if (t <= 3.35d-158) then
        tmp = t_1
    else if (t <= 6.8d-56) then
        tmp = a
    else if (t <= 9.7d+36) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1e+91) {
		tmp = t_2;
	} else if (t <= 3.35e-158) {
		tmp = t_1;
	} else if (t <= 6.8e-56) {
		tmp = a;
	} else if (t <= 9.7e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1e+91:
		tmp = t_2
	elif t <= 3.35e-158:
		tmp = t_1
	elif t <= 6.8e-56:
		tmp = a
	elif t <= 9.7e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1e+91)
		tmp = t_2;
	elseif (t <= 3.35e-158)
		tmp = t_1;
	elseif (t <= 6.8e-56)
		tmp = a;
	elseif (t <= 9.7e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1e+91)
		tmp = t_2;
	elseif (t <= 3.35e-158)
		tmp = t_1;
	elseif (t <= 6.8e-56)
		tmp = a;
	elseif (t <= 9.7e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+91], t$95$2, If[LessEqual[t, 3.35e-158], t$95$1, If[LessEqual[t, 6.8e-56], a, If[LessEqual[t, 9.7e+36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000008e91 or 9.69999999999999966e36 < t

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.6

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

   4. Applied rewrites 32.6%

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

   if -1.00000000000000008e91 < t < 3.35e-158 or 6.79999999999999964e-56 < t < 9.69999999999999966e36

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

   if 3.35e-158 < t < 6.79999999999999964e-56

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 11.2%

      \[\leadsto a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 41.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 240000:\\ \;\;\;\;a - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.9e-8) t_1 (if (<= t 240000.0) (- a (* a t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.9e-8) {
		tmp = t_1;
	} else if (t <= 240000.0) {
		tmp = a - (a * t);
	} 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 = t * (b - a)
    if (t <= (-1.9d-8)) then
        tmp = t_1
    else if (t <= 240000.0d0) then
        tmp = a - (a * t)
    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 = t * (b - a);
	double tmp;
	if (t <= -1.9e-8) {
		tmp = t_1;
	} else if (t <= 240000.0) {
		tmp = a - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.9e-8:
		tmp = t_1
	elif t <= 240000.0:
		tmp = a - (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.9e-8)
		tmp = t_1;
	elseif (t <= 240000.0)
		tmp = Float64(a - Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.9e-8)
		tmp = t_1;
	elseif (t <= 240000.0)
		tmp = a - (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e-8], t$95$1, If[LessEqual[t, 240000.0], N[(a - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000014e-8 or 2.4e5 < t

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.6

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

   4. Applied rewrites 32.6%

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

   if -1.90000000000000014e-8 < t < 2.4e5

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 24.4

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

   7. Applied rewrites 24.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. add-flip N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\frac{a}{t} \cdot t\right)\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\frac{a}{t} \cdot t\right)\right) \]

      6. mult-flip N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\left(a \cdot \frac{1}{t}\right) \cdot t\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot \left(\frac{1}{t} \cdot t\right)\right)\right) \]

      8. inv-pow N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot \left({t}^{-1} \cdot t\right)\right)\right) \]

      9. pow-plus N/A

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

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot {t}^{0}\right)\right) \]

      11. metadata-eval N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. add-flip N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, a\right) \]

      19. lower-neg.f64 28.6

          \[\leadsto \mathsf{fma}\left(-a, t, a\right) \]

   9. Applied rewrites 28.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, a\right)} \]
   10. Step-by-step derivation

       1. lift-fma.f64 N/A

          \[\leadsto \left(-a\right) \cdot t + a \]

       2. lift-*.f64 N/A

          \[\leadsto \left(-a\right) \cdot t + a \]

       3. +-commutative N/A

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

       4. lift-*.f64 N/A

          \[\leadsto a + \left(-a\right) \cdot t \]

       5. lift-neg.f64 N/A

          \[\leadsto a + \left(\mathsf{neg}\left(a\right)\right) \cdot t \]

       6. fp-cancel-sub-sign N/A

          \[\leadsto a - a \cdot \color{blue}{t} \]

       7. lift-*.f64 N/A

          \[\leadsto a - a \cdot t \]

       8. lower--.f64 28.6

          \[\leadsto a - a \cdot \color{blue}{t} \]

   11. Applied rewrites 28.6%

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

Alternative 13: 34.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+92}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+126}:\\ \;\;\;\;a - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.95e+92) (* y b) (if (<= b 8e+126) (- a (* a t)) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e+92) {
		tmp = y * b;
	} else if (b <= 8e+126) {
		tmp = a - (a * t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.95d+92)) then
        tmp = y * b
    else if (b <= 8d+126) then
        tmp = a - (a * t)
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.95e+92) {
		tmp = y * b;
	} else if (b <= 8e+126) {
		tmp = a - (a * t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.95e+92:
		tmp = y * b
	elif b <= 8e+126:
		tmp = a - (a * t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.95e+92)
		tmp = Float64(y * b);
	elseif (b <= 8e+126)
		tmp = Float64(a - Float64(a * t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.95e+92)
		tmp = y * b;
	elseif (b <= 8e+126)
		tmp = a - (a * t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.95e+92], N[(y * b), $MachinePrecision], If[LessEqual[b, 8e+126], N[(a - N[(a * t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.95000000000000006e92 or 7.9999999999999994e126 < b

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto y \cdot b \]
   6. Step-by-step derivation

   7. Applied rewrites 17.1%

      \[\leadsto y \cdot b \]

   if -1.95000000000000006e92 < b < 7.9999999999999994e126

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 24.4

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

   7. Applied rewrites 24.4%

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

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. distribute-rgt-in N/A

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

      4. add-flip N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\frac{a}{t} \cdot t\right)\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\frac{a}{t} \cdot t\right)\right) \]

      6. mult-flip N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(\left(a \cdot \frac{1}{t}\right) \cdot t\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot \left(\frac{1}{t} \cdot t\right)\right)\right) \]

      8. inv-pow N/A

         \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot \left({t}^{-1} \cdot t\right)\right)\right) \]

      9. pow-plus N/A

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

      10. metadata-eval N/A

          \[\leadsto \left(-1 \cdot a\right) \cdot t - \left(\mathsf{neg}\left(a \cdot {t}^{0}\right)\right) \]

      11. metadata-eval N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. add-flip N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(a\right), t, a\right) \]

      19. lower-neg.f64 28.6

          \[\leadsto \mathsf{fma}\left(-a, t, a\right) \]

   9. Applied rewrites 28.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-a, t, a\right)} \]
   10. Step-by-step derivation

       1. lift-fma.f64 N/A

          \[\leadsto \left(-a\right) \cdot t + a \]

       2. lift-*.f64 N/A

          \[\leadsto \left(-a\right) \cdot t + a \]

       3. +-commutative N/A

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

       4. lift-*.f64 N/A

          \[\leadsto a + \left(-a\right) \cdot t \]

       5. lift-neg.f64 N/A

          \[\leadsto a + \left(\mathsf{neg}\left(a\right)\right) \cdot t \]

       6. fp-cancel-sub-sign N/A

          \[\leadsto a - a \cdot \color{blue}{t} \]

       7. lift-*.f64 N/A

          \[\leadsto a - a \cdot t \]

       8. lower--.f64 28.6

          \[\leadsto a - a \cdot \color{blue}{t} \]

   11. Applied rewrites 28.6%

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

Alternative 14: 22.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+31}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.7e+31) (* y b) (if (<= y 2.6e+59) a (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.7e+31) {
		tmp = y * b;
	} else if (y <= 2.6e+59) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.7d+31)) then
        tmp = y * b
    else if (y <= 2.6d+59) then
        tmp = a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.7e+31) {
		tmp = y * b;
	} else if (y <= 2.6e+59) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.7e+31:
		tmp = y * b
	elif y <= 2.6e+59:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.7e+31)
		tmp = Float64(y * b);
	elseif (y <= 2.6e+59)
		tmp = a;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.7e+31)
		tmp = y * b;
	elseif (y <= 2.6e+59)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.7e+31], N[(y * b), $MachinePrecision], If[LessEqual[y, 2.6e+59], a, N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.70000000000000016e31 or 2.59999999999999999e59 < y

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 32.4

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

   4. Applied rewrites 32.4%

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

   5. Taylor expanded in z around 0

      \[\leadsto y \cdot b \]
   6. Step-by-step derivation

   7. Applied rewrites 17.1%

      \[\leadsto y \cdot b \]

   if -6.70000000000000016e31 < y < 2.59999999999999999e59

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 11.2%

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

Alternative 15: 17.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+80}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.2e+80) a (if (<= a 7e-49) z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+80) {
		tmp = a;
	} else if (a <= 7e-49) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-6.2d+80)) then
        tmp = a
    else if (a <= 7d-49) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+80) {
		tmp = a;
	} else if (a <= 7e-49) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.2e+80:
		tmp = a
	elif a <= 7e-49:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.2e+80)
		tmp = a;
	elseif (a <= 7e-49)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.2e+80)
		tmp = a;
	elseif (a <= 7e-49)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.2e+80], a, If[LessEqual[a, 7e-49], z, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999976e80 or 7.00000000000000012e-49 < a

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.6

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

   4. Applied rewrites 28.6%

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

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 11.2%

      \[\leadsto a \]

   if -6.19999999999999976e80 < a < 7.00000000000000012e-49

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-flip N/A

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

      5. distribute-lft-in N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. metadata-eval N/A

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

      9. mul-1-neg N/A

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

      10. lower-neg.f64 95.5

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

   3. Applied rewrites 95.5%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 28.9

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

   6. Applied rewrites 28.9%

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

   7. Taylor expanded in y around 0

      \[\leadsto z \]
   8. Step-by-step derivation

   9. Applied rewrites 11.4%

      \[\leadsto z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 11.2% accurate, 28.4× 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 95.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in a around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 28.6

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

4. Applied rewrites 28.6%

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

5. Taylor expanded in t around 0

   \[\leadsto a \]
6. Step-by-step derivation

7. Applied rewrites 11.2%

   \[\leadsto a \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025155 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))