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

Percentage Accurate: 95.2% → 97.9%

Time: 5.3s

Alternatives: 17

Speedup: 0.5×

• 63.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) 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), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) 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), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<=
     (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b))
     INFINITY)
  (- (- (+ (* (- 1 t) a) x) (* z (- y 1))) (* (- 2 (+ t y)) b))
  (* y (- b z))))

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x - N[(N[(y - 1), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(1 - t), $MachinePrecision] * a), $MachinePrecision] + x), $MachinePrecision] - N[(z * N[(y - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(2 - N[(t + y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $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 95.2%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

   3. Applied rewrites 95.2%

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

   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 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1
        (+
         (- (- x (* (- y 1) z)) (* (- t 1) a))
         (* (- (+ y t) 2) 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), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $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 95.2%

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

   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 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

Alternative 3: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -10499999999999999928819961080797093752847938640412672:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + t\_1\\ \mathbf{elif}\;b \leq 5700000000000000197784854593536:\\ \;\;\;\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right) + t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* (- (+ y t) 2) b)))
  (if (<= b -10499999999999999928819961080797093752847938640412672)
    (+ (- x (* a (- t 1))) t_1)
    (if (<= b 5700000000000000197784854593536)
      (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* b y))
      (+ (* a (- 1 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.05e+52) {
		tmp = (x - (a * (t - 1.0))) + t_1;
	} else if (b <= 5.7e+30) {
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	} else {
		tmp = (a * (1.0 - t)) + t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-1.05d+52)) then
        tmp = (x - (a * (t - 1.0d0))) + t_1
    else if (b <= 5.7d+30) then
        tmp = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (b * y)
    else
        tmp = (a * (1.0d0 - t)) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.05e+52) {
		tmp = (x - (a * (t - 1.0))) + t_1;
	} else if (b <= 5.7e+30) {
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	} else {
		tmp = (a * (1.0 - t)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -1.05e+52:
		tmp = (x - (a * (t - 1.0))) + t_1
	elif b <= 5.7e+30:
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y)
	else:
		tmp = (a * (1.0 - t)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.05e+52)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + t_1);
	elseif (b <= 5.7e+30)
		tmp = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * y));
	else
		tmp = Float64(Float64(a * Float64(1.0 - t)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.05e+52)
		tmp = (x - (a * (t - 1.0))) + t_1;
	elseif (b <= 5.7e+30)
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	else
		tmp = (a * (1.0 - t)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -10499999999999999928819961080797093752847938640412672], N[(N[(x - N[(a * N[(t - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 5700000000000000197784854593536], N[(N[(N[(x - N[(N[(y - 1), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(1 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e52

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   if -1.05e52 < b < 5.7000000000000002e30

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 77.8%

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

   4. Applied rewrites 77.8%

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

   if 5.7000000000000002e30 < b

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

Alternative 4: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)\\ \mathbf{if}\;z \leq -2199999999999999885260233413848058330640843229616793674173628649221800130588415029452562203177085987418885945263028424059069640212480:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 249999999999999995000867086848550295417201298224252129547162077957693103656857181366197358732498109938694018795269259264:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (- (+ x (* b (- (+ t y) 2))) (* z (- y 1)))))
  (if (<=
       z
       -2199999999999999885260233413848058330640843229616793674173628649221800130588415029452562203177085987418885945263028424059069640212480)
    t_1
    (if (<=
         z
         249999999999999995000867086848550295417201298224252129547162077957693103656857181366197358732498109938694018795269259264)
      (+ (- x (* a (- t 1))) (* (- (+ y t) 2) b))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	double tmp;
	if (z <= -2.2e+132) {
		tmp = t_1;
	} else if (z <= 2.5e+119) {
		tmp = (x - (a * (t - 1.0))) + (((y + 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 + (b * ((t + y) - 2.0d0))) - (z * (y - 1.0d0))
    if (z <= (-2.2d+132)) then
        tmp = t_1
    else if (z <= 2.5d+119) then
        tmp = (x - (a * (t - 1.0d0))) + (((y + 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 + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	double tmp;
	if (z <= -2.2e+132) {
		tmp = t_1;
	} else if (z <= 2.5e+119) {
		tmp = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (b * ((t + y) - 2.0))) - (z * (y - 1.0))
	tmp = 0
	if z <= -2.2e+132:
		tmp = t_1
	elif z <= 2.5e+119:
		tmp = (x - (a * (t - 1.0))) + (((y + t) - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) - Float64(z * Float64(y - 1.0)))
	tmp = 0.0
	if (z <= -2.2e+132)
		tmp = t_1;
	elseif (z <= 2.5e+119)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(Float64(Float64(y + 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 + (b * ((t + y) - 2.0))) - (z * (y - 1.0));
	tmp = 0.0;
	if (z <= -2.2e+132)
		tmp = t_1;
	elseif (z <= 2.5e+119)
		tmp = (x - (a * (t - 1.0))) + (((y + 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[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2199999999999999885260233413848058330640843229616793674173628649221800130588415029452562203177085987418885945263028424059069640212480], t$95$1, If[LessEqual[z, 249999999999999995000867086848550295417201298224252129547162077957693103656857181366197358732498109938694018795269259264], N[(N[(x - N[(a * N[(t - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e132 or 2.5e119 < z

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

   if -2.1999999999999999e132 < z < 2.5e119

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

Alternative 5: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(x - a \cdot \left(t - 1\right)\right) + b \cdot y\\ \mathbf{if}\;a \leq -37000000000000001098777444363636327681486635717165599167177722941531416978671695581500620980628105995830157385333382592595208025538432977972614384971354924283480249132168877205756841920176278592646542942967695862136832:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4499999999999999969494269034627325894077687988748288:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (- x (* a (- t 1))) (* b y))))
  (if (<=
       a
       -37000000000000001098777444363636327681486635717165599167177722941531416978671695581500620980628105995830157385333382592595208025538432977972614384971354924283480249132168877205756841920176278592646542942967695862136832)
    t_1
    (if (<= a 4499999999999999969494269034627325894077687988748288)
      (- (+ x (* b (- (+ t y) 2))) (* z (- y 1)))
      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))) + (b * y);
	double tmp;
	if (a <= -3.7e+217) {
		tmp = t_1;
	} else if (a <= 4.5e+51) {
		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))) + (b * y)
    if (a <= (-3.7d+217)) then
        tmp = t_1
    else if (a <= 4.5d+51) 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))) + (b * y);
	double tmp;
	if (a <= -3.7e+217) {
		tmp = t_1;
	} else if (a <= 4.5e+51) {
		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))) + (b * y)
	tmp = 0
	if a <= -3.7e+217:
		tmp = t_1
	elif a <= 4.5e+51:
		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(b * y))
	tmp = 0.0
	if (a <= -3.7e+217)
		tmp = t_1;
	elseif (a <= 4.5e+51)
		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))) + (b * y);
	tmp = 0.0;
	if (a <= -3.7e+217)
		tmp = t_1;
	elseif (a <= 4.5e+51)
		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), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -37000000000000001098777444363636327681486635717165599167177722941531416978671695581500620980628105995830157385333382592595208025538432977972614384971354924283480249132168877205756841920176278592646542942967695862136832], t$95$1, If[LessEqual[a, 4499999999999999969494269034627325894077687988748288], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(y - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.7000000000000001e217 or 4.5e51 < a

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 55.1%

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

   10. Applied rewrites 55.1%

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

   if -3.7000000000000001e217 < a < 4.5e51

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

Alternative 6: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \left(\left(x - y \cdot z\right) - a \cdot t\right) + b \cdot y\\ \mathbf{if}\;y \leq -2400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{93076680405667}{21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192}:\\ \;\;\;\;\left(x + b \cdot \left(t - 2\right)\right) - -1 \cdot z\\ \mathbf{elif}\;y \leq 155000000000000009583071010805379319582021290744086528:\\ \;\;\;\;a \cdot \left(1 - t\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (- (- x (* y z)) (* a t)) (* b y))))
  (if (<= y -2400000)
    t_1
    (if (<=
         y
         93076680405667/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192)
      (- (+ x (* b (- t 2))) (* -1 z))
      (if (<=
           y
           155000000000000009583071010805379319582021290744086528)
        (+ (* a (- 1 t)) (* (- (+ y t) 2) b))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - (y * z)) - (a * t)) + (b * y);
	double tmp;
	if (y <= -2400000.0) {
		tmp = t_1;
	} else if (y <= 4.4e-111) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.55e+53) {
		tmp = (a * (1.0 - t)) + (((y + 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 - (y * z)) - (a * t)) + (b * y)
    if (y <= (-2400000.0d0)) then
        tmp = t_1
    else if (y <= 4.4d-111) then
        tmp = (x + (b * (t - 2.0d0))) - ((-1.0d0) * z)
    else if (y <= 1.55d+53) then
        tmp = (a * (1.0d0 - t)) + (((y + 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 - (y * z)) - (a * t)) + (b * y);
	double tmp;
	if (y <= -2400000.0) {
		tmp = t_1;
	} else if (y <= 4.4e-111) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.55e+53) {
		tmp = (a * (1.0 - t)) + (((y + t) - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - (y * z)) - (a * t)) + (b * y)
	tmp = 0
	if y <= -2400000.0:
		tmp = t_1
	elif y <= 4.4e-111:
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z)
	elif y <= 1.55e+53:
		tmp = (a * (1.0 - t)) + (((y + 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 - Float64(y * z)) - Float64(a * t)) + Float64(b * y))
	tmp = 0.0
	if (y <= -2400000.0)
		tmp = t_1;
	elseif (y <= 4.4e-111)
		tmp = Float64(Float64(x + Float64(b * Float64(t - 2.0))) - Float64(-1.0 * z));
	elseif (y <= 1.55e+53)
		tmp = Float64(Float64(a * Float64(1.0 - t)) + Float64(Float64(Float64(y + 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 - (y * z)) - (a * t)) + (b * y);
	tmp = 0.0;
	if (y <= -2400000.0)
		tmp = t_1;
	elseif (y <= 4.4e-111)
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	elseif (y <= 1.55e+53)
		tmp = (a * (1.0 - t)) + (((y + 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 - N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2400000], t$95$1, If[LessEqual[y, 93076680405667/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192], N[(N[(x + N[(b * N[(t - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000000000000009583071010805379319582021290744086528], N[(N[(a * N[(1 - t), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e6 or 1.5500000000000001e53 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 77.8%

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

   4. Applied rewrites 77.8%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 67.9%

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

   7. Applied rewrites 67.9%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 58.4%

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

   10. Applied rewrites 58.4%

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

   if -2.4e6 < y < 4.3999999999999999e-111

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 46.5%

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

   7. Applied rewrites 46.5%

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

   if 4.3999999999999999e-111 < y < 1.5500000000000001e53

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

Alternative 7: 70.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -7000000000000000195090964334063318778005827328862580230404690162898436096:\\ \;\;\;\;t\_1 - \left(2 - \left(t + y\right)\right) \cdot b\\ \mathbf{elif}\;z \leq 6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \left(2 - t\right) \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* z (- 1 y))))
  (if (<=
       z
       -7000000000000000195090964334063318778005827328862580230404690162898436096)
    (- t_1 (* (- 2 (+ t y)) b))
    (if (<=
         z
         6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560)
      (+ (- x (* a (- t 1))) (* b y))
      (- t_1 (* (- 2 t) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -7e+72) {
		tmp = t_1 - ((2.0 - (t + y)) * b);
	} else if (z <= 6.4e+87) {
		tmp = (x - (a * (t - 1.0))) + (b * y);
	} else {
		tmp = t_1 - ((2.0 - t) * b);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-7d+72)) then
        tmp = t_1 - ((2.0d0 - (t + y)) * b)
    else if (z <= 6.4d+87) then
        tmp = (x - (a * (t - 1.0d0))) + (b * y)
    else
        tmp = t_1 - ((2.0d0 - t) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -7e+72) {
		tmp = t_1 - ((2.0 - (t + y)) * b);
	} else if (z <= 6.4e+87) {
		tmp = (x - (a * (t - 1.0))) + (b * y);
	} else {
		tmp = t_1 - ((2.0 - t) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -7e+72:
		tmp = t_1 - ((2.0 - (t + y)) * b)
	elif z <= 6.4e+87:
		tmp = (x - (a * (t - 1.0))) + (b * y)
	else:
		tmp = t_1 - ((2.0 - t) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -7e+72)
		tmp = Float64(t_1 - Float64(Float64(2.0 - Float64(t + y)) * b));
	elseif (z <= 6.4e+87)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(b * y));
	else
		tmp = Float64(t_1 - Float64(Float64(2.0 - t) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -7e+72)
		tmp = t_1 - ((2.0 - (t + y)) * b);
	elseif (z <= 6.4e+87)
		tmp = (x - (a * (t - 1.0))) + (b * y);
	else
		tmp = t_1 - ((2.0 - t) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7000000000000000195090964334063318778005827328862580230404690162898436096], N[(t$95$1 - N[(N[(2 - N[(t + y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560], N[(N[(x - N[(a * N[(t - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(2 - t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000002e72

   1. Initial program 95.2%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

   3. Applied rewrites 95.2%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   if -7.0000000000000002e72 < z < 6.4000000000000001e87

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 55.1%

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

   10. Applied rewrites 55.1%

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

   if 6.4000000000000001e87 < z

   1. Initial program 95.2%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

   3. Applied rewrites 95.2%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 49.7%

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

Alternative 8: 70.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right) - \left(2 - t\right) \cdot b\\ \mathbf{if}\;z \leq -7000000000000000195090964334063318778005827328862580230404690162898436096:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (- (* z (- 1 y)) (* (- 2 t) b))))
  (if (<=
       z
       -7000000000000000195090964334063318778005827328862580230404690162898436096)
    t_1
    (if (<=
         z
         6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560)
      (+ (- x (* a (- t 1))) (* b y))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (1.0 - y)) - ((2.0 - t) * b);
	double tmp;
	if (z <= -7e+72) {
		tmp = t_1;
	} else if (z <= 6.4e+87) {
		tmp = (x - (a * (t - 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 = (z * (1.0d0 - y)) - ((2.0d0 - t) * b)
    if (z <= (-7d+72)) then
        tmp = t_1
    else if (z <= 6.4d+87) then
        tmp = (x - (a * (t - 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 = (z * (1.0 - y)) - ((2.0 - t) * b);
	double tmp;
	if (z <= -7e+72) {
		tmp = t_1;
	} else if (z <= 6.4e+87) {
		tmp = (x - (a * (t - 1.0))) + (b * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (1.0 - y)) - ((2.0 - t) * b)
	tmp = 0
	if z <= -7e+72:
		tmp = t_1
	elif z <= 6.4e+87:
		tmp = (x - (a * (t - 1.0))) + (b * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(1.0 - y)) - Float64(Float64(2.0 - t) * b))
	tmp = 0.0
	if (z <= -7e+72)
		tmp = t_1;
	elseif (z <= 6.4e+87)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 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 = (z * (1.0 - y)) - ((2.0 - t) * b);
	tmp = 0.0;
	if (z <= -7e+72)
		tmp = t_1;
	elseif (z <= 6.4e+87)
		tmp = (x - (a * (t - 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[(N[(z * N[(1 - y), $MachinePrecision]), $MachinePrecision] - N[(N[(2 - t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7000000000000000195090964334063318778005827328862580230404690162898436096], t$95$1, If[LessEqual[z, 6400000000000000093636449476319187398208275122333792379383109037886696731207348581826560], N[(N[(x - N[(a * N[(t - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000002e72 or 6.4000000000000001e87 < z

   1. Initial program 95.2%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

   3. Applied rewrites 95.2%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 49.7%

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

   if -7.0000000000000002e72 < z < 6.4000000000000001e87

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 55.1%

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

   10. Applied rewrites 55.1%

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

Alternative 9: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(x - a \cdot \left(t - 1\right)\right) + b \cdot y\\ \mathbf{if}\;y \leq -1960000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{5648671608315113}{5043456793138493339171717132818382567050206626619577173497381555743452386751642958261026080625269202023248382759272448}:\\ \;\;\;\;\left(x + b \cdot \left(t - 2\right)\right) - -1 \cdot z\\ \mathbf{elif}\;y \leq 57000000000000001677201922670346782869445510907234784105077596356519050406796469980325465763994708026039730176:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ (- x (* a (- t 1))) (* b y))))
  (if (<= y -1960000)
    t_1
    (if (<=
         y
         5648671608315113/5043456793138493339171717132818382567050206626619577173497381555743452386751642958261026080625269202023248382759272448)
      (- (+ x (* b (- t 2))) (* -1 z))
      (if (<=
           y
           57000000000000001677201922670346782869445510907234784105077596356519050406796469980325465763994708026039730176)
        t_1
        (* y (- b z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - (a * (t - 1.0))) + (b * y);
	double tmp;
	if (y <= -1960000.0) {
		tmp = t_1;
	} else if (y <= 1.12e-102) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 5.7e+109) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (a * (t - 1.0d0))) + (b * y)
    if (y <= (-1960000.0d0)) then
        tmp = t_1
    else if (y <= 1.12d-102) then
        tmp = (x + (b * (t - 2.0d0))) - ((-1.0d0) * z)
    else if (y <= 5.7d+109) then
        tmp = t_1
    else
        tmp = y * (b - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - (a * (t - 1.0))) + (b * y);
	double tmp;
	if (y <= -1960000.0) {
		tmp = t_1;
	} else if (y <= 1.12e-102) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 5.7e+109) {
		tmp = t_1;
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x - (a * (t - 1.0))) + (b * y)
	tmp = 0
	if y <= -1960000.0:
		tmp = t_1
	elif y <= 1.12e-102:
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z)
	elif y <= 5.7e+109:
		tmp = t_1
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(b * y))
	tmp = 0.0
	if (y <= -1960000.0)
		tmp = t_1;
	elseif (y <= 1.12e-102)
		tmp = Float64(Float64(x + Float64(b * Float64(t - 2.0))) - Float64(-1.0 * z));
	elseif (y <= 5.7e+109)
		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 - (a * (t - 1.0))) + (b * y);
	tmp = 0.0;
	if (y <= -1960000.0)
		tmp = t_1;
	elseif (y <= 1.12e-102)
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	elseif (y <= 5.7e+109)
		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[(x - N[(a * N[(t - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1960000], t$95$1, If[LessEqual[y, 5648671608315113/5043456793138493339171717132818382567050206626619577173497381555743452386751642958261026080625269202023248382759272448], N[(N[(x + N[(b * N[(t - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 57000000000000001677201922670346782869445510907234784105077596356519050406796469980325465763994708026039730176], t$95$1, N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.96e6 or 1.1200000000000001e-102 < y < 5.7000000000000002e109

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 55.1%

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

   10. Applied rewrites 55.1%

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

   if -1.96e6 < y < 1.1200000000000001e-102

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 46.5%

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

   7. Applied rewrites 46.5%

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

   if 5.7000000000000002e109 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

Alternative 10: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{4160851854339257}{2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224}:\\ \;\;\;\;\left(x + b \cdot \left(t - 2\right)\right) - -1 \cdot z\\ \mathbf{elif}\;y \leq 164999999999999989746501660396935349620099883912192960188787403991810048:\\ \;\;\;\;a \cdot \left(1 - t\right) + \left(y - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* y (- b z))))
  (if (<= y -4800000)
    t_1
    (if (<=
         y
         4160851854339257/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224)
      (- (+ x (* b (- t 2))) (* -1 z))
      (if (<=
           y
           164999999999999989746501660396935349620099883912192960188787403991810048)
        (+ (* a (- 1 t)) (* (- y 2) b))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4800000.0) {
		tmp = t_1;
	} else if (y <= 1.65e-102) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.65e+71) {
		tmp = (a * (1.0 - t)) + ((y - 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 = y * (b - z)
    if (y <= (-4800000.0d0)) then
        tmp = t_1
    else if (y <= 1.65d-102) then
        tmp = (x + (b * (t - 2.0d0))) - ((-1.0d0) * z)
    else if (y <= 1.65d+71) then
        tmp = (a * (1.0d0 - t)) + ((y - 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 = y * (b - z);
	double tmp;
	if (y <= -4800000.0) {
		tmp = t_1;
	} else if (y <= 1.65e-102) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.65e+71) {
		tmp = (a * (1.0 - t)) + ((y - 2.0) * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4800000.0:
		tmp = t_1
	elif y <= 1.65e-102:
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z)
	elif y <= 1.65e+71:
		tmp = (a * (1.0 - t)) + ((y - 2.0) * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4800000.0)
		tmp = t_1;
	elseif (y <= 1.65e-102)
		tmp = Float64(Float64(x + Float64(b * Float64(t - 2.0))) - Float64(-1.0 * z));
	elseif (y <= 1.65e+71)
		tmp = Float64(Float64(a * Float64(1.0 - t)) + Float64(Float64(y - 2.0) * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4800000.0)
		tmp = t_1;
	elseif (y <= 1.65e-102)
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	elseif (y <= 1.65e+71)
		tmp = (a * (1.0 - t)) + ((y - 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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4800000], t$95$1, If[LessEqual[y, 4160851854339257/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224], N[(N[(x + N[(b * N[(t - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 164999999999999989746501660396935349620099883912192960188787403991810048], N[(N[(a * N[(1 - t), $MachinePrecision]), $MachinePrecision] + N[(N[(y - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e6 or 1.6499999999999999e71 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   if -4.8e6 < y < 1.65e-102

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 46.5%

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

   7. Applied rewrites 46.5%

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

   if 1.65e-102 < y < 1.6499999999999999e71

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 48.1%

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

   7. Applied rewrites 48.1%

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

Alternative 11: 64.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{1891296297426935}{2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224}:\\ \;\;\;\;\left(x + b \cdot \left(t - 2\right)\right) - -1 \cdot z\\ \mathbf{elif}\;y \leq 164999999999999989746501660396935349620099883912192960188787403991810048:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* y (- b z))))
  (if (<= y -4800000)
    t_1
    (if (<=
         y
         1891296297426935/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224)
      (- (+ x (* b (- t 2))) (* -1 z))
      (if (<=
           y
           164999999999999989746501660396935349620099883912192960188787403991810048)
        (* t (- b a))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4800000.0) {
		tmp = t_1;
	} else if (y <= 7.5e-103) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-4800000.0d0)) then
        tmp = t_1
    else if (y <= 7.5d-103) then
        tmp = (x + (b * (t - 2.0d0))) - ((-1.0d0) * z)
    else if (y <= 1.65d+71) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4800000.0) {
		tmp = t_1;
	} else if (y <= 7.5e-103) {
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -4800000.0:
		tmp = t_1
	elif y <= 7.5e-103:
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z)
	elif y <= 1.65e+71:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4800000.0)
		tmp = t_1;
	elseif (y <= 7.5e-103)
		tmp = Float64(Float64(x + Float64(b * Float64(t - 2.0))) - Float64(-1.0 * z));
	elseif (y <= 1.65e+71)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -4800000.0)
		tmp = t_1;
	elseif (y <= 7.5e-103)
		tmp = (x + (b * (t - 2.0))) - (-1.0 * z);
	elseif (y <= 1.65e+71)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4800000], t$95$1, If[LessEqual[y, 1891296297426935/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224], N[(N[(x + N[(b * N[(t - 2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-1 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 164999999999999989746501660396935349620099883912192960188787403991810048], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e6 or 1.6499999999999999e71 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   if -4.8e6 < y < 7.5e-103

   1. Initial program 95.2%

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

   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 73.8%

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 46.5%

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

   7. Applied rewrites 46.5%

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

   if 7.5e-103 < y < 1.6499999999999999e71

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

Alternative 12: 57.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq \frac{2420859260706477}{80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168}:\\ \;\;\;\;z - \left(2 - \left(t + y\right)\right) \cdot b\\ \mathbf{elif}\;y \leq 164999999999999989746501660396935349620099883912192960188787403991810048:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* y (- b z))))
  (if (<= y -3400000000)
    t_1
    (if (<=
         y
         2420859260706477/80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168)
      (- z (* (- 2 (+ t y)) b))
      (if (<=
           y
           164999999999999989746501660396935349620099883912192960188787403991810048)
        (* t (- b a))
        t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3400000000.0) {
		tmp = t_1;
	} else if (y <= 3e-104) {
		tmp = z - ((2.0 - (t + y)) * b);
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-3400000000.0d0)) then
        tmp = t_1
    else if (y <= 3d-104) then
        tmp = z - ((2.0d0 - (t + y)) * b)
    else if (y <= 1.65d+71) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -3400000000.0) {
		tmp = t_1;
	} else if (y <= 3e-104) {
		tmp = z - ((2.0 - (t + y)) * b);
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -3400000000.0:
		tmp = t_1
	elif y <= 3e-104:
		tmp = z - ((2.0 - (t + y)) * b)
	elif y <= 1.65e+71:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3400000000.0)
		tmp = t_1;
	elseif (y <= 3e-104)
		tmp = Float64(z - Float64(Float64(2.0 - Float64(t + y)) * b));
	elseif (y <= 1.65e+71)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -3400000000.0)
		tmp = t_1;
	elseif (y <= 3e-104)
		tmp = z - ((2.0 - (t + y)) * b);
	elseif (y <= 1.65e+71)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3400000000], t$95$1, If[LessEqual[y, 2420859260706477/80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307232371974124148359168], N[(z - N[(N[(2 - N[(t + y), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 164999999999999989746501660396935349620099883912192960188787403991810048], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e9 or 1.6499999999999999e71 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   if -3.4e9 < y < 3.0000000000000002e-104

   1. Initial program 95.2%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

   3. Applied rewrites 95.2%

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

   4. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 60.5%

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

   6. Applied rewrites 60.5%

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

   7. Taylor expanded in y around 0

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

   9. Applied rewrites 46.8%

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

   if 3.0000000000000002e-104 < y < 1.6499999999999999e71

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

Alternative 13: 55.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -23999999999999998558342357087346829272603695633019749798744112831287262393139200:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq \frac{-1478383000718271}{1606938044258990275541962092341162602522202993782792835301376}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{3302638007025703}{36695977855841144185773134324833391052745039826692497979801421430190766017415756929120296849762010984873984}:\\ \;\;\;\;a + \left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq \frac{1770887431076117}{1180591620717411303424}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
  (if (<=
       t
       -23999999999999998558342357087346829272603695633019749798744112831287262393139200)
    t_2
    (if (<=
         t
         -1478383000718271/1606938044258990275541962092341162602522202993782792835301376)
      t_1
      (if (<=
           t
           3302638007025703/36695977855841144185773134324833391052745039826692497979801421430190766017415756929120296849762010984873984)
        (+ a (* (- y 2) b))
        (if (<= t 1770887431076117/1180591620717411303424)
          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 <= -2.4e+79) {
		tmp = t_2;
	} else if (t <= -9.2e-46) {
		tmp = t_1;
	} else if (t <= 9e-92) {
		tmp = a + ((y - 2.0) * b);
	} else if (t <= 1.5e-6) {
		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 <= (-2.4d+79)) then
        tmp = t_2
    else if (t <= (-9.2d-46)) then
        tmp = t_1
    else if (t <= 9d-92) then
        tmp = a + ((y - 2.0d0) * b)
    else if (t <= 1.5d-6) 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 <= -2.4e+79) {
		tmp = t_2;
	} else if (t <= -9.2e-46) {
		tmp = t_1;
	} else if (t <= 9e-92) {
		tmp = a + ((y - 2.0) * b);
	} else if (t <= 1.5e-6) {
		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 <= -2.4e+79:
		tmp = t_2
	elif t <= -9.2e-46:
		tmp = t_1
	elif t <= 9e-92:
		tmp = a + ((y - 2.0) * b)
	elif t <= 1.5e-6:
		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 <= -2.4e+79)
		tmp = t_2;
	elseif (t <= -9.2e-46)
		tmp = t_1;
	elseif (t <= 9e-92)
		tmp = Float64(a + Float64(Float64(y - 2.0) * b));
	elseif (t <= 1.5e-6)
		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 <= -2.4e+79)
		tmp = t_2;
	elseif (t <= -9.2e-46)
		tmp = t_1;
	elseif (t <= 9e-92)
		tmp = a + ((y - 2.0) * b);
	elseif (t <= 1.5e-6)
		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, -23999999999999998558342357087346829272603695633019749798744112831287262393139200], t$95$2, If[LessEqual[t, -1478383000718271/1606938044258990275541962092341162602522202993782792835301376], t$95$1, If[LessEqual[t, 3302638007025703/36695977855841144185773134324833391052745039826692497979801421430190766017415756929120296849762010984873984], N[(a + N[(N[(y - 2), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1770887431076117/1180591620717411303424], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3999999999999999e79 or 1.5e-6 < t

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

   if -2.3999999999999999e79 < t < -9.1999999999999997e-46 or 9.0000000000000001e-92 < t < 1.5e-6

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   if -9.1999999999999997e-46 < t < 9.0000000000000001e-92

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 48.1%

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

   7. Applied rewrites 48.1%

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

   8. Taylor expanded in t around 0

      \[\leadsto a + \left(y - 2\right) \cdot b \]
   9. Step-by-step derivation

   10. Applied rewrites 33.1%

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

Alternative 14: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -255000000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 164999999999999989746501660396935349620099883912192960188787403991810048:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* y (- b z))))
  (if (<= y -255000000000000000)
    t_1
    (if (<=
         y
         164999999999999989746501660396935349620099883912192960188787403991810048)
      (* t (- b a))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.55e+17) {
		tmp = t_1;
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-2.55d+17)) then
        tmp = t_1
    else if (y <= 1.65d+71) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.55e+17) {
		tmp = t_1;
	} else if (y <= 1.65e+71) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.55e+17:
		tmp = t_1
	elif y <= 1.65e+71:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.55e+17)
		tmp = t_1;
	elseif (y <= 1.65e+71)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.55e+17)
		tmp = t_1;
	elseif (y <= 1.65e+71)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -255000000000000000], t$95$1, If[LessEqual[y, 164999999999999989746501660396935349620099883912192960188787403991810048], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e17 or 1.6499999999999999e71 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   if -2.55e17 < y < 1.6499999999999999e71

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

Alternative 15: 41.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq \frac{-8341588155340941}{604462909807314587353088}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{1470053796651389}{154742504910672534362390528}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (* t (- b a))))
  (if (<= t -8341588155340941/604462909807314587353088)
    t_1
    (if (<= t 1470053796651389/154742504910672534362390528)
      (* y b)
      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 <= -1.38e-8) {
		tmp = t_1;
	} else if (t <= 9.5e-12) {
		tmp = y * 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 = t * (b - a)
    if (t <= (-1.38d-8)) then
        tmp = t_1
    else if (t <= 9.5d-12) then
        tmp = y * 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 = t * (b - a);
	double tmp;
	if (t <= -1.38e-8) {
		tmp = t_1;
	} else if (t <= 9.5e-12) {
		tmp = y * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.38e-8:
		tmp = t_1
	elif t <= 9.5e-12:
		tmp = y * b
	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 <= -1.38e-8)
		tmp = t_1;
	elseif (t <= 9.5e-12)
		tmp = Float64(y * b);
	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 <= -1.38e-8)
		tmp = t_1;
	elseif (t <= 9.5e-12)
		tmp = y * b;
	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, -8341588155340941/604462909807314587353088], t$95$1, If[LessEqual[t, 1470053796651389/154742504910672534362390528], N[(y * b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3799999999999999e-8 or 9.4999999999999995e-12 < t

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

   if -1.3799999999999999e-8 < t < 9.4999999999999995e-12

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 17.6%

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

Alternative 16: 27.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -4800000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 160000000000000011605029821044677620185339905543443512882913624876646400:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<= y -4800000)
  (* y b)
  (if (<=
       y
       160000000000000011605029821044677620185339905543443512882913624876646400)
    (* t b)
    (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4800000.0) {
		tmp = y * b;
	} else if (y <= 1.6e+71) {
		tmp = t * b;
	} 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 <= (-4800000.0d0)) then
        tmp = y * b
    else if (y <= 1.6d+71) then
        tmp = t * b
    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 <= -4800000.0) {
		tmp = y * b;
	} else if (y <= 1.6e+71) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4800000.0:
		tmp = y * b
	elif y <= 1.6e+71:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4800000.0)
		tmp = Float64(y * b);
	elseif (y <= 1.6e+71)
		tmp = Float64(t * b);
	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 <= -4800000.0)
		tmp = y * b;
	elseif (y <= 1.6e+71)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4800000], N[(y * b), $MachinePrecision], If[LessEqual[y, 160000000000000011605029821044677620185339905543443512882913624876646400], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e6 or 1.6000000000000001e71 < y

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 59.0%

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

   4. Applied rewrites 59.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   6. 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 72.5%

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

   7. Applied rewrites 72.5%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 33.4%

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

   10. Applied rewrites 33.4%

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

   11. Taylor expanded in z around 0

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

   13. Applied rewrites 17.6%

       \[\leadsto y \cdot b \]

   if -4.8e6 < y < 1.6000000000000001e71

   1. Initial program 95.2%

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

   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 32.5%

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

   4. Applied rewrites 32.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 18.0%

      \[\leadsto t \cdot b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 18.0% accurate, 6.2× speedup

Math

\[t \cdot b \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t * b), $MachinePrecision]

Derivation

1. Initial program 95.2%

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

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 32.5%

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

4. Applied rewrites 32.5%

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

5. Taylor expanded in a around 0

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

7. Applied rewrites 18.0%

   \[\leadsto t \cdot b \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))