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

Percentage Accurate: 95.6% → 98.0%

Time: 9.4s

Alternatives: 16

Speedup: 0.5×

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

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 = (b - a) * t;
	}
	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 = (b - a) * t;
	}
	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 = (b - a) * t
	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(Float64(b - a) * t);
	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 = (b - a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(b - a), $MachinePrecision] * t), $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 100.0%

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

   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 0.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 92.9

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

   5. Applied rewrites 92.9%

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

Alternative 2: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+92} \lor \neg \left(t \leq 3.4 \cdot 10^{+153}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.45e+92) (not (<= t 3.4e+153)))
   (* (- b a) t)
   (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.45e+92) || !(t <= 3.4e+153)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.45e+92) || !(t <= 3.4e+153))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.45e+92], N[Not[LessEqual[t, 3.4e+153]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.4500000000000001e92 or 3.3999999999999997e153 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 81.3

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

   5. Applied rewrites 81.3%

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

   if -2.4500000000000001e92 < t < 3.3999999999999997e153

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 89.4

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

   5. Applied rewrites 89.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+92} \lor \neg \left(t \leq 3.4 \cdot 10^{+153}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+18}:\\ \;\;\;\;\left(-z\right) \cdot y + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.7e+95)
     t_1
     (if (<= t -5.5e+18)
       (+ (* (- z) y) (* (- (+ y t) 2.0) b))
       (if (<= t 4.1e+86) (fma (- y 2.0) b (+ a x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.7e+95) {
		tmp = t_1;
	} else if (t <= -5.5e+18) {
		tmp = (-z * y) + (((y + t) - 2.0) * b);
	} else if (t <= 4.1e+86) {
		tmp = fma((y - 2.0), b, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.7e+95)
		tmp = t_1;
	elseif (t <= -5.5e+18)
		tmp = Float64(Float64(Float64(-z) * y) + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (t <= 4.1e+86)
		tmp = fma(Float64(y - 2.0), b, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.7e+95], t$95$1, If[LessEqual[t, -5.5e+18], N[(N[((-z) * y), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+86], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000011e95 or 4.0999999999999999e86 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -1.70000000000000011e95 < t < -5.5e18

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 68.0

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

   5. Applied rewrites 68.0%

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

   if -5.5e18 < t < 4.0999999999999999e86

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 94.5

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y - 2, b, a + x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 64.8%

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

Alternative 4: 47.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-243}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 115:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)) (t_2 (* (- b a) t)))
   (if (<= t -1.1e+92)
     t_2
     (if (<= t -2.6e-254)
       t_1
       (if (<= t 2e-243) (* (- y 2.0) b) (if (<= t 115.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.1e+92) {
		tmp = t_2;
	} else if (t <= -2.6e-254) {
		tmp = t_1;
	} else if (t <= 2e-243) {
		tmp = (y - 2.0) * b;
	} else if (t <= 115.0) {
		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 = (1.0d0 - y) * z
    t_2 = (b - a) * t
    if (t <= (-1.1d+92)) then
        tmp = t_2
    else if (t <= (-2.6d-254)) then
        tmp = t_1
    else if (t <= 2d-243) then
        tmp = (y - 2.0d0) * b
    else if (t <= 115.0d0) 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 = (1.0 - y) * z;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.1e+92) {
		tmp = t_2;
	} else if (t <= -2.6e-254) {
		tmp = t_1;
	} else if (t <= 2e-243) {
		tmp = (y - 2.0) * b;
	} else if (t <= 115.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 - y) * z
	t_2 = (b - a) * t
	tmp = 0
	if t <= -1.1e+92:
		tmp = t_2
	elif t <= -2.6e-254:
		tmp = t_1
	elif t <= 2e-243:
		tmp = (y - 2.0) * b
	elif t <= 115.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.1e+92)
		tmp = t_2;
	elseif (t <= -2.6e-254)
		tmp = t_1;
	elseif (t <= 2e-243)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 115.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 - y) * z;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.1e+92)
		tmp = t_2;
	elseif (t <= -2.6e-254)
		tmp = t_1;
	elseif (t <= 2e-243)
		tmp = (y - 2.0) * b;
	elseif (t <= 115.0)
		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[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.1e+92], t$95$2, If[LessEqual[t, -2.6e-254], t$95$1, If[LessEqual[t, 2e-243], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 115.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.09999999999999996e92 or 115 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.1

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

   5. Applied rewrites 71.1%

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

   if -1.09999999999999996e92 < t < -2.6e-254 or 1.99999999999999999e-243 < t < 115

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.6

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

   5. Applied rewrites 43.6%

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

   if -2.6e-254 < t < 1.99999999999999999e-243

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 50.4%

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

Alternative 5: 28.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-t\right) \cdot a\\ t_2 := \left(-z\right) \cdot y\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-159}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t) a)) (t_2 (* (- z) y)))
   (if (<= y -4.4e+30)
     t_2
     (if (<= y -5e-113)
       t_1
       (if (<= y 3.7e-159) (* b t) (if (<= y 4.4e+50) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -t * a;
	double t_2 = -z * y;
	double tmp;
	if (y <= -4.4e+30) {
		tmp = t_2;
	} else if (y <= -5e-113) {
		tmp = t_1;
	} else if (y <= 3.7e-159) {
		tmp = b * t;
	} else if (y <= 4.4e+50) {
		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 = -t * a
    t_2 = -z * y
    if (y <= (-4.4d+30)) then
        tmp = t_2
    else if (y <= (-5d-113)) then
        tmp = t_1
    else if (y <= 3.7d-159) then
        tmp = b * t
    else if (y <= 4.4d+50) 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 = -t * a;
	double t_2 = -z * y;
	double tmp;
	if (y <= -4.4e+30) {
		tmp = t_2;
	} else if (y <= -5e-113) {
		tmp = t_1;
	} else if (y <= 3.7e-159) {
		tmp = b * t;
	} else if (y <= 4.4e+50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -t * a
	t_2 = -z * y
	tmp = 0
	if y <= -4.4e+30:
		tmp = t_2
	elif y <= -5e-113:
		tmp = t_1
	elif y <= 3.7e-159:
		tmp = b * t
	elif y <= 4.4e+50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-t) * a)
	t_2 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (y <= -4.4e+30)
		tmp = t_2;
	elseif (y <= -5e-113)
		tmp = t_1;
	elseif (y <= 3.7e-159)
		tmp = Float64(b * t);
	elseif (y <= 4.4e+50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -t * a;
	t_2 = -z * y;
	tmp = 0.0;
	if (y <= -4.4e+30)
		tmp = t_2;
	elseif (y <= -5e-113)
		tmp = t_1;
	elseif (y <= 3.7e-159)
		tmp = b * t;
	elseif (y <= 4.4e+50)
		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[((-t) * a), $MachinePrecision]}, Block[{t$95$2 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[y, -4.4e+30], t$95$2, If[LessEqual[y, -5e-113], t$95$1, If[LessEqual[y, 3.7e-159], N[(b * t), $MachinePrecision], If[LessEqual[y, 4.4e+50], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4e30 or 4.40000000000000034e50 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 49.9%

      \[\leadsto \left(-z\right) \cdot y \]

   if -4.4e30 < y < -4.9999999999999997e-113 or 3.6999999999999999e-159 < y < 4.40000000000000034e50

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.9

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

   5. Applied rewrites 44.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 33.6%

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

   if -4.9999999999999997e-113 < y < 3.6999999999999999e-159

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.0

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

   5. Applied rewrites 49.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 35.9%

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

Alternative 6: 40.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.65 \cdot 10^{-227}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+111}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 2.0) b)))
   (if (<= b -1.02e+51)
     t_1
     (if (<= b 3.65e-227)
       (* (- 1.0 y) z)
       (if (<= b 1.85e+111) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 2.0) * b;
	double tmp;
	if (b <= -1.02e+51) {
		tmp = t_1;
	} else if (b <= 3.65e-227) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.85e+111) {
		tmp = (1.0 - t) * 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 = (t - 2.0d0) * b
    if (b <= (-1.02d+51)) then
        tmp = t_1
    else if (b <= 3.65d-227) then
        tmp = (1.0d0 - y) * z
    else if (b <= 1.85d+111) then
        tmp = (1.0d0 - t) * 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 = (t - 2.0) * b;
	double tmp;
	if (b <= -1.02e+51) {
		tmp = t_1;
	} else if (b <= 3.65e-227) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.85e+111) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 2.0) * b
	tmp = 0
	if b <= -1.02e+51:
		tmp = t_1
	elif b <= 3.65e-227:
		tmp = (1.0 - y) * z
	elif b <= 1.85e+111:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 2.0) * b)
	tmp = 0.0
	if (b <= -1.02e+51)
		tmp = t_1;
	elseif (b <= 3.65e-227)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 1.85e+111)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.02e+51)
		tmp = t_1;
	elseif (b <= 3.65e-227)
		tmp = (1.0 - y) * z;
	elseif (b <= 1.85e+111)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.02e+51], t$95$1, If[LessEqual[b, 3.65e-227], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 1.85e+111], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.02e51 or 1.8500000000000001e111 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 53.0

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

   5. Applied rewrites 53.0%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 82.5

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

   8. Applied rewrites 82.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 59.6%

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

   if -1.02e51 < b < 3.6500000000000001e-227

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.5

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

   5. Applied rewrites 44.5%

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

   if 3.6500000000000001e-227 < b < 1.8500000000000001e111

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 39.3

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

   5. Applied rewrites 39.3%

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

Alternative 7: 34.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot y\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-59}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+50}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- z) y)))
   (if (<= y -1.05e+35)
     t_1
     (if (<= y 6.5e-59) (* (- t 2.0) b) (if (<= y 4.4e+50) (* (- t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (y <= -1.05e+35) {
		tmp = t_1;
	} else if (y <= 6.5e-59) {
		tmp = (t - 2.0) * b;
	} else if (y <= 4.4e+50) {
		tmp = -t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * y
    if (y <= (-1.05d+35)) then
        tmp = t_1
    else if (y <= 6.5d-59) then
        tmp = (t - 2.0d0) * b
    else if (y <= 4.4d+50) then
        tmp = -t * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -z * y;
	double tmp;
	if (y <= -1.05e+35) {
		tmp = t_1;
	} else if (y <= 6.5e-59) {
		tmp = (t - 2.0) * b;
	} else if (y <= 4.4e+50) {
		tmp = -t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -z * y
	tmp = 0
	if y <= -1.05e+35:
		tmp = t_1
	elif y <= 6.5e-59:
		tmp = (t - 2.0) * b
	elif y <= 4.4e+50:
		tmp = -t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (y <= -1.05e+35)
		tmp = t_1;
	elseif (y <= 6.5e-59)
		tmp = Float64(Float64(t - 2.0) * b);
	elseif (y <= 4.4e+50)
		tmp = Float64(Float64(-t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -z * y;
	tmp = 0.0;
	if (y <= -1.05e+35)
		tmp = t_1;
	elseif (y <= 6.5e-59)
		tmp = (t - 2.0) * b;
	elseif (y <= 4.4e+50)
		tmp = -t * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[y, -1.05e+35], t$95$1, If[LessEqual[y, 6.5e-59], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y, 4.4e+50], N[((-t) * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0499999999999999e35 or 4.40000000000000034e50 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 50.3%

      \[\leadsto \left(-z\right) \cdot y \]

   if -1.0499999999999999e35 < y < 6.50000000000000017e-59

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 40.5

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

   8. Applied rewrites 40.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 37.6%

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

   if 6.50000000000000017e-59 < y < 4.40000000000000034e50

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.2

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

   5. Applied rewrites 43.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 38.9%

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

Alternative 8: 65.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+80} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.3e+80) (not (<= t 4.1e+86)))
   (* (- b a) t)
   (fma (- y 2.0) b (+ a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.3e+80) || !(t <= 4.1e+86)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma((y - 2.0), b, (a + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.3e+80) || !(t <= 4.1e+86))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(Float64(y - 2.0), b, Float64(a + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.3e+80], N[Not[LessEqual[t, 4.1e+86]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + N[(a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999991e80 or 4.0999999999999999e86 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if -1.29999999999999991e80 < t < 4.0999999999999999e86

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y - 2, b, a + x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+80} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+76} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.5e+76) (not (<= t 4.1e+86)))
   (* (- b a) t)
   (+ (fma -2.0 b (+ a x)) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -6.5e+76) || !(t <= 4.1e+86)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(-2.0, b, (a + x)) + z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -6.5e+76) || !(t <= 4.1e+86))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(fma(-2.0, b, Float64(a + x)) + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -6.5e+76], N[Not[LessEqual[t, 4.1e+86]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(-2.0 * b + N[(a + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000005e76 or 4.0999999999999999e86 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if -6.5000000000000005e76 < t < 4.0999999999999999e86

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+76} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+19} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, a + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3e+19) (not (<= t 4.1e+86)))
   (* (- b a) t)
   (fma -2.0 b (+ a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3e+19) || !(t <= 4.1e+86)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(-2.0, b, (a + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3e+19) || !(t <= 4.1e+86))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(-2.0, b, Float64(a + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3e+19], N[Not[LessEqual[t, 4.1e+86]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(-2.0 * b + N[(a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3e19 or 4.0999999999999999e86 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.7

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

   5. Applied rewrites 72.7%

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

   if -3e19 < t < 4.0999999999999999e86

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 94.5

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y - 2, b, a + x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 64.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-2, b, a + x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 49.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+19} \lor \neg \left(t \leq 4.1 \cdot 10^{+86}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, a + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+17} \lor \neg \left(y \leq 2.3 \cdot 10^{+51}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+17) (not (<= y 2.3e+51))) (* (- b z) y) (* (- b a) t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.5e+17) || !(y <= 2.3e+51)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	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 <= (-4.5d+17)) .or. (.not. (y <= 2.3d+51))) then
        tmp = (b - z) * y
    else
        tmp = (b - a) * t
    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 <= -4.5e+17) || !(y <= 2.3e+51)) {
		tmp = (b - z) * y;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.5e+17) or not (y <= 2.3e+51):
		tmp = (b - z) * y
	else:
		tmp = (b - a) * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.5e+17) || !(y <= 2.3e+51))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.5e+17) || ~((y <= 2.3e+51)))
		tmp = (b - z) * y;
	else
		tmp = (b - a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.5e+17], N[Not[LessEqual[y, 2.3e+51]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e17 or 2.30000000000000005e51 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.9

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

   5. Applied rewrites 71.9%

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

   if -4.5e17 < y < 2.30000000000000005e51

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.2

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

   5. Applied rewrites 49.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+17} \lor \neg \left(y \leq 2.3 \cdot 10^{+51}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+59} \lor \neg \left(b \leq 1.85 \cdot 10^{+111}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.6e+59) (not (<= b 1.85e+111)))
   (* (- t 2.0) b)
   (* (- 1.0 t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.6e+59) || !(b <= 1.85e+111)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.6d+59)) .or. (.not. (b <= 1.85d+111))) then
        tmp = (t - 2.0d0) * b
    else
        tmp = (1.0d0 - t) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.6e+59) || !(b <= 1.85e+111)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = (1.0 - t) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.6e+59) or not (b <= 1.85e+111):
		tmp = (t - 2.0) * b
	else:
		tmp = (1.0 - t) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.6e+59) || !(b <= 1.85e+111))
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = Float64(Float64(1.0 - t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.6e+59) || ~((b <= 1.85e+111)))
		tmp = (t - 2.0) * b;
	else
		tmp = (1.0 - t) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.6e+59], N[Not[LessEqual[b, 1.85e+111]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.59999999999999999e59 or 1.8500000000000001e111 < b

   1. Initial program 87.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 53.6

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

   5. Applied rewrites 53.6%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 83.3

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

   8. Applied rewrites 83.3%

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

   9. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 60.2%

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

   if -2.59999999999999999e59 < b < 1.8500000000000001e111

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.7

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

   5. Applied rewrites 38.7%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+59} \lor \neg \left(b \leq 1.85 \cdot 10^{+111}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 27.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+58} \lor \neg \left(b \leq 4.4 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.4e+58) (not (<= b 4.4e+102))) (* b t) (* (- t) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.4e+58) || !(b <= 4.4e+102)) {
		tmp = b * t;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.4d+58)) .or. (.not. (b <= 4.4d+102))) then
        tmp = b * t
    else
        tmp = -t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.4e+58) || !(b <= 4.4e+102)) {
		tmp = b * t;
	} else {
		tmp = -t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.4e+58) or not (b <= 4.4e+102):
		tmp = b * t
	else:
		tmp = -t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.4e+58) || !(b <= 4.4e+102))
		tmp = Float64(b * t);
	else
		tmp = Float64(Float64(-t) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.4e+58) || ~((b <= 4.4e+102)))
		tmp = b * t;
	else
		tmp = -t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.4e+58], N[Not[LessEqual[b, 4.4e+102]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[((-t) * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.40000000000000048e58 or 4.40000000000000015e102 < b

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 46.1%

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

   if -8.40000000000000048e58 < b < 4.40000000000000015e102

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 38.9

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

   5. Applied rewrites 38.9%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 28.2%

      \[\leadsto \left(-t\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+58} \lor \neg \left(b \leq 4.4 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -130000 \lor \neg \left(t \leq 0.04\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -130000.0) (not (<= t 0.04))) (* b t) (* 1.0 a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -130000.0) || !(t <= 0.04)) {
		tmp = b * t;
	} else {
		tmp = 1.0 * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-130000.0d0)) .or. (.not. (t <= 0.04d0))) then
        tmp = b * t
    else
        tmp = 1.0d0 * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -130000.0) || !(t <= 0.04)) {
		tmp = b * t;
	} else {
		tmp = 1.0 * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -130000.0) or not (t <= 0.04):
		tmp = b * t
	else:
		tmp = 1.0 * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -130000.0) || !(t <= 0.04))
		tmp = Float64(b * t);
	else
		tmp = Float64(1.0 * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -130000.0) || ~((t <= 0.04)))
		tmp = b * t;
	else
		tmp = 1.0 * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -130000.0], N[Not[LessEqual[t, 0.04]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(1.0 * a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e5 or 0.0400000000000000008 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 35.5%

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

   if -1.3e5 < t < 0.0400000000000000008

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 21.7

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

   5. Applied rewrites 21.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot t\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 2.4%

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

   9. Taylor expanded in t around 0

      \[\leadsto 1 \cdot a \]
   10. Step-by-step derivation

   11. Applied rewrites 21.5%

       \[\leadsto 1 \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -130000 \lor \neg \left(t \leq 0.04\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+18} \lor \neg \left(t \leq 3.3 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.15e+18) (not (<= t 3.3e+153))) (* b t) (* b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+18) || !(t <= 3.3e+153)) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.15d+18)) .or. (.not. (t <= 3.3d+153))) then
        tmp = b * t
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+18) || !(t <= 3.3e+153)) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.15e+18) or not (t <= 3.3e+153):
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.15e+18) || !(t <= 3.3e+153))
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.15e+18) || ~((t <= 3.3e+153)))
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.15e+18], N[Not[LessEqual[t, 3.3e+153]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e18 or 3.29999999999999994e153 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 42.6%

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

   if -2.15e18 < t < 3.29999999999999994e153

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.4

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

   5. Applied rewrites 41.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 19.1%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+18} \lor \neg \left(t \leq 3.3 \cdot 10^{+153}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 17.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ b \cdot t \end{array} \]

FPCore

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

C

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

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 = b * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

3. Taylor expanded in t around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 39.7

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

5. Applied rewrites 39.7%

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

6. Taylor expanded in a around 0

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

8. Applied rewrites 21.6%

   \[\leadsto b \cdot \color{blue}{t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024352 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))