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

Percentage Accurate: 95.5% → 97.3%

Time: 5.9s

Alternatives: 29

Speedup: 1.0×

• 35.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.5× speedup

Math

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

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 (+ (* (- 1.0 y) z) (* t b)))))

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 = ((1.0 - y) * z) + (t * b);
	}
	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 = ((1.0 - y) * z) + (t * b);
	}
	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 = ((1.0 - y) * z) + (t * b)
	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(Float64(1.0 - y) * z) + Float64(t * b));
	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 = ((1.0 - y) * z) + (t * b);
	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[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 25.1

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

   4. Applied rewrites 25.1%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 40.5%

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

Alternative 2: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

2. Taylor expanded in t around 0

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

   1. associate--l+ N/A

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

   2. lower-+.f64 N/A

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

   3. lower--.f64 N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lower--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower--.f64 N/A

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

   11. +-commutative N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lift--.f64 N/A

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

   15. mul-1-neg N/A

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

   16. lower-neg.f64 96.5

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

4. Applied rewrites 96.5%

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

Alternative 3: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;\left(1 - y\right) \cdot z + t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+116}:\\ \;\;\;\;\left(1 - t\right) \cdot a + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+95)
     (+ (* (- 1.0 y) z) t_1)
     (if (<= b 1.15e+35)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (if (<= b 6.2e+116) (+ (* (- 1.0 t) a) t_1) (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+95) {
		tmp = ((1.0 - y) * z) + t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (b <= 6.2e+116) {
		tmp = ((1.0 - t) * a) + t_1;
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+95)
		tmp = Float64(Float64(Float64(1.0 - y) * z) + t_1);
	elseif (b <= 1.15e+35)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 6.2e+116)
		tmp = Float64(Float64(Float64(1.0 - t) * a) + t_1);
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+95], N[(N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.15e+35], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+116], N[(N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.29999999999999997e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   if -2.29999999999999997e95 < b < 1.1499999999999999e35

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 87.5

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

   4. Applied rewrites 87.5%

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

   if 1.1499999999999999e35 < b < 6.19999999999999992e116

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.5

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

   4. Applied rewrites 62.5%

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

   if 6.19999999999999992e116 < b

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 84.8%

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

Alternative 4: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+116}:\\ \;\;\;\;\left(1 - t\right) \cdot a + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+95)
     (+ z t_1)
     (if (<= b 1.15e+35)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (if (<= b 6.2e+116) (+ (* (- 1.0 t) a) t_1) (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+95) {
		tmp = z + t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (b <= 6.2e+116) {
		tmp = ((1.0 - t) * a) + t_1;
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+95)
		tmp = Float64(z + t_1);
	elseif (b <= 1.15e+35)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 6.2e+116)
		tmp = Float64(Float64(Float64(1.0 - t) * a) + t_1);
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+95], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, 1.15e+35], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+116], N[(N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.29999999999999997e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 80.2%

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

   if -2.29999999999999997e95 < b < 1.1499999999999999e35

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 87.5

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

   4. Applied rewrites 87.5%

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

   if 1.1499999999999999e35 < b < 6.19999999999999992e116

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 62.5

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

   4. Applied rewrites 62.5%

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

   if 6.19999999999999992e116 < b

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 84.8%

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

Alternative 5: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right) - \left(t - 1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (fma (- t 1.0) a (* (- y 1.0) z)))))
   (if (<= z -1.5e+120)
     t_1
     (if (<= z 6.8e+115) (- (fma (- (+ t y) 2.0) b x) (* (- t 1.0) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - fma((t - 1.0), a, ((y - 1.0) * z));
	double tmp;
	if (z <= -1.5e+120) {
		tmp = t_1;
	} else if (z <= 6.8e+115) {
		tmp = fma(((t + y) - 2.0), b, x) - ((t - 1.0) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)))
	tmp = 0.0
	if (z <= -1.5e+120)
		tmp = t_1;
	elseif (z <= 6.8e+115)
		tmp = Float64(fma(Float64(Float64(t + y) - 2.0), b, x) - Float64(Float64(t - 1.0) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+120], t$95$1, If[LessEqual[z, 6.8e+115], N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e120 or 6.8000000000000001e115 < z

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 83.2

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

   4. Applied rewrites 83.2%

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

   if -1.5e120 < z < 6.8000000000000001e115

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lift--.f64 N/A

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

      11. lift-*.f64 87.4

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

   4. Applied rewrites 87.4%

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

Alternative 6: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - \mathsf{fma}\left(t - 1, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;\left(-a\right) \cdot t + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+95)
     (+ z t_1)
     (if (<= b 1.15e+35)
       (- x (fma (- t 1.0) a (* (- y 1.0) z)))
       (if (<= b 5.2e+116) (+ (* (- a) t) t_1) (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+95) {
		tmp = z + t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - fma((t - 1.0), a, ((y - 1.0) * z));
	} else if (b <= 5.2e+116) {
		tmp = (-a * t) + t_1;
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+95)
		tmp = Float64(z + t_1);
	elseif (b <= 1.15e+35)
		tmp = Float64(x - fma(Float64(t - 1.0), a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 5.2e+116)
		tmp = Float64(Float64(Float64(-a) * t) + t_1);
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+95], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, 1.15e+35], N[(x - N[(N[(t - 1.0), $MachinePrecision] * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+116], N[(N[((-a) * t), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.29999999999999997e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 80.2%

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

   if -2.29999999999999997e95 < b < 1.1499999999999999e35

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 87.5

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

   4. Applied rewrites 87.5%

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

   if 1.1499999999999999e35 < b < 5.19999999999999973e116

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 54.4

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

   4. Applied rewrites 54.4%

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

   if 5.19999999999999973e116 < b

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 84.8%

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

Alternative 7: 76.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - \mathsf{fma}\left(t, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;\left(-a\right) \cdot t + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+95)
     (+ z t_1)
     (if (<= b 1.15e+35)
       (- x (fma t a (* (- y 1.0) z)))
       (if (<= b 5.2e+116) (+ (* (- a) t) t_1) (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+95) {
		tmp = z + t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - fma(t, a, ((y - 1.0) * z));
	} else if (b <= 5.2e+116) {
		tmp = (-a * t) + t_1;
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+95)
		tmp = Float64(z + t_1);
	elseif (b <= 1.15e+35)
		tmp = Float64(x - fma(t, a, Float64(Float64(y - 1.0) * z)));
	elseif (b <= 5.2e+116)
		tmp = Float64(Float64(Float64(-a) * t) + t_1);
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+95], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, 1.15e+35], N[(x - N[(t * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+116], N[(N[((-a) * t), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.29999999999999997e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 80.2%

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

   if -2.29999999999999997e95 < b < 1.1499999999999999e35

   1. Initial program 98.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 87.5

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 74.7%

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

   if 1.1499999999999999e35 < b < 5.19999999999999973e116

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 54.4

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

   4. Applied rewrites 54.4%

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

   if 5.19999999999999973e116 < b

   1. Initial program 89.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 84.8%

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

Alternative 8: 75.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{+19}:\\ \;\;\;\;x - \mathsf{fma}\left(t, a, \left(y - 1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+95)
     (+ z t_1)
     (if (<= b 4.9e+19) (- x (fma t a (* (- y 1.0) z))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+95) {
		tmp = z + t_1;
	} else if (b <= 4.9e+19) {
		tmp = x - fma(t, a, ((y - 1.0) * z));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+95)
		tmp = Float64(z + t_1);
	elseif (b <= 4.9e+19)
		tmp = Float64(x - fma(t, a, Float64(Float64(y - 1.0) * z)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+95], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, 4.9e+19], N[(x - N[(t * a + N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999997e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 80.2%

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

   if -2.29999999999999997e95 < b < 4.9e19

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 88.0

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

   4. Applied rewrites 88.0%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 75.1%

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

   if 4.9e19 < b

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 75.3%

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

Alternative 9: 71.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.32 \cdot 10^{+76}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y - 1, -a\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -1.32e+76)
     (+ z t_1)
     (if (<= b 2.1e+18) (- x (fma z (- y 1.0) (- a))) (+ x t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -1.32e+76) {
		tmp = z + t_1;
	} else if (b <= 2.1e+18) {
		tmp = x - fma(z, (y - 1.0), -a);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.32e+76)
		tmp = Float64(z + t_1);
	elseif (b <= 2.1e+18)
		tmp = Float64(x - fma(z, Float64(y - 1.0), Float64(-a)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.32e+76], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, 2.1e+18], N[(x - N[(z * N[(y - 1.0), $MachinePrecision] + (-a)), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.31999999999999999e76

   1. Initial program 89.8%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.0

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

   4. Applied rewrites 79.0%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 78.7%

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

   if -1.31999999999999999e76 < b < 2.1e18

   1. Initial program 98.9%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 88.8

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

   4. Applied rewrites 88.8%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 67.0

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

   7. Applied rewrites 67.0%

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

   if 2.1e18 < b

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 75.2%

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

Alternative 10: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;z + t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;x + \left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-149}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -a\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.8e+95)
     (+ z t_1)
     (if (<= b -3.8e-35)
       (+ x (* (- b a) t))
       (if (<= b -2.1e-149)
         (- x (* z (- y 1.0)))
         (if (<= b 2.1e+18) (- x (fma z y (- a))) (+ x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.8e+95) {
		tmp = z + t_1;
	} else if (b <= -3.8e-35) {
		tmp = x + ((b - a) * t);
	} else if (b <= -2.1e-149) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 2.1e+18) {
		tmp = x - fma(z, y, -a);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.8e+95)
		tmp = Float64(z + t_1);
	elseif (b <= -3.8e-35)
		tmp = Float64(x + Float64(Float64(b - a) * t));
	elseif (b <= -2.1e-149)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 2.1e+18)
		tmp = Float64(x - fma(z, y, Float64(-a)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.8e+95], N[(z + t$95$1), $MachinePrecision], If[LessEqual[b, -3.8e-35], N[(x + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-149], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+18], N[(x - N[(z * y + (-a)), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.7999999999999998e95

   1. Initial program 89.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.8

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 80.2%

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

   if -2.7999999999999998e95 < b < -3.8000000000000001e-35

   1. Initial program 96.2%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

   if -3.8000000000000001e-35 < b < -2.10000000000000011e-149

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 89.5

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 55.8

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 55.8%

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

   if -2.10000000000000011e-149 < b < 2.1e18

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 92.7

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 69.6

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

   7. Applied rewrites 69.6%

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

   8. Taylor expanded in y around inf

      \[\leadsto x - \mathsf{fma}\left(z, y, -a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 57.0%

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

   if 2.1e18 < b

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 75.2%

      \[\leadsto \color{blue}{x} + \left(\left(y + t\right) - 2\right) \cdot b \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \left(y - 1\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+122}:\\ \;\;\;\;x + \left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (- y 1.0)))))
   (if (<= z -1.5e+120)
     t_1
     (if (<= z 5e-26)
       (+ x (* (- (+ y t) 2.0) b))
       (if (<= z 2.55e+122) (+ x (* (- b a) t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y - 1.0));
	double tmp;
	if (z <= -1.5e+120) {
		tmp = t_1;
	} else if (z <= 5e-26) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 2.55e+122) {
		tmp = x + ((b - a) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * (y - 1.0d0))
    if (z <= (-1.5d+120)) then
        tmp = t_1
    else if (z <= 5d-26) then
        tmp = x + (((y + t) - 2.0d0) * b)
    else if (z <= 2.55d+122) then
        tmp = x + ((b - a) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y - 1.0));
	double tmp;
	if (z <= -1.5e+120) {
		tmp = t_1;
	} else if (z <= 5e-26) {
		tmp = x + (((y + t) - 2.0) * b);
	} else if (z <= 2.55e+122) {
		tmp = x + ((b - a) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (y - 1.0))
	tmp = 0
	if z <= -1.5e+120:
		tmp = t_1
	elif z <= 5e-26:
		tmp = x + (((y + t) - 2.0) * b)
	elif z <= 2.55e+122:
		tmp = x + ((b - a) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(y - 1.0)))
	tmp = 0.0
	if (z <= -1.5e+120)
		tmp = t_1;
	elseif (z <= 5e-26)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	elseif (z <= 2.55e+122)
		tmp = Float64(x + Float64(Float64(b - a) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (y - 1.0));
	tmp = 0.0;
	if (z <= -1.5e+120)
		tmp = t_1;
	elseif (z <= 5e-26)
		tmp = x + (((y + t) - 2.0) * b);
	elseif (z <= 2.55e+122)
		tmp = x + ((b - a) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+120], t$95$1, If[LessEqual[z, 5e-26], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e+122], N[(x + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e120 or 2.55e122 < z

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 83.3

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

   4. Applied rewrites 83.3%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 69.2

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 69.2%

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

   if -1.5e120 < z < 5.00000000000000019e-26

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 61.0%

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

   if 5.00000000000000019e-26 < z < 2.55e122

   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. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 48.9

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

   7. Applied rewrites 48.9%

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

Alternative 12: 61.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;x + \left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-149}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.8e+95)
     t_1
     (if (<= b -3.8e-35)
       (+ x (* (- b a) t))
       (if (<= b -2.1e-149)
         (- x (* z (- y 1.0)))
         (if (<= b 5.6e+28) (- x (fma z y (- a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.8e+95) {
		tmp = t_1;
	} else if (b <= -3.8e-35) {
		tmp = x + ((b - a) * t);
	} else if (b <= -2.1e-149) {
		tmp = x - (z * (y - 1.0));
	} else if (b <= 5.6e+28) {
		tmp = x - fma(z, y, -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.8e+95)
		tmp = t_1;
	elseif (b <= -3.8e-35)
		tmp = Float64(x + Float64(Float64(b - a) * t));
	elseif (b <= -2.1e-149)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	elseif (b <= 5.6e+28)
		tmp = Float64(x - fma(z, y, Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.8e+95], t$95$1, If[LessEqual[b, -3.8e-35], N[(x + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.1e-149], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+28], N[(x - N[(z * y + (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.7999999999999998e95 or 5.6000000000000003e28 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 71.5

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 71.5

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

   4. Applied rewrites 71.5%

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

   if -2.7999999999999998e95 < b < -3.8000000000000001e-35

   1. Initial program 96.2%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

   if -3.8000000000000001e-35 < b < -2.10000000000000011e-149

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 89.5

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 55.8

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 55.8%

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

   if -2.10000000000000011e-149 < b < 5.6000000000000003e28

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 92.0

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 69.1

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

   7. Applied rewrites 69.1%

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

   8. Taylor expanded in y around inf

      \[\leadsto x - \mathsf{fma}\left(z, y, -a\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 56.5%

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

Alternative 13: 61.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;x + \left(b - a\right) \cdot t\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.8e+95)
     t_1
     (if (<= b -3.8e-35)
       (+ x (* (- b a) t))
       (if (<= b 1.15e+35) (- x (* z (- y 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.8e+95) {
		tmp = t_1;
	} else if (b <= -3.8e-35) {
		tmp = x + ((b - a) * t);
	} else if (b <= 1.15e+35) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-2.8d+95)) then
        tmp = t_1
    else if (b <= (-3.8d-35)) then
        tmp = x + ((b - a) * t)
    else if (b <= 1.15d+35) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.8e+95) {
		tmp = t_1;
	} else if (b <= -3.8e-35) {
		tmp = x + ((b - a) * t);
	} else if (b <= 1.15e+35) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -2.8e+95:
		tmp = t_1
	elif b <= -3.8e-35:
		tmp = x + ((b - a) * t)
	elif b <= 1.15e+35:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.8e+95)
		tmp = t_1;
	elseif (b <= -3.8e-35)
		tmp = Float64(x + Float64(Float64(b - a) * t));
	elseif (b <= 1.15e+35)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.8e+95)
		tmp = t_1;
	elseif (b <= -3.8e-35)
		tmp = x + ((b - a) * t);
	elseif (b <= 1.15e+35)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.8e+95], t$95$1, If[LessEqual[b, -3.8e-35], N[(x + N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+35], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7999999999999998e95 or 1.1499999999999999e35 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 71.9

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 71.9

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

   4. Applied rewrites 71.9%

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

   if -2.7999999999999998e95 < b < -3.8000000000000001e-35

   1. Initial program 96.2%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 N/A

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

      11. +-commutative N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift--.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 97.7

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

   4. Applied rewrites 97.7%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

   if -3.8000000000000001e-35 < b < 1.1499999999999999e35

   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. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 91.4

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

   4. Applied rewrites 91.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 56.0

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 56.0%

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

Alternative 14: 61.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.5e+75) t_1 (if (<= b 1.15e+35) (- x (* z (- y 1.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.5e+75) {
		tmp = t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-2.5d+75)) then
        tmp = t_1
    else if (b <= 1.15d+35) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.5e+75) {
		tmp = t_1;
	} else if (b <= 1.15e+35) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -2.5e+75:
		tmp = t_1
	elif b <= 1.15e+35:
		tmp = x - (z * (y - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.5e+75)
		tmp = t_1;
	elseif (b <= 1.15e+35)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.5e+75)
		tmp = t_1;
	elseif (b <= 1.15e+35)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.5e+75], t$95$1, If[LessEqual[b, 1.15e+35], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5000000000000001e75 or 1.1499999999999999e35 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 71.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 71.1

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

   4. Applied rewrites 71.1%

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

   if -2.5000000000000001e75 < b < 1.1499999999999999e35

   1. Initial program 98.9%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 88.4

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

   4. Applied rewrites 88.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 54.1

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 54.1%

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

Alternative 15: 59.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.05 \cdot 10^{-16}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 4800000:\\ \;\;\;\;x - \left(\left(-z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -9.2e+85)
     t_1
     (if (<= t -4.05e-16)
       (* (- b z) y)
       (if (<= t 4800000.0) (- x (- (- z) a)) 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 <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4.05e-16) {
		tmp = (b - z) * y;
	} else if (t <= 4800000.0) {
		tmp = x - (-z - 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 = (b - a) * t
    if (t <= (-9.2d+85)) then
        tmp = t_1
    else if (t <= (-4.05d-16)) then
        tmp = (b - z) * y
    else if (t <= 4800000.0d0) then
        tmp = x - (-z - 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 = (b - a) * t;
	double tmp;
	if (t <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4.05e-16) {
		tmp = (b - z) * y;
	} else if (t <= 4800000.0) {
		tmp = x - (-z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -9.2e+85:
		tmp = t_1
	elif t <= -4.05e-16:
		tmp = (b - z) * y
	elif t <= 4800000.0:
		tmp = x - (-z - a)
	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 <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4.05e-16)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 4800000.0)
		tmp = Float64(x - Float64(Float64(-z) - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4.05e-16)
		tmp = (b - z) * y;
	elseif (t <= 4800000.0)
		tmp = x - (-z - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.2e+85], t$95$1, If[LessEqual[t, -4.05e-16], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 4800000.0], N[(x - N[((-z) - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999996e85 or 4.8e6 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.2

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

   4. Applied rewrites 68.2%

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

   if -9.1999999999999996e85 < t < -4.05000000000000024e-16

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 36.1

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

   4. Applied rewrites 36.1%

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

   if -4.05000000000000024e-16 < t < 4.8e6

   1. Initial program 97.9%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 71.2

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 70.8

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

   7. Applied rewrites 70.8%

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

   8. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto x - \left(\left(\mathsf{neg}\left(z\right)\right) - a\right) \]

      3. lower-neg.f64 51.4

         \[\leadsto x - \left(\left(-z\right) - a\right) \]

   10. Applied rewrites 51.4%

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

Alternative 16: 57.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+75}:\\ \;\;\;\;x - z \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.95e+76) t_1 (if (<= t 3.9e+75) (- x (* z (- y 1.0))) 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 <= -1.95e+76) {
		tmp = t_1;
	} else if (t <= 3.9e+75) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-1.95d+76)) then
        tmp = t_1
    else if (t <= 3.9d+75) then
        tmp = x - (z * (y - 1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.95e+76) {
		tmp = t_1;
	} else if (t <= 3.9e+75) {
		tmp = x - (z * (y - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.95e+76:
		tmp = t_1
	elif t <= 3.9e+75:
		tmp = x - (z * (y - 1.0))
	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 <= -1.95e+76)
		tmp = t_1;
	elseif (t <= 3.9e+75)
		tmp = Float64(x - Float64(z * Float64(y - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.95e+76)
		tmp = t_1;
	elseif (t <= 3.9e+75)
		tmp = x - (z * (y - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.95e+76], t$95$1, If[LessEqual[t, 3.9e+75], N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.94999999999999995e76 or 3.90000000000000038e75 < t

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.0

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

   4. Applied rewrites 72.0%

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

   if -1.94999999999999995e76 < t < 3.90000000000000038e75

   1. Initial program 97.7%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 71.0

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

   4. Applied rewrites 71.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 51.0

         \[\leadsto x - z \cdot \left(y - 1\right) \]

   7. Applied rewrites 51.0%

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

Alternative 17: 51.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-16}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-206}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{elif}\;t \leq 31500000000:\\ \;\;\;\;x - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -9.2e+85)
     t_1
     (if (<= t -4e-16)
       (* (- b z) y)
       (if (<= t 3e-206)
         (- x (- a))
         (if (<= t 31500000000.0) (- x (* z y)) 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 <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4e-16) {
		tmp = (b - z) * y;
	} else if (t <= 3e-206) {
		tmp = x - -a;
	} else if (t <= 31500000000.0) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-9.2d+85)) then
        tmp = t_1
    else if (t <= (-4d-16)) then
        tmp = (b - z) * y
    else if (t <= 3d-206) then
        tmp = x - -a
    else if (t <= 31500000000.0d0) then
        tmp = x - (z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4e-16) {
		tmp = (b - z) * y;
	} else if (t <= 3e-206) {
		tmp = x - -a;
	} else if (t <= 31500000000.0) {
		tmp = x - (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -9.2e+85:
		tmp = t_1
	elif t <= -4e-16:
		tmp = (b - z) * y
	elif t <= 3e-206:
		tmp = x - -a
	elif t <= 31500000000.0:
		tmp = x - (z * y)
	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 <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4e-16)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 3e-206)
		tmp = Float64(x - Float64(-a));
	elseif (t <= 31500000000.0)
		tmp = Float64(x - Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4e-16)
		tmp = (b - z) * y;
	elseif (t <= 3e-206)
		tmp = x - -a;
	elseif (t <= 31500000000.0)
		tmp = x - (z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.2e+85], t$95$1, If[LessEqual[t, -4e-16], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 3e-206], N[(x - (-a)), $MachinePrecision], If[LessEqual[t, 31500000000.0], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.1999999999999996e85 or 3.15e10 < t

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.5

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

   4. Applied rewrites 68.5%

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

   if -9.1999999999999996e85 < t < -3.9999999999999999e-16

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 36.1

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

   4. Applied rewrites 36.1%

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

   if -3.9999999999999999e-16 < t < 3.0000000000000002e-206

   1. Initial program 97.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 70.6

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

   7. Applied rewrites 70.6%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 38.8

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 38.8%

       \[\leadsto x - \left(-a\right) \]

   if 3.0000000000000002e-206 < t < 3.15e10

   1. Initial program 98.0%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 72.5

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

   4. Applied rewrites 72.5%

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

   5. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto x - z \cdot y \]

      2. lower-*.f64 39.6

         \[\leadsto x - z \cdot y \]

   7. Applied rewrites 39.6%

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

Alternative 18: 51.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-16}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;t \leq 1900000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -9.2e+85)
     t_1
     (if (<= t -4e-16) (* (- b z) y) (if (<= t 1900000.0) (- x (- a)) 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 <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4e-16) {
		tmp = (b - z) * y;
	} else if (t <= 1900000.0) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-9.2d+85)) then
        tmp = t_1
    else if (t <= (-4d-16)) then
        tmp = (b - z) * y
    else if (t <= 1900000.0d0) then
        tmp = x - -a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -9.2e+85) {
		tmp = t_1;
	} else if (t <= -4e-16) {
		tmp = (b - z) * y;
	} else if (t <= 1900000.0) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -9.2e+85:
		tmp = t_1
	elif t <= -4e-16:
		tmp = (b - z) * y
	elif t <= 1900000.0:
		tmp = x - -a
	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 <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4e-16)
		tmp = Float64(Float64(b - z) * y);
	elseif (t <= 1900000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -9.2e+85)
		tmp = t_1;
	elseif (t <= -4e-16)
		tmp = (b - z) * y;
	elseif (t <= 1900000.0)
		tmp = x - -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.2e+85], t$95$1, If[LessEqual[t, -4e-16], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 1900000.0], N[(x - (-a)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999996e85 or 1.9e6 < t

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.2

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

   4. Applied rewrites 68.2%

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

   if -9.1999999999999996e85 < t < -3.9999999999999999e-16

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 36.1

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

   4. Applied rewrites 36.1%

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

   if -3.9999999999999999e-16 < t < 1.9e6

   1. Initial program 97.9%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 71.3

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 70.9

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

   7. Applied rewrites 70.9%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 38.7

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 38.7%

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

Alternative 19: 51.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.000175:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 1900000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.95e+76)
     t_1
     (if (<= t -0.000175)
       (* (- 1.0 y) z)
       (if (<= t 1900000.0) (- x (- a)) 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 <= -1.95e+76) {
		tmp = t_1;
	} else if (t <= -0.000175) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1900000.0) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - a) * t
    if (t <= (-1.95d+76)) then
        tmp = t_1
    else if (t <= (-0.000175d0)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 1900000.0d0) then
        tmp = x - -a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.95e+76) {
		tmp = t_1;
	} else if (t <= -0.000175) {
		tmp = (1.0 - y) * z;
	} else if (t <= 1900000.0) {
		tmp = x - -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.95e+76:
		tmp = t_1
	elif t <= -0.000175:
		tmp = (1.0 - y) * z
	elif t <= 1900000.0:
		tmp = x - -a
	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 <= -1.95e+76)
		tmp = t_1;
	elseif (t <= -0.000175)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 1900000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.95e+76)
		tmp = t_1;
	elseif (t <= -0.000175)
		tmp = (1.0 - y) * z;
	elseif (t <= 1900000.0)
		tmp = x - -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.95e+76], t$95$1, If[LessEqual[t, -0.000175], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 1900000.0], N[(x - (-a)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999995e76 or 1.9e6 < t

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.7

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

   4. Applied rewrites 67.7%

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

   if -1.94999999999999995e76 < t < -1.74999999999999998e-4

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.6

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

   4. Applied rewrites 33.6%

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

   if -1.74999999999999998e-4 < t < 1.9e6

   1. Initial program 97.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 71.2

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 70.7

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

   7. Applied rewrites 70.7%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 38.6

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 38.6%

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

Alternative 20: 46.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+114}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 y) z)))
   (if (<= z -4.2e+123) t_1 (if (<= z 6.5e+114) (fma t b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - y) * z;
	double tmp;
	if (z <= -4.2e+123) {
		tmp = t_1;
	} else if (z <= 6.5e+114) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -4.2e+123)
		tmp = t_1;
	elseif (z <= 6.5e+114)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+123], t$95$1, If[LessEqual[z, 6.5e+114], N[(t * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999988e123 or 6.5000000000000001e114 < z

   1. Initial program 90.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.6

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

   4. Applied rewrites 63.6%

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

   if -4.19999999999999988e123 < z < 6.5000000000000001e114

   1. Initial program 97.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 59.2%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 36.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 36.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, b, x\right)} \]

   9. Applied rewrites 36.2%

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

Alternative 21: 44.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -1.58 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -1.58e+32) t_1 (if (<= a 5e+130) (fma t b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.58e+32) {
		tmp = t_1;
	} else if (a <= 5e+130) {
		tmp = fma(t, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -1.58e+32)
		tmp = t_1;
	elseif (a <= 5e+130)
		tmp = fma(t, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.58e+32], t$95$1, If[LessEqual[a, 5e+130], N[(t * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.58000000000000006e32 or 4.9999999999999996e130 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 58.0

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

   4. Applied rewrites 58.0%

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

   if -1.58000000000000006e32 < a < 4.9999999999999996e130

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 60.9%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 39.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 39.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, b, x\right)} \]

   9. Applied rewrites 39.4%

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

Alternative 22: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+20}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+58}:\\ \;\;\;\;\mathsf{fma}\left(t, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e+20) (* (- z) y) (if (<= y 3.3e+58) (fma t b x) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e+20) {
		tmp = -z * y;
	} else if (y <= 3.3e+58) {
		tmp = fma(t, b, x);
	} else {
		tmp = b * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e+20)
		tmp = Float64(Float64(-z) * y);
	elseif (y <= 3.3e+58)
		tmp = fma(t, b, x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e+20], N[((-z) * y), $MachinePrecision], If[LessEqual[y, 3.3e+58], N[(t * b + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e20

   1. Initial program 91.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 65.3

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

   4. Applied rewrites 65.3%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y \]

      2. lower-neg.f64 36.5

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

   7. Applied rewrites 36.5%

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

   if -2.4e20 < y < 3.29999999999999983e58

   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. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 39.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 39.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, b, x\right)} \]

   9. Applied rewrites 39.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, b, x\right)} \]

   if 3.29999999999999983e58 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.2

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

   4. Applied rewrites 69.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 35.4%

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

Alternative 23: 35.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+129}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -0.00018:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.85e+129)
   (* b t)
   (if (<= t -0.00018)
     (* (- z) y)
     (if (<= t 7.2e+77) (- x (- a)) (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.85e+129) {
		tmp = b * t;
	} else if (t <= -0.00018) {
		tmp = -z * y;
	} else if (t <= 7.2e+77) {
		tmp = x - -a;
	} else {
		tmp = -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 (t <= (-1.85d+129)) then
        tmp = b * t
    else if (t <= (-0.00018d0)) then
        tmp = -z * y
    else if (t <= 7.2d+77) then
        tmp = x - -a
    else
        tmp = -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 (t <= -1.85e+129) {
		tmp = b * t;
	} else if (t <= -0.00018) {
		tmp = -z * y;
	} else if (t <= 7.2e+77) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.85e+129:
		tmp = b * t
	elif t <= -0.00018:
		tmp = -z * y
	elif t <= 7.2e+77:
		tmp = x - -a
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.85e+129)
		tmp = Float64(b * t);
	elseif (t <= -0.00018)
		tmp = Float64(Float64(-z) * y);
	elseif (t <= 7.2e+77)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.85e+129)
		tmp = b * t;
	elseif (t <= -0.00018)
		tmp = -z * y;
	elseif (t <= 7.2e+77)
		tmp = x - -a;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.85e+129], N[(b * t), $MachinePrecision], If[LessEqual[t, -0.00018], N[((-z) * y), $MachinePrecision], If[LessEqual[t, 7.2e+77], N[(x - (-a)), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.84999999999999989e129

   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. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.8

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

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 39.8%

      \[\leadsto b \cdot t \]

   if -1.84999999999999989e129 < t < -1.80000000000000011e-4

   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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 33.4

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

   4. Applied rewrites 33.4%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(z\right)\right) \cdot y \]

      2. lower-neg.f64 20.5

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

   7. Applied rewrites 20.5%

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

   if -1.80000000000000011e-4 < t < 7.1999999999999996e77

   1. Initial program 97.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 70.7

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

   4. Applied rewrites 70.7%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 67.6

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

   7. Applied rewrites 67.6%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 36.1

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 36.1%

       \[\leadsto x - \left(-a\right) \]

   if 7.1999999999999996e77 < t

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.1

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 40.3

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

   7. Applied rewrites 40.3%

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

Alternative 24: 35.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.8e+132)
   (* b t)
   (if (<= t -5.4e-14) (* b y) (if (<= t 7.2e+77) (- x (- a)) (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -5.4e-14) {
		tmp = b * y;
	} else if (t <= 7.2e+77) {
		tmp = x - -a;
	} else {
		tmp = -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 (t <= (-9.8d+132)) then
        tmp = b * t
    else if (t <= (-5.4d-14)) then
        tmp = b * y
    else if (t <= 7.2d+77) then
        tmp = x - -a
    else
        tmp = -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 (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -5.4e-14) {
		tmp = b * y;
	} else if (t <= 7.2e+77) {
		tmp = x - -a;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.8e+132:
		tmp = b * t
	elif t <= -5.4e-14:
		tmp = b * y
	elif t <= 7.2e+77:
		tmp = x - -a
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.8e+132)
		tmp = Float64(b * t);
	elseif (t <= -5.4e-14)
		tmp = Float64(b * y);
	elseif (t <= 7.2e+77)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.8e+132)
		tmp = b * t;
	elseif (t <= -5.4e-14)
		tmp = b * y;
	elseif (t <= 7.2e+77)
		tmp = x - -a;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.8e+132], N[(b * t), $MachinePrecision], If[LessEqual[t, -5.4e-14], N[(b * y), $MachinePrecision], If[LessEqual[t, 7.2e+77], N[(x - (-a)), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.8000000000000003e132

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.4

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

   4. Applied rewrites 77.4%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 40.2%

      \[\leadsto b \cdot t \]

   if -9.8000000000000003e132 < t < -5.3999999999999997e-14

   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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.0

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

   4. Applied rewrites 34.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 17.7%

      \[\leadsto b \cdot y \]

   if -5.3999999999999997e-14 < t < 7.1999999999999996e77

   1. Initial program 97.8%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 70.7

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

   4. Applied rewrites 70.7%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 67.6

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

   7. Applied rewrites 67.6%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 36.1

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 36.1%

       \[\leadsto x - \left(-a\right) \]

   if 7.1999999999999996e77 < t

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.1

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 40.3

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

   7. Applied rewrites 40.3%

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

Alternative 25: 35.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 4800000:\\ \;\;\;\;x - \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.8e+132)
   (* b t)
   (if (<= t -5.4e-14) (* b y) (if (<= t 4800000.0) (- x (- a)) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -5.4e-14) {
		tmp = b * y;
	} else if (t <= 4800000.0) {
		tmp = x - -a;
	} else {
		tmp = b * 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 (t <= (-9.8d+132)) then
        tmp = b * t
    else if (t <= (-5.4d-14)) then
        tmp = b * y
    else if (t <= 4800000.0d0) then
        tmp = x - -a
    else
        tmp = b * 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 (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -5.4e-14) {
		tmp = b * y;
	} else if (t <= 4800000.0) {
		tmp = x - -a;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.8e+132:
		tmp = b * t
	elif t <= -5.4e-14:
		tmp = b * y
	elif t <= 4800000.0:
		tmp = x - -a
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.8e+132)
		tmp = Float64(b * t);
	elseif (t <= -5.4e-14)
		tmp = Float64(b * y);
	elseif (t <= 4800000.0)
		tmp = Float64(x - Float64(-a));
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.8e+132)
		tmp = b * t;
	elseif (t <= -5.4e-14)
		tmp = b * y;
	elseif (t <= 4800000.0)
		tmp = x - -a;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.8e+132], N[(b * t), $MachinePrecision], If[LessEqual[t, -5.4e-14], N[(b * y), $MachinePrecision], If[LessEqual[t, 4800000.0], N[(x - (-a)), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.8000000000000003e132 or 4.8e6 < t

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.7

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

   4. Applied rewrites 68.7%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 35.9%

      \[\leadsto b \cdot t \]

   if -9.8000000000000003e132 < t < -5.3999999999999997e-14

   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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 34.0

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

   4. Applied rewrites 34.0%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 17.7%

      \[\leadsto b \cdot y \]

   if -5.3999999999999997e-14 < t < 4.8e6

   1. Initial program 97.9%

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

   2. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 N/A

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

      5. *-commutative N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 71.2

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lift-neg.f64 70.8

         \[\leadsto x - \mathsf{fma}\left(z, y - 1, -a\right) \]

   7. Applied rewrites 70.8%

      \[\leadsto x - \mathsf{fma}\left(z, \color{blue}{y - 1}, -a\right) \]

   8. Taylor expanded in z around 0

      \[\leadsto x - -1 \cdot a \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(a\right)\right) \]

      2. lift-neg.f64 38.6

         \[\leadsto x - \left(-a\right) \]

   10. Applied rewrites 38.6%

       \[\leadsto x - \left(-a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 26: 26.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+132}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-146}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-207}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 4800000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.8e+132)
   (* b t)
   (if (<= t -6e-146)
     (* b y)
     (if (<= t 6.1e-207) a (if (<= t 4800000.0) x (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -6e-146) {
		tmp = b * y;
	} else if (t <= 6.1e-207) {
		tmp = a;
	} else if (t <= 4800000.0) {
		tmp = x;
	} else {
		tmp = b * 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 (t <= (-9.8d+132)) then
        tmp = b * t
    else if (t <= (-6d-146)) then
        tmp = b * y
    else if (t <= 6.1d-207) then
        tmp = a
    else if (t <= 4800000.0d0) then
        tmp = x
    else
        tmp = b * 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 (t <= -9.8e+132) {
		tmp = b * t;
	} else if (t <= -6e-146) {
		tmp = b * y;
	} else if (t <= 6.1e-207) {
		tmp = a;
	} else if (t <= 4800000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.8e+132:
		tmp = b * t
	elif t <= -6e-146:
		tmp = b * y
	elif t <= 6.1e-207:
		tmp = a
	elif t <= 4800000.0:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.8e+132)
		tmp = Float64(b * t);
	elseif (t <= -6e-146)
		tmp = Float64(b * y);
	elseif (t <= 6.1e-207)
		tmp = a;
	elseif (t <= 4800000.0)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.8e+132)
		tmp = b * t;
	elseif (t <= -6e-146)
		tmp = b * y;
	elseif (t <= 6.1e-207)
		tmp = a;
	elseif (t <= 4800000.0)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.8e+132], N[(b * t), $MachinePrecision], If[LessEqual[t, -6e-146], N[(b * y), $MachinePrecision], If[LessEqual[t, 6.1e-207], a, If[LessEqual[t, 4800000.0], x, N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.8000000000000003e132 or 4.8e6 < t

   1. Initial program 92.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 68.7

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 68.7%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 35.9%

      \[\leadsto b \cdot t \]

   if -9.8000000000000003e132 < t < -6.00000000000000038e-146

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - z\right) \cdot \color{blue}{y} \]

      3. lower--.f64 36.0

         \[\leadsto \left(b - z\right) \cdot y \]

   4. Applied rewrites 36.0%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 19.4%

      \[\leadsto b \cdot y \]

   if -6.00000000000000038e-146 < t < 6.10000000000000008e-207

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      3. lower--.f64 20.4

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 20.4%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 20.4%

      \[\leadsto a \]

   if 6.10000000000000008e-207 < t < 4.8e6

   1. Initial program 98.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 19.9%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 27: 26.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0029:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 4800000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -0.0029) (* b t) (if (<= t 4800000.0) x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -0.0029) {
		tmp = b * t;
	} else if (t <= 4800000.0) {
		tmp = x;
	} else {
		tmp = b * 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 (t <= (-0.0029d0)) then
        tmp = b * t
    else if (t <= 4800000.0d0) then
        tmp = x
    else
        tmp = b * 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 (t <= -0.0029) {
		tmp = b * t;
	} else if (t <= 4800000.0) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -0.0029:
		tmp = b * t
	elif t <= 4800000.0:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -0.0029)
		tmp = Float64(b * t);
	elseif (t <= 4800000.0)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -0.0029)
		tmp = b * t;
	elseif (t <= 4800000.0)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -0.0029], N[(b * t), $MachinePrecision], If[LessEqual[t, 4800000.0], x, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0029 or 4.8e6 < t

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(b - a\right) \cdot \color{blue}{t} \]

      3. lower--.f64 63.9

         \[\leadsto \left(b - a\right) \cdot t \]

   4. Applied rewrites 63.9%

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} \]

   5. Taylor expanded in a around 0

      \[\leadsto b \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 32.9%

      \[\leadsto b \cdot t \]

   if -0.0029 < t < 4.8e6

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 20.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 21.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+23}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.8e+79) x (if (<= x 1.32e+23) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+79) {
		tmp = x;
	} else if (x <= 1.32e+23) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.8d+79)) then
        tmp = x
    else if (x <= 1.32d+23) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.8e+79) {
		tmp = x;
	} else if (x <= 1.32e+23) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.8e+79:
		tmp = x
	elif x <= 1.32e+23:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.8e+79)
		tmp = x;
	elseif (x <= 1.32e+23)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.8e+79)
		tmp = x;
	elseif (x <= 1.32e+23)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.8e+79], x, If[LessEqual[x, 1.32e+23], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999996e79 or 1.3199999999999999e23 < x

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 32.0%

      \[\leadsto \color{blue}{x} \]

   if -8.7999999999999996e79 < x < 1.3199999999999999e23

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 - t\right) \cdot \color{blue}{a} \]

      3. lower--.f64 33.4

         \[\leadsto \left(1 - t\right) \cdot a \]

   4. Applied rewrites 33.4%

      \[\leadsto \color{blue}{\left(1 - t\right) \cdot a} \]

   5. Taylor expanded in t around 0

      \[\leadsto a \]
   6. Step-by-step derivation

   7. Applied rewrites 13.2%

      \[\leadsto a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 15.7% accurate, 28.4× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 95.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 15.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(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)))